diff --git a/stwo_cairo_prover/crates/prover/src/cairo_air/debug_tools.rs b/stwo_cairo_prover/crates/prover/src/cairo_air/debug_tools.rs
index 9a46f24f..a599b5a9 100644
--- a/stwo_cairo_prover/crates/prover/src/cairo_air/debug_tools.rs
+++ b/stwo_cairo_prover/crates/prover/src/cairo_air/debug_tools.rs
@@ -15,14 +15,13 @@ use stwo_prover::core::poly::circle::CanonicCoset;
 
 use super::air::CairoClaim;
 use crate::components::{
-    add_ap_opcode, add_ap_opcode_imm, add_ap_opcode_op_1_base_fp, add_opcode_is_small_f_is_imm_f,
-    add_opcode_is_small_f_is_imm_t, add_opcode_is_small_t_is_imm_f, add_opcode_is_small_t_is_imm_t,
-    assert_eq_opcode_is_double_deref_f_is_imm_f, assert_eq_opcode_is_double_deref_f_is_imm_t,
-    assert_eq_opcode_is_double_deref_t_is_imm_f, call_opcode_is_rel_f_op_1_base_fp_f,
-    call_opcode_is_rel_f_op_1_base_fp_t, call_opcode_is_rel_t_op_1_base_fp_f, generic_opcode,
-    jnz_opcode_is_taken_f_dst_base_fp_f, jnz_opcode_is_taken_f_dst_base_fp_t,
-    jnz_opcode_is_taken_t_dst_base_fp_f, jnz_opcode_is_taken_t_dst_base_fp_t,
-    jump_opcode_is_rel_f_is_imm_f_is_double_deref_f,
+    add_ap_opcode, add_ap_opcode_imm, add_ap_opcode_op_1_base_fp, add_opcode, add_opcode_imm,
+    add_opcode_small, add_opcode_small_imm, assert_eq_opcode_is_double_deref_f_is_imm_f,
+    assert_eq_opcode_is_double_deref_f_is_imm_t, assert_eq_opcode_is_double_deref_t_is_imm_f,
+    call_opcode_is_rel_f_op_1_base_fp_f, call_opcode_is_rel_f_op_1_base_fp_t,
+    call_opcode_is_rel_t_op_1_base_fp_f, generic_opcode, jnz_opcode_is_taken_f_dst_base_fp_f,
+    jnz_opcode_is_taken_f_dst_base_fp_t, jnz_opcode_is_taken_t_dst_base_fp_f,
+    jnz_opcode_is_taken_t_dst_base_fp_t, jump_opcode_is_rel_f_is_imm_f_is_double_deref_f,
     jump_opcode_is_rel_f_is_imm_f_is_double_deref_t,
     jump_opcode_is_rel_t_is_imm_f_is_double_deref_f,
     jump_opcode_is_rel_t_is_imm_t_is_double_deref_f, memory_address_to_id, memory_id_to_big,
@@ -54,11 +53,11 @@ where
     let mut entries = vec![];
 
     // TODO(Ohad): reduce boilerplate.
-    for claim in claim.opcodes.add_f_f.clone() {
+    for claim in claim.opcodes.add.clone() {
         entries.extend(
             RelationTrackerComponent::new(
                 tree_span_provider,
-                add_opcode_is_small_f_is_imm_f::Eval {
+                add_opcode::Eval {
                     claim,
                     memory_address_to_id_lookup_elements: relations::MemoryAddressToId::dummy(),
                     memory_id_to_big_lookup_elements: relations::MemoryIdToBig::dummy(),
@@ -70,11 +69,11 @@ where
             .entries(trace),
         );
     }
-    for claim in claim.opcodes.add_f_t.clone() {
+    for claim in claim.opcodes.add_imm.clone() {
         entries.extend(
             RelationTrackerComponent::new(
                 tree_span_provider,
-                add_opcode_is_small_f_is_imm_t::Eval {
+                add_opcode_imm::Eval {
                     claim,
                     memory_address_to_id_lookup_elements: relations::MemoryAddressToId::dummy(),
                     memory_id_to_big_lookup_elements: relations::MemoryIdToBig::dummy(),
@@ -86,11 +85,11 @@ where
             .entries(trace),
         );
     }
-    for claim in claim.opcodes.add_t_f.clone() {
+    for claim in claim.opcodes.add_small.clone() {
         entries.extend(
             RelationTrackerComponent::new(
                 tree_span_provider,
-                add_opcode_is_small_t_is_imm_f::Eval {
+                add_opcode_small::Eval {
                     claim,
                     memory_address_to_id_lookup_elements: relations::MemoryAddressToId::dummy(),
                     memory_id_to_big_lookup_elements: relations::MemoryIdToBig::dummy(),
@@ -102,11 +101,11 @@ where
             .entries(trace),
         );
     }
-    for claim in claim.opcodes.add_t_t.clone() {
+    for claim in claim.opcodes.add_small_imm.clone() {
         entries.extend(
             RelationTrackerComponent::new(
                 tree_span_provider,
-                add_opcode_is_small_t_is_imm_t::Eval {
+                add_opcode_small_imm::Eval {
                     claim,
                     memory_address_to_id_lookup_elements: relations::MemoryAddressToId::dummy(),
                     memory_id_to_big_lookup_elements: relations::MemoryIdToBig::dummy(),
diff --git a/stwo_cairo_prover/crates/prover/src/cairo_air/opcodes_air.rs b/stwo_cairo_prover/crates/prover/src/cairo_air/opcodes_air.rs
index 61757d44..cb681e26 100644
--- a/stwo_cairo_prover/crates/prover/src/cairo_air/opcodes_air.rs
+++ b/stwo_cairo_prover/crates/prover/src/cairo_air/opcodes_air.rs
@@ -13,14 +13,13 @@ use stwo_prover::core::pcs::{TreeBuilder, TreeVec};
 use super::air::CairoInteractionElements;
 use super::debug_tools::display_components;
 use crate::components::{
-    add_ap_opcode, add_ap_opcode_imm, add_ap_opcode_op_1_base_fp, add_opcode_is_small_f_is_imm_f,
-    add_opcode_is_small_f_is_imm_t, add_opcode_is_small_t_is_imm_f, add_opcode_is_small_t_is_imm_t,
-    assert_eq_opcode_is_double_deref_f_is_imm_f, assert_eq_opcode_is_double_deref_f_is_imm_t,
-    assert_eq_opcode_is_double_deref_t_is_imm_f, call_opcode_is_rel_f_op_1_base_fp_f,
-    call_opcode_is_rel_f_op_1_base_fp_t, call_opcode_is_rel_t_op_1_base_fp_f, generic_opcode,
-    jnz_opcode_is_taken_f_dst_base_fp_f, jnz_opcode_is_taken_f_dst_base_fp_t,
-    jnz_opcode_is_taken_t_dst_base_fp_f, jnz_opcode_is_taken_t_dst_base_fp_t,
-    jump_opcode_is_rel_f_is_imm_f_is_double_deref_f,
+    add_ap_opcode, add_ap_opcode_imm, add_ap_opcode_op_1_base_fp, add_opcode, add_opcode_imm,
+    add_opcode_small, add_opcode_small_imm, assert_eq_opcode_is_double_deref_f_is_imm_f,
+    assert_eq_opcode_is_double_deref_f_is_imm_t, assert_eq_opcode_is_double_deref_t_is_imm_f,
+    call_opcode_is_rel_f_op_1_base_fp_f, call_opcode_is_rel_f_op_1_base_fp_t,
+    call_opcode_is_rel_t_op_1_base_fp_f, generic_opcode, jnz_opcode_is_taken_f_dst_base_fp_f,
+    jnz_opcode_is_taken_f_dst_base_fp_t, jnz_opcode_is_taken_t_dst_base_fp_f,
+    jnz_opcode_is_taken_t_dst_base_fp_t, jump_opcode_is_rel_f_is_imm_f_is_double_deref_f,
     jump_opcode_is_rel_f_is_imm_f_is_double_deref_t,
     jump_opcode_is_rel_t_is_imm_f_is_double_deref_f,
     jump_opcode_is_rel_t_is_imm_t_is_double_deref_f, memory_address_to_id, memory_id_to_big,
@@ -31,10 +30,10 @@ use crate::input::state_transitions::StateTransitions;
 
 #[derive(Serialize, Deserialize, CairoSerialize)]
 pub struct OpcodeClaim {
-    pub add_f_f: Vec<add_opcode_is_small_f_is_imm_f::Claim>,
-    pub add_f_t: Vec<add_opcode_is_small_f_is_imm_t::Claim>,
-    pub add_t_f: Vec<add_opcode_is_small_t_is_imm_f::Claim>,
-    pub add_t_t: Vec<add_opcode_is_small_t_is_imm_t::Claim>,
+    pub add: Vec<add_opcode::Claim>,
+    pub add_imm: Vec<add_opcode_imm::Claim>,
+    pub add_small: Vec<add_opcode_small::Claim>,
+    pub add_small_imm: Vec<add_opcode_small_imm::Claim>,
     pub add_ap: Vec<add_ap_opcode::Claim>,
     pub add_ap_op_1_base_fp: Vec<add_ap_opcode_op_1_base_fp::Claim>,
     pub add_ap_imm: Vec<add_ap_opcode_imm::Claim>,
@@ -59,10 +58,10 @@ pub struct OpcodeClaim {
 }
 impl OpcodeClaim {
     pub fn mix_into(&self, channel: &mut impl Channel) {
-        self.add_f_f.iter().for_each(|c| c.mix_into(channel));
-        self.add_f_t.iter().for_each(|c| c.mix_into(channel));
-        self.add_t_f.iter().for_each(|c| c.mix_into(channel));
-        self.add_t_t.iter().for_each(|c| c.mix_into(channel));
+        self.add.iter().for_each(|c| c.mix_into(channel));
+        self.add_imm.iter().for_each(|c| c.mix_into(channel));
+        self.add_small.iter().for_each(|c| c.mix_into(channel));
+        self.add_small_imm.iter().for_each(|c| c.mix_into(channel));
         self.add_ap.iter().for_each(|c| c.mix_into(channel));
         self.add_ap_op_1_base_fp
             .iter()
@@ -90,10 +89,10 @@ impl OpcodeClaim {
 
     pub fn log_sizes(&self) -> TreeVec<Vec<u32>> {
         TreeVec::concat_cols(chain!(
-            self.add_f_f.iter().map(|c| c.log_sizes()),
-            self.add_f_t.iter().map(|c| c.log_sizes()),
-            self.add_t_f.iter().map(|c| c.log_sizes()),
-            self.add_t_t.iter().map(|c| c.log_sizes()),
+            self.add.iter().map(|c| c.log_sizes()),
+            self.add_imm.iter().map(|c| c.log_sizes()),
+            self.add_small.iter().map(|c| c.log_sizes()),
+            self.add_small_imm.iter().map(|c| c.log_sizes()),
             self.add_ap.iter().map(|c| c.log_sizes()),
             self.add_ap_op_1_base_fp.iter().map(|c| c.log_sizes()),
             self.add_ap_imm.iter().map(|c| c.log_sizes()),
@@ -120,10 +119,10 @@ impl OpcodeClaim {
 }
 
 pub struct OpcodesClaimGenerator {
-    add_f_f: Vec<add_opcode_is_small_f_is_imm_f::ClaimGenerator>,
-    add_f_t: Vec<add_opcode_is_small_f_is_imm_t::ClaimGenerator>,
-    add_t_f: Vec<add_opcode_is_small_t_is_imm_f::ClaimGenerator>,
-    add_t_t: Vec<add_opcode_is_small_t_is_imm_t::ClaimGenerator>,
+    add: Vec<add_opcode::ClaimGenerator>,
+    add_imm: Vec<add_opcode_imm::ClaimGenerator>,
+    add_small: Vec<add_opcode_small::ClaimGenerator>,
+    add_small_imm: Vec<add_opcode_small_imm::ClaimGenerator>,
     add_ap: Vec<add_ap_opcode::ClaimGenerator>,
     add_ap_op_1_base_fp: Vec<add_ap_opcode_op_1_base_fp::ClaimGenerator>,
     add_ap_imm: Vec<add_ap_opcode_imm::ClaimGenerator>,
@@ -149,10 +148,10 @@ pub struct OpcodesClaimGenerator {
 impl OpcodesClaimGenerator {
     pub fn new(input: StateTransitions) -> Self {
         // TODO(Ohad): decide split sizes for opcode traces.
-        let mut add_f_f = vec![];
-        let mut add_f_t = vec![];
-        let mut add_t_f = vec![];
-        let mut add_t_t = vec![];
+        let mut add = vec![];
+        let mut add_imm = vec![];
+        let mut add_small = vec![];
+        let mut add_small_imm = vec![];
         let mut add_ap = vec![];
         let mut add_ap_op_1_base_fp = vec![];
         let mut add_ap_imm = vec![];
@@ -174,40 +173,24 @@ impl OpcodesClaimGenerator {
         let mut mul_f_f = vec![];
         let mut mul_f_t = vec![];
         let mut ret = vec![];
-        if !input
-            .casm_states_by_opcode
-            .add_opcode_is_small_f_is_imm_f
-            .is_empty()
-        {
-            add_f_f.push(add_opcode_is_small_f_is_imm_f::ClaimGenerator::new(
-                input.casm_states_by_opcode.add_opcode_is_small_f_is_imm_f,
+        if !input.casm_states_by_opcode.add_opcode.is_empty() {
+            add.push(add_opcode::ClaimGenerator::new(
+                input.casm_states_by_opcode.add_opcode,
             ));
         }
-        if !input
-            .casm_states_by_opcode
-            .add_opcode_is_small_f_is_imm_t
-            .is_empty()
-        {
-            add_f_t.push(add_opcode_is_small_f_is_imm_t::ClaimGenerator::new(
-                input.casm_states_by_opcode.add_opcode_is_small_f_is_imm_t,
+        if !input.casm_states_by_opcode.add_opcode_imm.is_empty() {
+            add_imm.push(add_opcode_imm::ClaimGenerator::new(
+                input.casm_states_by_opcode.add_opcode_imm,
             ));
         }
-        if !input
-            .casm_states_by_opcode
-            .add_opcode_is_small_t_is_imm_f
-            .is_empty()
-        {
-            add_t_f.push(add_opcode_is_small_t_is_imm_f::ClaimGenerator::new(
-                input.casm_states_by_opcode.add_opcode_is_small_t_is_imm_f,
+        if !input.casm_states_by_opcode.add_opcode_small.is_empty() {
+            add_small.push(add_opcode_small::ClaimGenerator::new(
+                input.casm_states_by_opcode.add_opcode_small,
             ));
         }
-        if !input
-            .casm_states_by_opcode
-            .add_opcode_is_small_t_is_imm_t
-            .is_empty()
-        {
-            add_t_t.push(add_opcode_is_small_t_is_imm_t::ClaimGenerator::new(
-                input.casm_states_by_opcode.add_opcode_is_small_t_is_imm_t,
+        if !input.casm_states_by_opcode.add_opcode_small_imm.is_empty() {
+            add_small_imm.push(add_opcode_small_imm::ClaimGenerator::new(
+                input.casm_states_by_opcode.add_opcode_small_imm,
             ));
         }
         if !input.casm_states_by_opcode.add_ap_opcode.is_empty() {
@@ -428,10 +411,10 @@ impl OpcodesClaimGenerator {
             ));
         }
         Self {
-            add_f_f,
-            add_f_t,
-            add_t_f,
-            add_t_t,
+            add,
+            add_imm,
+            add_small,
+            add_small_imm,
             add_ap,
             add_ap_op_1_base_fp,
             add_ap_imm,
@@ -468,8 +451,8 @@ impl OpcodesClaimGenerator {
     where
         SimdBackend: BackendForChannel<MC>,
     {
-        let (add_f_f_claims, add_f_f_interaction_gens) = self
-            .add_f_f
+        let (add_claims, add_interaction_gens) = self
+            .add
             .into_iter()
             .map(|gen| {
                 gen.write_trace(
@@ -480,8 +463,8 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_f_t_claims, add_f_t_interaction_gens) = self
-            .add_f_t
+        let (add_imm_claims, add_imm_interaction_gens) = self
+            .add_imm
             .into_iter()
             .map(|gen| {
                 gen.write_trace(
@@ -492,8 +475,8 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_t_f_claims, add_t_f_interaction_gens) = self
-            .add_t_f
+        let (add_small_claims, add_small_interaction_gens) = self
+            .add_small
             .into_iter()
             .map(|gen| {
                 gen.write_trace(
@@ -504,8 +487,8 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_t_t_claims, add_t_t_interaction_gens) = self
-            .add_t_t
+        let (add_small_imm_claims, add_small_imm_interaction_gens) = self
+            .add_small_imm
             .into_iter()
             .map(|gen| {
                 gen.write_trace(
@@ -516,7 +499,7 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_ap_f_f_claims, add_ap_f_f_interaction_gens) = self
+        let (add_ap_claims, add_ap_interaction_gens) = self
             .add_ap
             .into_iter()
             .map(|gen| {
@@ -528,7 +511,7 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_ap_f_t_claims, add_ap_f_t_interaction_gens) = self
+        let (add_ap_op_1_base_fp_claims, add_ap_op_1_base_fp_interaction_gens) = self
             .add_ap_op_1_base_fp
             .into_iter()
             .map(|gen| {
@@ -540,7 +523,7 @@ impl OpcodesClaimGenerator {
                 )
             })
             .unzip();
-        let (add_ap_t_f_claims, add_ap_t_f_interaction_gens) = self
+        let (add_ap_imm_claims, add_ap_imm_interaction_gens) = self
             .add_ap_imm
             .into_iter()
             .map(|gen| {
@@ -774,13 +757,13 @@ impl OpcodesClaimGenerator {
             .unzip();
         (
             OpcodeClaim {
-                add_f_f: add_f_f_claims,
-                add_f_t: add_f_t_claims,
-                add_t_f: add_t_f_claims,
-                add_t_t: add_t_t_claims,
-                add_ap: add_ap_f_f_claims,
-                add_ap_op_1_base_fp: add_ap_f_t_claims,
-                add_ap_imm: add_ap_t_f_claims,
+                add: add_claims,
+                add_imm: add_imm_claims,
+                add_small: add_small_claims,
+                add_small_imm: add_small_imm_claims,
+                add_ap: add_ap_claims,
+                add_ap_op_1_base_fp: add_ap_op_1_base_fp_claims,
+                add_ap_imm: add_ap_imm_claims,
                 assert_eq_f_f: assert_eq_f_f_claims,
                 assert_eq_f_t: assert_eq_f_t_claims,
                 assert_eq_t_f: assert_eq_t_f_claims,
@@ -801,13 +784,13 @@ impl OpcodesClaimGenerator {
                 ret: ret_claims,
             },
             OpcodesInteractionClaimGenerator {
-                add_f_f: add_f_f_interaction_gens,
-                add_f_t: add_f_t_interaction_gens,
-                add_t_f: add_t_f_interaction_gens,
-                add_t_t: add_t_t_interaction_gens,
-                add_ap: add_ap_f_f_interaction_gens,
-                add_ap_op_1_base_fp: add_ap_f_t_interaction_gens,
-                add_ap_imm: add_ap_t_f_interaction_gens,
+                add: add_interaction_gens,
+                add_imm: add_imm_interaction_gens,
+                add_small: add_small_interaction_gens,
+                add_small_imm: add_small_imm_interaction_gens,
+                add_ap: add_ap_interaction_gens,
+                add_ap_op_1_base_fp: add_ap_op_1_base_fp_interaction_gens,
+                add_ap_imm: add_ap_imm_interaction_gens,
                 assert_eq_f_f: assert_eq_f_f_interaction_gens,
                 assert_eq_f_t: assert_eq_f_t_interaction_gens,
                 assert_eq_t_f: assert_eq_t_f_interaction_gens,
@@ -833,10 +816,10 @@ impl OpcodesClaimGenerator {
 
 #[derive(Serialize, Deserialize, CairoSerialize)]
 pub struct OpcodeInteractionClaim {
-    add_f_f: Vec<add_opcode_is_small_f_is_imm_f::InteractionClaim>,
-    add_f_t: Vec<add_opcode_is_small_f_is_imm_t::InteractionClaim>,
-    add_t_f: Vec<add_opcode_is_small_t_is_imm_f::InteractionClaim>,
-    add_t_t: Vec<add_opcode_is_small_t_is_imm_t::InteractionClaim>,
+    add: Vec<add_opcode::InteractionClaim>,
+    add_imm: Vec<add_opcode_imm::InteractionClaim>,
+    add_small: Vec<add_opcode_small::InteractionClaim>,
+    add_small_imm: Vec<add_opcode_small_imm::InteractionClaim>,
     add_ap: Vec<add_ap_opcode::InteractionClaim>,
     add_ap_op_1_base_fp: Vec<add_ap_opcode_op_1_base_fp::InteractionClaim>,
     add_ap_imm: Vec<add_ap_opcode_imm::InteractionClaim>,
@@ -861,10 +844,10 @@ pub struct OpcodeInteractionClaim {
 }
 impl OpcodeInteractionClaim {
     pub fn mix_into(&self, channel: &mut impl Channel) {
-        self.add_f_f.iter().for_each(|c| c.mix_into(channel));
-        self.add_f_t.iter().for_each(|c| c.mix_into(channel));
-        self.add_t_f.iter().for_each(|c| c.mix_into(channel));
-        self.add_t_t.iter().for_each(|c| c.mix_into(channel));
+        self.add.iter().for_each(|c| c.mix_into(channel));
+        self.add_imm.iter().for_each(|c| c.mix_into(channel));
+        self.add_small.iter().for_each(|c| c.mix_into(channel));
+        self.add_small_imm.iter().for_each(|c| c.mix_into(channel));
         self.add_ap.iter().for_each(|c| c.mix_into(channel));
         self.add_ap_op_1_base_fp
             .iter()
@@ -892,28 +875,28 @@ impl OpcodeInteractionClaim {
 
     pub fn sum(&self) -> SecureField {
         let mut sum = QM31::zero();
-        for interaction_claim in &self.add_f_f {
+        for interaction_claim in &self.add {
             let (total_sum, claimed_sum) = interaction_claim.logup_sums;
             sum += match claimed_sum {
                 Some((claimed_sum, ..)) => claimed_sum,
                 None => total_sum,
             };
         }
-        for interaction_claim in &self.add_f_t {
+        for interaction_claim in &self.add_imm {
             let (total_sum, claimed_sum) = interaction_claim.logup_sums;
             sum += match claimed_sum {
                 Some((claimed_sum, ..)) => claimed_sum,
                 None => total_sum,
             };
         }
-        for interaction_claim in &self.add_t_f {
+        for interaction_claim in &self.add_small {
             let (total_sum, claimed_sum) = interaction_claim.logup_sums;
             sum += match claimed_sum {
                 Some((claimed_sum, ..)) => claimed_sum,
                 None => total_sum,
             };
         }
-        for interaction_claim in &self.add_t_t {
+        for interaction_claim in &self.add_small_imm {
             let (total_sum, claimed_sum) = interaction_claim.logup_sums;
             sum += match claimed_sum {
                 Some((claimed_sum, ..)) => claimed_sum,
@@ -1072,10 +1055,10 @@ impl OpcodeInteractionClaim {
 }
 
 pub struct OpcodesInteractionClaimGenerator {
-    add_f_f: Vec<add_opcode_is_small_f_is_imm_f::InteractionClaimGenerator>,
-    add_f_t: Vec<add_opcode_is_small_f_is_imm_t::InteractionClaimGenerator>,
-    add_t_f: Vec<add_opcode_is_small_t_is_imm_f::InteractionClaimGenerator>,
-    add_t_t: Vec<add_opcode_is_small_t_is_imm_t::InteractionClaimGenerator>,
+    add: Vec<add_opcode::InteractionClaimGenerator>,
+    add_imm: Vec<add_opcode_imm::InteractionClaimGenerator>,
+    add_small: Vec<add_opcode_small::InteractionClaimGenerator>,
+    add_small_imm: Vec<add_opcode_small_imm::InteractionClaimGenerator>,
     add_ap: Vec<add_ap_opcode::InteractionClaimGenerator>,
     add_ap_op_1_base_fp: Vec<add_ap_opcode_op_1_base_fp::InteractionClaimGenerator>,
     add_ap_imm: Vec<add_ap_opcode_imm::InteractionClaimGenerator>,
@@ -1107,8 +1090,8 @@ impl OpcodesInteractionClaimGenerator {
     where
         SimdBackend: BackendForChannel<MC>,
     {
-        let add_f_f_interaction_claims = self
-            .add_f_f
+        let add_interaction_claims = self
+            .add
             .into_iter()
             .map(|gen| {
                 gen.write_interaction_trace(
@@ -1120,8 +1103,8 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_f_t_interaction_claims = self
-            .add_f_t
+        let add_imm_interaction_claims = self
+            .add_imm
             .into_iter()
             .map(|gen| {
                 gen.write_interaction_trace(
@@ -1133,8 +1116,8 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_t_f_interaction_claims = self
-            .add_t_f
+        let add_small_interaction_claims = self
+            .add_small
             .into_iter()
             .map(|gen| {
                 gen.write_interaction_trace(
@@ -1146,8 +1129,8 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_t_t_interaction_claims = self
-            .add_t_t
+        let add_small_imm_interaction_claims = self
+            .add_small_imm
             .into_iter()
             .map(|gen| {
                 gen.write_interaction_trace(
@@ -1159,7 +1142,7 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_ap_f_f_interaction_claims = self
+        let add_ap_interaction_claims = self
             .add_ap
             .into_iter()
             .map(|gen| {
@@ -1172,7 +1155,7 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_ap_f_t_interaction_claims = self
+        let add_ap_op_1_base_fp_interaction_claims = self
             .add_ap_op_1_base_fp
             .into_iter()
             .map(|gen| {
@@ -1185,7 +1168,7 @@ impl OpcodesInteractionClaimGenerator {
                 )
             })
             .collect();
-        let add_ap_t_f_interaction_claims = self
+        let add_ap_imm_interaction_claims = self
             .add_ap_imm
             .into_iter()
             .map(|gen| {
@@ -1435,13 +1418,13 @@ impl OpcodesInteractionClaimGenerator {
             })
             .collect();
         OpcodeInteractionClaim {
-            add_f_f: add_f_f_interaction_claims,
-            add_f_t: add_f_t_interaction_claims,
-            add_t_f: add_t_f_interaction_claims,
-            add_t_t: add_t_t_interaction_claims,
-            add_ap: add_ap_f_f_interaction_claims,
-            add_ap_op_1_base_fp: add_ap_f_t_interaction_claims,
-            add_ap_imm: add_ap_t_f_interaction_claims,
+            add: add_interaction_claims,
+            add_imm: add_imm_interaction_claims,
+            add_small: add_small_interaction_claims,
+            add_small_imm: add_small_imm_interaction_claims,
+            add_ap: add_ap_interaction_claims,
+            add_ap_op_1_base_fp: add_ap_op_1_base_fp_interaction_claims,
+            add_ap_imm: add_ap_imm_interaction_claims,
             assert_eq_f_f: assert_eq_f_f_interaction_claims,
             assert_eq_f_t: assert_eq_f_t_interaction_claims,
             assert_eq_t_f: assert_eq_t_f_interaction_claims,
@@ -1465,10 +1448,10 @@ impl OpcodesInteractionClaimGenerator {
 }
 
 pub struct OpcodeComponents {
-    add_f_f: Vec<add_opcode_is_small_f_is_imm_f::Component>,
-    add_f_t: Vec<add_opcode_is_small_f_is_imm_t::Component>,
-    add_t_f: Vec<add_opcode_is_small_t_is_imm_f::Component>,
-    add_t_t: Vec<add_opcode_is_small_t_is_imm_t::Component>,
+    add: Vec<add_opcode::Component>,
+    add_imm: Vec<add_opcode_imm::Component>,
+    add_small: Vec<add_opcode_small::Component>,
+    add_small_imm: Vec<add_opcode_small_imm::Component>,
     add_ap: Vec<add_ap_opcode::Component>,
     add_ap_op_1_base_fp: Vec<add_ap_opcode_op_1_base_fp::Component>,
     add_ap_imm: Vec<add_ap_opcode_imm::Component>,
@@ -1498,14 +1481,14 @@ impl OpcodeComponents {
         interaction_elements: &CairoInteractionElements,
         interaction_claim: &OpcodeInteractionClaim,
     ) -> Self {
-        let add_f_f_components = claim
-            .add_f_f
+        let add_components = claim
+            .add
             .iter()
-            .zip(interaction_claim.add_f_f.iter())
+            .zip(interaction_claim.add.iter())
             .map(|(&claim, &interaction_claim)| {
-                add_opcode_is_small_f_is_imm_f::Component::new(
+                add_opcode::Component::new(
                     tree_span_provider,
-                    add_opcode_is_small_f_is_imm_f::Eval {
+                    add_opcode::Eval {
                         claim,
                         memory_address_to_id_lookup_elements: interaction_elements
                             .memory_address_to_id
@@ -1522,14 +1505,14 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_f_t_components = claim
-            .add_f_t
+        let add_imm_components = claim
+            .add_imm
             .iter()
-            .zip(interaction_claim.add_f_t.iter())
+            .zip(interaction_claim.add_imm.iter())
             .map(|(&claim, &interaction_claim)| {
-                add_opcode_is_small_f_is_imm_t::Component::new(
+                add_opcode_imm::Component::new(
                     tree_span_provider,
-                    add_opcode_is_small_f_is_imm_t::Eval {
+                    add_opcode_imm::Eval {
                         claim,
                         memory_address_to_id_lookup_elements: interaction_elements
                             .memory_address_to_id
@@ -1546,14 +1529,14 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_t_f_components = claim
-            .add_t_f
+        let add_small_components = claim
+            .add_small
             .iter()
-            .zip(interaction_claim.add_t_f.iter())
+            .zip(interaction_claim.add_small.iter())
             .map(|(&claim, &interaction_claim)| {
-                add_opcode_is_small_t_is_imm_f::Component::new(
+                add_opcode_small::Component::new(
                     tree_span_provider,
-                    add_opcode_is_small_t_is_imm_f::Eval {
+                    add_opcode_small::Eval {
                         claim,
                         memory_address_to_id_lookup_elements: interaction_elements
                             .memory_address_to_id
@@ -1570,14 +1553,14 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_t_t_components = claim
-            .add_t_t
+        let add_small_imm_components = claim
+            .add_small_imm
             .iter()
-            .zip(interaction_claim.add_t_t.iter())
+            .zip(interaction_claim.add_small_imm.iter())
             .map(|(&claim, &interaction_claim)| {
-                add_opcode_is_small_t_is_imm_t::Component::new(
+                add_opcode_small_imm::Component::new(
                     tree_span_provider,
-                    add_opcode_is_small_t_is_imm_t::Eval {
+                    add_opcode_small_imm::Eval {
                         claim,
                         memory_address_to_id_lookup_elements: interaction_elements
                             .memory_address_to_id
@@ -1594,7 +1577,7 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_ap_f_f_components = claim
+        let add_ap_components = claim
             .add_ap
             .iter()
             .zip(interaction_claim.add_ap.iter())
@@ -1618,7 +1601,7 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_ap_f_t_components = claim
+        let add_ap_op_1_base_fp_components = claim
             .add_ap_op_1_base_fp
             .iter()
             .zip(interaction_claim.add_ap_op_1_base_fp.iter())
@@ -1642,7 +1625,7 @@ impl OpcodeComponents {
                 )
             })
             .collect_vec();
-        let add_ap_t_f_components = claim
+        let add_ap_imm_components = claim
             .add_ap_imm
             .iter()
             .zip(interaction_claim.add_ap_imm.iter())
@@ -2099,13 +2082,13 @@ impl OpcodeComponents {
             })
             .collect_vec();
         Self {
-            add_f_f: add_f_f_components,
-            add_f_t: add_f_t_components,
-            add_t_f: add_t_f_components,
-            add_t_t: add_t_t_components,
-            add_ap: add_ap_f_f_components,
-            add_ap_op_1_base_fp: add_ap_f_t_components,
-            add_ap_imm: add_ap_t_f_components,
+            add: add_components,
+            add_imm: add_imm_components,
+            add_small: add_small_components,
+            add_small_imm: add_small_imm_components,
+            add_ap: add_ap_components,
+            add_ap_op_1_base_fp: add_ap_op_1_base_fp_components,
+            add_ap_imm: add_ap_imm_components,
             assert_eq_f_f: assert_eq_f_f_components,
             assert_eq_f_t: assert_eq_f_t_components,
             assert_eq_t_f: assert_eq_t_f_components,
@@ -2130,22 +2113,22 @@ impl OpcodeComponents {
     pub fn provers(&self) -> Vec<&dyn ComponentProver<SimdBackend>> {
         let mut vec: Vec<&dyn ComponentProver<SimdBackend>> = vec![];
         vec.extend(
-            self.add_f_f
+            self.add
                 .iter()
                 .map(|component| component as &dyn ComponentProver<SimdBackend>),
         );
         vec.extend(
-            self.add_f_t
+            self.add_imm
                 .iter()
                 .map(|component| component as &dyn ComponentProver<SimdBackend>),
         );
         vec.extend(
-            self.add_t_f
+            self.add_small
                 .iter()
                 .map(|component| component as &dyn ComponentProver<SimdBackend>),
         );
         vec.extend(
-            self.add_t_t
+            self.add_small_imm
                 .iter()
                 .map(|component| component as &dyn ComponentProver<SimdBackend>),
         );
@@ -2260,14 +2243,14 @@ impl OpcodeComponents {
 
 impl std::fmt::Display for OpcodeComponents {
     fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
-        writeln!(f, "add_f_f:")?;
-        writeln!(f, "{}", display_components(&self.add_f_f))?;
-        writeln!(f, "add_f_t:")?;
-        writeln!(f, "{}", display_components(&self.add_f_t))?;
-        writeln!(f, "add_t_f:")?;
-        writeln!(f, "{}", display_components(&self.add_t_f))?;
-        writeln!(f, "add_t_t:")?;
-        writeln!(f, "{}", display_components(&self.add_t_t))?;
+        writeln!(f, "add:")?;
+        writeln!(f, "{}", display_components(&self.add))?;
+        writeln!(f, "add_imm:")?;
+        writeln!(f, "{}", display_components(&self.add_imm))?;
+        writeln!(f, "add_small:")?;
+        writeln!(f, "{}", display_components(&self.add_small))?;
+        writeln!(f, "add_small_imm:")?;
+        writeln!(f, "{}", display_components(&self.add_small_imm))?;
         writeln!(f, "add_ap:")?;
         writeln!(f, "{}", display_components(&self.add_ap))?;
         writeln!(f, "add_ap_op_1_base_fp:")?;
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/component.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode/component.rs
similarity index 81%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/component.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode/component.rs
index 3671f5be..e81cd4b0 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/component.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode/component.rs
@@ -4,6 +4,7 @@ use num_traits::{One, Zero};
 use serde::{Deserialize, Serialize};
 use stwo_cairo_serialize::CairoSerialize;
 use stwo_prover::constraint_framework::logup::{LogupAtRow, LogupSums, LookupElements};
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::{
     EvalAtRow, FrameworkComponent, FrameworkEval, RelationEntry,
 };
@@ -383,305 +384,305 @@ impl FrameworkEval for Eval {
         eval.add_constraint(
             (sub_p_bit_col101.clone() * (sub_p_bit_col101.clone() - M31_1.clone())),
         );
-        let carry_tmp_f459d_18 = eval.add_intermediate(
+        let carry_tmp_3fa46_18 = eval.add_intermediate(
             (((((op0_limb_0_col44.clone() + op1_limb_0_col73.clone()) + M31_0.clone())
                 - dst_limb_0_col15.clone())
                 - (M31_1.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_18.clone()
-                * ((carry_tmp_f459d_18.clone() * carry_tmp_f459d_18.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_18.clone()
+                * ((carry_tmp_3fa46_18.clone() * carry_tmp_3fa46_18.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_19 = eval.add_intermediate(
+        let carry_tmp_3fa46_19 = eval.add_intermediate(
             (((((op0_limb_1_col45.clone() + op1_limb_1_col74.clone())
-                + carry_tmp_f459d_18.clone())
+                + carry_tmp_3fa46_18.clone())
                 - dst_limb_1_col16.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_19.clone()
-                * ((carry_tmp_f459d_19.clone() * carry_tmp_f459d_19.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_19.clone()
+                * ((carry_tmp_3fa46_19.clone() * carry_tmp_3fa46_19.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_20 = eval.add_intermediate(
+        let carry_tmp_3fa46_20 = eval.add_intermediate(
             (((((op0_limb_2_col46.clone() + op1_limb_2_col75.clone())
-                + carry_tmp_f459d_19.clone())
+                + carry_tmp_3fa46_19.clone())
                 - dst_limb_2_col17.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_20.clone()
-                * ((carry_tmp_f459d_20.clone() * carry_tmp_f459d_20.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_20.clone()
+                * ((carry_tmp_3fa46_20.clone() * carry_tmp_3fa46_20.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_21 = eval.add_intermediate(
+        let carry_tmp_3fa46_21 = eval.add_intermediate(
             (((((op0_limb_3_col47.clone() + op1_limb_3_col76.clone())
-                + carry_tmp_f459d_20.clone())
+                + carry_tmp_3fa46_20.clone())
                 - dst_limb_3_col18.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_21.clone()
-                * ((carry_tmp_f459d_21.clone() * carry_tmp_f459d_21.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_21.clone()
+                * ((carry_tmp_3fa46_21.clone() * carry_tmp_3fa46_21.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_22 = eval.add_intermediate(
+        let carry_tmp_3fa46_22 = eval.add_intermediate(
             (((((op0_limb_4_col48.clone() + op1_limb_4_col77.clone())
-                + carry_tmp_f459d_21.clone())
+                + carry_tmp_3fa46_21.clone())
                 - dst_limb_4_col19.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_22.clone()
-                * ((carry_tmp_f459d_22.clone() * carry_tmp_f459d_22.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_22.clone()
+                * ((carry_tmp_3fa46_22.clone() * carry_tmp_3fa46_22.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_23 = eval.add_intermediate(
+        let carry_tmp_3fa46_23 = eval.add_intermediate(
             (((((op0_limb_5_col49.clone() + op1_limb_5_col78.clone())
-                + carry_tmp_f459d_22.clone())
+                + carry_tmp_3fa46_22.clone())
                 - dst_limb_5_col20.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_23.clone()
-                * ((carry_tmp_f459d_23.clone() * carry_tmp_f459d_23.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_23.clone()
+                * ((carry_tmp_3fa46_23.clone() * carry_tmp_3fa46_23.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_24 = eval.add_intermediate(
+        let carry_tmp_3fa46_24 = eval.add_intermediate(
             (((((op0_limb_6_col50.clone() + op1_limb_6_col79.clone())
-                + carry_tmp_f459d_23.clone())
+                + carry_tmp_3fa46_23.clone())
                 - dst_limb_6_col21.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_24.clone()
-                * ((carry_tmp_f459d_24.clone() * carry_tmp_f459d_24.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_24.clone()
+                * ((carry_tmp_3fa46_24.clone() * carry_tmp_3fa46_24.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_25 = eval.add_intermediate(
+        let carry_tmp_3fa46_25 = eval.add_intermediate(
             (((((op0_limb_7_col51.clone() + op1_limb_7_col80.clone())
-                + carry_tmp_f459d_24.clone())
+                + carry_tmp_3fa46_24.clone())
                 - dst_limb_7_col22.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_25.clone()
-                * ((carry_tmp_f459d_25.clone() * carry_tmp_f459d_25.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_25.clone()
+                * ((carry_tmp_3fa46_25.clone() * carry_tmp_3fa46_25.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_26 = eval.add_intermediate(
+        let carry_tmp_3fa46_26 = eval.add_intermediate(
             (((((op0_limb_8_col52.clone() + op1_limb_8_col81.clone())
-                + carry_tmp_f459d_25.clone())
+                + carry_tmp_3fa46_25.clone())
                 - dst_limb_8_col23.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_26.clone()
-                * ((carry_tmp_f459d_26.clone() * carry_tmp_f459d_26.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_26.clone()
+                * ((carry_tmp_3fa46_26.clone() * carry_tmp_3fa46_26.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_27 = eval.add_intermediate(
+        let carry_tmp_3fa46_27 = eval.add_intermediate(
             (((((op0_limb_9_col53.clone() + op1_limb_9_col82.clone())
-                + carry_tmp_f459d_26.clone())
+                + carry_tmp_3fa46_26.clone())
                 - dst_limb_9_col24.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_27.clone()
-                * ((carry_tmp_f459d_27.clone() * carry_tmp_f459d_27.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_27.clone()
+                * ((carry_tmp_3fa46_27.clone() * carry_tmp_3fa46_27.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_28 = eval.add_intermediate(
+        let carry_tmp_3fa46_28 = eval.add_intermediate(
             (((((op0_limb_10_col54.clone() + op1_limb_10_col83.clone())
-                + carry_tmp_f459d_27.clone())
+                + carry_tmp_3fa46_27.clone())
                 - dst_limb_10_col25.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_28.clone()
-                * ((carry_tmp_f459d_28.clone() * carry_tmp_f459d_28.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_28.clone()
+                * ((carry_tmp_3fa46_28.clone() * carry_tmp_3fa46_28.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_29 = eval.add_intermediate(
+        let carry_tmp_3fa46_29 = eval.add_intermediate(
             (((((op0_limb_11_col55.clone() + op1_limb_11_col84.clone())
-                + carry_tmp_f459d_28.clone())
+                + carry_tmp_3fa46_28.clone())
                 - dst_limb_11_col26.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_29.clone()
-                * ((carry_tmp_f459d_29.clone() * carry_tmp_f459d_29.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_29.clone()
+                * ((carry_tmp_3fa46_29.clone() * carry_tmp_3fa46_29.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_30 = eval.add_intermediate(
+        let carry_tmp_3fa46_30 = eval.add_intermediate(
             (((((op0_limb_12_col56.clone() + op1_limb_12_col85.clone())
-                + carry_tmp_f459d_29.clone())
+                + carry_tmp_3fa46_29.clone())
                 - dst_limb_12_col27.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_30.clone()
-                * ((carry_tmp_f459d_30.clone() * carry_tmp_f459d_30.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_30.clone()
+                * ((carry_tmp_3fa46_30.clone() * carry_tmp_3fa46_30.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_31 = eval.add_intermediate(
+        let carry_tmp_3fa46_31 = eval.add_intermediate(
             (((((op0_limb_13_col57.clone() + op1_limb_13_col86.clone())
-                + carry_tmp_f459d_30.clone())
+                + carry_tmp_3fa46_30.clone())
                 - dst_limb_13_col28.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_31.clone()
-                * ((carry_tmp_f459d_31.clone() * carry_tmp_f459d_31.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_31.clone()
+                * ((carry_tmp_3fa46_31.clone() * carry_tmp_3fa46_31.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_32 = eval.add_intermediate(
+        let carry_tmp_3fa46_32 = eval.add_intermediate(
             (((((op0_limb_14_col58.clone() + op1_limb_14_col87.clone())
-                + carry_tmp_f459d_31.clone())
+                + carry_tmp_3fa46_31.clone())
                 - dst_limb_14_col29.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_32.clone()
-                * ((carry_tmp_f459d_32.clone() * carry_tmp_f459d_32.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_32.clone()
+                * ((carry_tmp_3fa46_32.clone() * carry_tmp_3fa46_32.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_33 = eval.add_intermediate(
+        let carry_tmp_3fa46_33 = eval.add_intermediate(
             (((((op0_limb_15_col59.clone() + op1_limb_15_col88.clone())
-                + carry_tmp_f459d_32.clone())
+                + carry_tmp_3fa46_32.clone())
                 - dst_limb_15_col30.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_33.clone()
-                * ((carry_tmp_f459d_33.clone() * carry_tmp_f459d_33.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_33.clone()
+                * ((carry_tmp_3fa46_33.clone() * carry_tmp_3fa46_33.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_34 = eval.add_intermediate(
+        let carry_tmp_3fa46_34 = eval.add_intermediate(
             (((((op0_limb_16_col60.clone() + op1_limb_16_col89.clone())
-                + carry_tmp_f459d_33.clone())
+                + carry_tmp_3fa46_33.clone())
                 - dst_limb_16_col31.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_34.clone()
-                * ((carry_tmp_f459d_34.clone() * carry_tmp_f459d_34.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_34.clone()
+                * ((carry_tmp_3fa46_34.clone() * carry_tmp_3fa46_34.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_35 = eval.add_intermediate(
+        let carry_tmp_3fa46_35 = eval.add_intermediate(
             (((((op0_limb_17_col61.clone() + op1_limb_17_col90.clone())
-                + carry_tmp_f459d_34.clone())
+                + carry_tmp_3fa46_34.clone())
                 - dst_limb_17_col32.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_35.clone()
-                * ((carry_tmp_f459d_35.clone() * carry_tmp_f459d_35.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_35.clone()
+                * ((carry_tmp_3fa46_35.clone() * carry_tmp_3fa46_35.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_36 = eval.add_intermediate(
+        let carry_tmp_3fa46_36 = eval.add_intermediate(
             (((((op0_limb_18_col62.clone() + op1_limb_18_col91.clone())
-                + carry_tmp_f459d_35.clone())
+                + carry_tmp_3fa46_35.clone())
                 - dst_limb_18_col33.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_36.clone()
-                * ((carry_tmp_f459d_36.clone() * carry_tmp_f459d_36.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_36.clone()
+                * ((carry_tmp_3fa46_36.clone() * carry_tmp_3fa46_36.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_37 = eval.add_intermediate(
+        let carry_tmp_3fa46_37 = eval.add_intermediate(
             (((((op0_limb_19_col63.clone() + op1_limb_19_col92.clone())
-                + carry_tmp_f459d_36.clone())
+                + carry_tmp_3fa46_36.clone())
                 - dst_limb_19_col34.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_37.clone()
-                * ((carry_tmp_f459d_37.clone() * carry_tmp_f459d_37.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_37.clone()
+                * ((carry_tmp_3fa46_37.clone() * carry_tmp_3fa46_37.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_38 = eval.add_intermediate(
+        let carry_tmp_3fa46_38 = eval.add_intermediate(
             (((((op0_limb_20_col64.clone() + op1_limb_20_col93.clone())
-                + carry_tmp_f459d_37.clone())
+                + carry_tmp_3fa46_37.clone())
                 - dst_limb_20_col35.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_38.clone()
-                * ((carry_tmp_f459d_38.clone() * carry_tmp_f459d_38.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_38.clone()
+                * ((carry_tmp_3fa46_38.clone() * carry_tmp_3fa46_38.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_39 = eval.add_intermediate(
+        let carry_tmp_3fa46_39 = eval.add_intermediate(
             (((((op0_limb_21_col65.clone() + op1_limb_21_col94.clone())
-                + carry_tmp_f459d_38.clone())
+                + carry_tmp_3fa46_38.clone())
                 - dst_limb_21_col36.clone())
                 - (M31_136.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_39.clone()
-                * ((carry_tmp_f459d_39.clone() * carry_tmp_f459d_39.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_39.clone()
+                * ((carry_tmp_3fa46_39.clone() * carry_tmp_3fa46_39.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_40 = eval.add_intermediate(
+        let carry_tmp_3fa46_40 = eval.add_intermediate(
             (((((op0_limb_22_col66.clone() + op1_limb_22_col95.clone())
-                + carry_tmp_f459d_39.clone())
+                + carry_tmp_3fa46_39.clone())
                 - dst_limb_22_col37.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_40.clone()
-                * ((carry_tmp_f459d_40.clone() * carry_tmp_f459d_40.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_40.clone()
+                * ((carry_tmp_3fa46_40.clone() * carry_tmp_3fa46_40.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_41 = eval.add_intermediate(
+        let carry_tmp_3fa46_41 = eval.add_intermediate(
             (((((op0_limb_23_col67.clone() + op1_limb_23_col96.clone())
-                + carry_tmp_f459d_40.clone())
+                + carry_tmp_3fa46_40.clone())
                 - dst_limb_23_col38.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_41.clone()
-                * ((carry_tmp_f459d_41.clone() * carry_tmp_f459d_41.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_41.clone()
+                * ((carry_tmp_3fa46_41.clone() * carry_tmp_3fa46_41.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_42 = eval.add_intermediate(
+        let carry_tmp_3fa46_42 = eval.add_intermediate(
             (((((op0_limb_24_col68.clone() + op1_limb_24_col97.clone())
-                + carry_tmp_f459d_41.clone())
+                + carry_tmp_3fa46_41.clone())
                 - dst_limb_24_col39.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_42.clone()
-                * ((carry_tmp_f459d_42.clone() * carry_tmp_f459d_42.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_42.clone()
+                * ((carry_tmp_3fa46_42.clone() * carry_tmp_3fa46_42.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_43 = eval.add_intermediate(
+        let carry_tmp_3fa46_43 = eval.add_intermediate(
             (((((op0_limb_25_col69.clone() + op1_limb_25_col98.clone())
-                + carry_tmp_f459d_42.clone())
+                + carry_tmp_3fa46_42.clone())
                 - dst_limb_25_col40.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_43.clone()
-                * ((carry_tmp_f459d_43.clone() * carry_tmp_f459d_43.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_43.clone()
+                * ((carry_tmp_3fa46_43.clone() * carry_tmp_3fa46_43.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f459d_44 = eval.add_intermediate(
+        let carry_tmp_3fa46_44 = eval.add_intermediate(
             (((((op0_limb_26_col70.clone() + op1_limb_26_col99.clone())
-                + carry_tmp_f459d_43.clone())
+                + carry_tmp_3fa46_43.clone())
                 - dst_limb_26_col41.clone())
                 - (M31_0.clone() * sub_p_bit_col101.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f459d_44.clone()
-                * ((carry_tmp_f459d_44.clone() * carry_tmp_f459d_44.clone()) - M31_1.clone())),
+            (carry_tmp_3fa46_44.clone()
+                * ((carry_tmp_3fa46_44.clone() * carry_tmp_3fa46_44.clone()) - M31_1.clone())),
         );
         eval.add_constraint(
             ((((op0_limb_27_col71.clone() + op1_limb_27_col100.clone())
-                + carry_tmp_f459d_44.clone())
+                + carry_tmp_3fa46_44.clone())
                 - dst_limb_27_col42.clone())
                 - (M31_256.clone() * sub_p_bit_col101.clone())),
         );
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/mod.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode/mod.rs
similarity index 100%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/mod.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode/mod.rs
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/prover.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode/prover.rs
similarity index 85%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/prover.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode/prover.rs
index c59a9687..51a40849 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_f/prover.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode/prover.rs
@@ -7,10 +7,13 @@ use itertools::{chain, zip_eq, Itertools};
 use num_traits::{One, Zero};
 use prover_types::cpu::*;
 use prover_types::simd::*;
-use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
+use rayon::iter::{
+    IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator, ParallelIterator,
+};
 use stwo_air_utils::trace::component_trace::ComponentTrace;
 use stwo_air_utils_derive::{IterMut, ParIterMut, Uninitialized};
 use stwo_prover::constraint_framework::logup::LogupTraceGenerator;
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::Relation;
 use stwo_prover::core::air::Component;
 use stwo_prover::core::backend::simd::column::BaseColumn;
@@ -21,6 +24,7 @@ use stwo_prover::core::backend::simd::SimdBackend;
 use stwo_prover::core::backend::{BackendForChannel, Col, Column};
 use stwo_prover::core::channel::{Channel, MerkleChannel};
 use stwo_prover::core::fields::m31::M31;
+use stwo_prover::core::fields::FieldExpOps;
 use stwo_prover::core::pcs::TreeBuilder;
 use stwo_prover::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use stwo_prover::core::poly::BitReversedOrder;
@@ -66,6 +70,7 @@ impl ClaimGenerator {
 
         let packed_inputs = pack_values(&self.inputs);
         let (trace, mut sub_components_inputs, lookup_data) = write_trace_simd(
+            n_rows,
             packed_inputs,
             memory_address_to_id_state,
             memory_id_to_big_state,
@@ -104,8 +109,8 @@ impl ClaimGenerator {
         )
     }
 
-    pub fn add_inputs(&mut self, inputs: &[InputType]) {
-        self.inputs.extend(inputs);
+    pub fn add_inputs(&self, _inputs: &[InputType]) {
+        unimplemented!("Implement manually");
     }
 }
 
@@ -121,6 +126,7 @@ pub struct SubComponentInputs {
 #[allow(clippy::double_parens)]
 #[allow(non_snake_case)]
 fn write_trace_simd(
+    n_rows: usize,
     inputs: Vec<PackedInputType>,
     memory_address_to_id_state: &memory_address_to_id::ClaimGenerator,
     memory_id_to_big_state: &memory_id_to_big::ClaimGenerator,
@@ -158,111 +164,108 @@ fn write_trace_simd(
 
     trace
         .par_iter_mut()
-        .zip(inputs.par_iter())
+        .enumerate()
+        .zip(inputs.into_par_iter())
         .zip(lookup_data.par_iter_mut())
         .zip(sub_components_inputs.par_iter_mut().chunks(N_LANES))
         .for_each(
-            |(
-                ((row, add_opcode_is_small_f_is_imm_f_input), lookup_data),
-                mut sub_components_inputs,
-            )| {
-                let input_tmp_f459d_0 = add_opcode_is_small_f_is_imm_f_input;
-                let input_pc_col0 = input_tmp_f459d_0.pc;
+            |((((row_index, row), add_opcode_input), lookup_data), mut sub_components_inputs)| {
+                let input_tmp_3fa46_0 = add_opcode_input;
+                let input_pc_col0 = input_tmp_3fa46_0.pc;
                 *row[0] = input_pc_col0;
-                let input_ap_col1 = input_tmp_f459d_0.ap;
+                let input_ap_col1 = input_tmp_3fa46_0.ap;
                 *row[1] = input_ap_col1;
-                let input_fp_col2 = input_tmp_f459d_0.fp;
+                let input_fp_col2 = input_tmp_3fa46_0.fp;
                 *row[2] = input_fp_col2;
 
                 // Decode Instruction.
 
-                let memory_address_to_id_value_tmp_f459d_1 =
+                let memory_address_to_id_value_tmp_3fa46_1 =
                     memory_address_to_id_state.deduce_output(input_pc_col0);
-                let memory_id_to_big_value_tmp_f459d_2 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f459d_1);
-                let offset0_tmp_f459d_3 =
-                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(0)))
+                let memory_id_to_big_value_tmp_3fa46_2 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_3fa46_1);
+                let offset0_tmp_3fa46_3 =
+                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(0)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(1),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(1),
                         )) & (UInt16_127))
                             << (UInt16_9)));
-                let offset0_col3 = offset0_tmp_f459d_3.as_m31();
+                let offset0_col3 = offset0_tmp_3fa46_3.as_m31();
                 *row[3] = offset0_col3;
-                let offset1_tmp_f459d_4 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(1)))
+                let offset1_tmp_3fa46_4 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(1)))
                         >> (UInt16_7))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(2),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(2),
                         )) << (UInt16_2)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(3),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(3),
                         )) & (UInt16_31))
                             << (UInt16_11)));
-                let offset1_col4 = offset1_tmp_f459d_4.as_m31();
+                let offset1_col4 = offset1_tmp_3fa46_4.as_m31();
                 *row[4] = offset1_col4;
-                let offset2_tmp_f459d_5 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(3)))
+                let offset2_tmp_3fa46_5 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(3)))
                         >> (UInt16_5))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(4),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(4),
                         )) << (UInt16_4)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(5),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(5),
                         )) & (UInt16_7))
                             << (UInt16_13)));
-                let offset2_col5 = offset2_tmp_f459d_5.as_m31();
+                let offset2_col5 = offset2_tmp_3fa46_5.as_m31();
                 *row[5] = offset2_col5;
-                let dst_base_fp_tmp_f459d_6 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(5)))
+                let dst_base_fp_tmp_3fa46_6 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(6),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_0))
                         & (UInt16_1));
-                let dst_base_fp_col6 = dst_base_fp_tmp_f459d_6.as_m31();
+                let dst_base_fp_col6 = dst_base_fp_tmp_3fa46_6.as_m31();
                 *row[6] = dst_base_fp_col6;
-                let op0_base_fp_tmp_f459d_7 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(5)))
+                let op0_base_fp_tmp_3fa46_7 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(6),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_1))
                         & (UInt16_1));
-                let op0_base_fp_col7 = op0_base_fp_tmp_f459d_7.as_m31();
+                let op0_base_fp_col7 = op0_base_fp_tmp_3fa46_7.as_m31();
                 *row[7] = op0_base_fp_col7;
-                let op1_base_fp_tmp_f459d_8 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(5)))
+                let op1_base_fp_tmp_3fa46_8 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(6),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_3))
                         & (UInt16_1));
-                let op1_base_fp_col8 = op1_base_fp_tmp_f459d_8.as_m31();
+                let op1_base_fp_col8 = op1_base_fp_tmp_3fa46_8.as_m31();
                 *row[8] = op1_base_fp_col8;
-                let op1_base_ap_tmp_f459d_9 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(5)))
+                let op1_base_ap_tmp_3fa46_9 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(6),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_4))
                         & (UInt16_1));
-                let op1_base_ap_col9 = op1_base_ap_tmp_f459d_9.as_m31();
+                let op1_base_ap_col9 = op1_base_ap_tmp_3fa46_9.as_m31();
                 *row[9] = op1_base_ap_col9;
-                let ap_update_add_1_tmp_f459d_10 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f459d_2.get_m31(5)))
+                let ap_update_add_1_tmp_3fa46_10 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_3fa46_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f459d_2.get_m31(6),
+                            memory_id_to_big_value_tmp_3fa46_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_11))
                         & (UInt16_1));
-                let ap_update_add_1_col10 = ap_update_add_1_tmp_f459d_10.as_m31();
+                let ap_update_add_1_col10 = ap_update_add_1_tmp_3fa46_10.as_m31();
                 *row[10] = ap_update_add_1_col10;
-
                 for (i, &input) in (
                     input_pc_col0,
                     [offset0_col3, offset1_col4, offset2_col5],
@@ -324,11 +327,11 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f459d_11 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_3fa46_11 = memory_address_to_id_state
                     .deduce_output(((mem_dst_base_col11) + ((offset0_col3) - (M31_32768))));
-                let memory_id_to_big_value_tmp_f459d_12 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f459d_11);
-                let dst_id_col14 = memory_address_to_id_value_tmp_f459d_11;
+                let memory_id_to_big_value_tmp_3fa46_12 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_3fa46_11);
+                let dst_id_col14 = memory_address_to_id_value_tmp_3fa46_11;
                 *row[14] = dst_id_col14;
                 for (i, &input) in ((mem_dst_base_col11) + ((offset0_col3) - (M31_32768)))
                     .unpack()
@@ -341,61 +344,61 @@ fn write_trace_simd(
                     ((mem_dst_base_col11) + ((offset0_col3) - (M31_32768))),
                     dst_id_col14,
                 ];
-                let dst_limb_0_col15 = memory_id_to_big_value_tmp_f459d_12.get_m31(0);
+                let dst_limb_0_col15 = memory_id_to_big_value_tmp_3fa46_12.get_m31(0);
                 *row[15] = dst_limb_0_col15;
-                let dst_limb_1_col16 = memory_id_to_big_value_tmp_f459d_12.get_m31(1);
+                let dst_limb_1_col16 = memory_id_to_big_value_tmp_3fa46_12.get_m31(1);
                 *row[16] = dst_limb_1_col16;
-                let dst_limb_2_col17 = memory_id_to_big_value_tmp_f459d_12.get_m31(2);
+                let dst_limb_2_col17 = memory_id_to_big_value_tmp_3fa46_12.get_m31(2);
                 *row[17] = dst_limb_2_col17;
-                let dst_limb_3_col18 = memory_id_to_big_value_tmp_f459d_12.get_m31(3);
+                let dst_limb_3_col18 = memory_id_to_big_value_tmp_3fa46_12.get_m31(3);
                 *row[18] = dst_limb_3_col18;
-                let dst_limb_4_col19 = memory_id_to_big_value_tmp_f459d_12.get_m31(4);
+                let dst_limb_4_col19 = memory_id_to_big_value_tmp_3fa46_12.get_m31(4);
                 *row[19] = dst_limb_4_col19;
-                let dst_limb_5_col20 = memory_id_to_big_value_tmp_f459d_12.get_m31(5);
+                let dst_limb_5_col20 = memory_id_to_big_value_tmp_3fa46_12.get_m31(5);
                 *row[20] = dst_limb_5_col20;
-                let dst_limb_6_col21 = memory_id_to_big_value_tmp_f459d_12.get_m31(6);
+                let dst_limb_6_col21 = memory_id_to_big_value_tmp_3fa46_12.get_m31(6);
                 *row[21] = dst_limb_6_col21;
-                let dst_limb_7_col22 = memory_id_to_big_value_tmp_f459d_12.get_m31(7);
+                let dst_limb_7_col22 = memory_id_to_big_value_tmp_3fa46_12.get_m31(7);
                 *row[22] = dst_limb_7_col22;
-                let dst_limb_8_col23 = memory_id_to_big_value_tmp_f459d_12.get_m31(8);
+                let dst_limb_8_col23 = memory_id_to_big_value_tmp_3fa46_12.get_m31(8);
                 *row[23] = dst_limb_8_col23;
-                let dst_limb_9_col24 = memory_id_to_big_value_tmp_f459d_12.get_m31(9);
+                let dst_limb_9_col24 = memory_id_to_big_value_tmp_3fa46_12.get_m31(9);
                 *row[24] = dst_limb_9_col24;
-                let dst_limb_10_col25 = memory_id_to_big_value_tmp_f459d_12.get_m31(10);
+                let dst_limb_10_col25 = memory_id_to_big_value_tmp_3fa46_12.get_m31(10);
                 *row[25] = dst_limb_10_col25;
-                let dst_limb_11_col26 = memory_id_to_big_value_tmp_f459d_12.get_m31(11);
+                let dst_limb_11_col26 = memory_id_to_big_value_tmp_3fa46_12.get_m31(11);
                 *row[26] = dst_limb_11_col26;
-                let dst_limb_12_col27 = memory_id_to_big_value_tmp_f459d_12.get_m31(12);
+                let dst_limb_12_col27 = memory_id_to_big_value_tmp_3fa46_12.get_m31(12);
                 *row[27] = dst_limb_12_col27;
-                let dst_limb_13_col28 = memory_id_to_big_value_tmp_f459d_12.get_m31(13);
+                let dst_limb_13_col28 = memory_id_to_big_value_tmp_3fa46_12.get_m31(13);
                 *row[28] = dst_limb_13_col28;
-                let dst_limb_14_col29 = memory_id_to_big_value_tmp_f459d_12.get_m31(14);
+                let dst_limb_14_col29 = memory_id_to_big_value_tmp_3fa46_12.get_m31(14);
                 *row[29] = dst_limb_14_col29;
-                let dst_limb_15_col30 = memory_id_to_big_value_tmp_f459d_12.get_m31(15);
+                let dst_limb_15_col30 = memory_id_to_big_value_tmp_3fa46_12.get_m31(15);
                 *row[30] = dst_limb_15_col30;
-                let dst_limb_16_col31 = memory_id_to_big_value_tmp_f459d_12.get_m31(16);
+                let dst_limb_16_col31 = memory_id_to_big_value_tmp_3fa46_12.get_m31(16);
                 *row[31] = dst_limb_16_col31;
-                let dst_limb_17_col32 = memory_id_to_big_value_tmp_f459d_12.get_m31(17);
+                let dst_limb_17_col32 = memory_id_to_big_value_tmp_3fa46_12.get_m31(17);
                 *row[32] = dst_limb_17_col32;
-                let dst_limb_18_col33 = memory_id_to_big_value_tmp_f459d_12.get_m31(18);
+                let dst_limb_18_col33 = memory_id_to_big_value_tmp_3fa46_12.get_m31(18);
                 *row[33] = dst_limb_18_col33;
-                let dst_limb_19_col34 = memory_id_to_big_value_tmp_f459d_12.get_m31(19);
+                let dst_limb_19_col34 = memory_id_to_big_value_tmp_3fa46_12.get_m31(19);
                 *row[34] = dst_limb_19_col34;
-                let dst_limb_20_col35 = memory_id_to_big_value_tmp_f459d_12.get_m31(20);
+                let dst_limb_20_col35 = memory_id_to_big_value_tmp_3fa46_12.get_m31(20);
                 *row[35] = dst_limb_20_col35;
-                let dst_limb_21_col36 = memory_id_to_big_value_tmp_f459d_12.get_m31(21);
+                let dst_limb_21_col36 = memory_id_to_big_value_tmp_3fa46_12.get_m31(21);
                 *row[36] = dst_limb_21_col36;
-                let dst_limb_22_col37 = memory_id_to_big_value_tmp_f459d_12.get_m31(22);
+                let dst_limb_22_col37 = memory_id_to_big_value_tmp_3fa46_12.get_m31(22);
                 *row[37] = dst_limb_22_col37;
-                let dst_limb_23_col38 = memory_id_to_big_value_tmp_f459d_12.get_m31(23);
+                let dst_limb_23_col38 = memory_id_to_big_value_tmp_3fa46_12.get_m31(23);
                 *row[38] = dst_limb_23_col38;
-                let dst_limb_24_col39 = memory_id_to_big_value_tmp_f459d_12.get_m31(24);
+                let dst_limb_24_col39 = memory_id_to_big_value_tmp_3fa46_12.get_m31(24);
                 *row[39] = dst_limb_24_col39;
-                let dst_limb_25_col40 = memory_id_to_big_value_tmp_f459d_12.get_m31(25);
+                let dst_limb_25_col40 = memory_id_to_big_value_tmp_3fa46_12.get_m31(25);
                 *row[40] = dst_limb_25_col40;
-                let dst_limb_26_col41 = memory_id_to_big_value_tmp_f459d_12.get_m31(26);
+                let dst_limb_26_col41 = memory_id_to_big_value_tmp_3fa46_12.get_m31(26);
                 *row[41] = dst_limb_26_col41;
-                let dst_limb_27_col42 = memory_id_to_big_value_tmp_f459d_12.get_m31(27);
+                let dst_limb_27_col42 = memory_id_to_big_value_tmp_3fa46_12.get_m31(27);
                 *row[42] = dst_limb_27_col42;
                 for (i, &input) in dst_id_col14.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[0] = input;
@@ -434,11 +437,11 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f459d_13 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_3fa46_13 = memory_address_to_id_state
                     .deduce_output(((mem0_base_col12) + ((offset1_col4) - (M31_32768))));
-                let memory_id_to_big_value_tmp_f459d_14 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f459d_13);
-                let op0_id_col43 = memory_address_to_id_value_tmp_f459d_13;
+                let memory_id_to_big_value_tmp_3fa46_14 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_3fa46_13);
+                let op0_id_col43 = memory_address_to_id_value_tmp_3fa46_13;
                 *row[43] = op0_id_col43;
                 for (i, &input) in ((mem0_base_col12) + ((offset1_col4) - (M31_32768)))
                     .unpack()
@@ -451,61 +454,61 @@ fn write_trace_simd(
                     ((mem0_base_col12) + ((offset1_col4) - (M31_32768))),
                     op0_id_col43,
                 ];
-                let op0_limb_0_col44 = memory_id_to_big_value_tmp_f459d_14.get_m31(0);
+                let op0_limb_0_col44 = memory_id_to_big_value_tmp_3fa46_14.get_m31(0);
                 *row[44] = op0_limb_0_col44;
-                let op0_limb_1_col45 = memory_id_to_big_value_tmp_f459d_14.get_m31(1);
+                let op0_limb_1_col45 = memory_id_to_big_value_tmp_3fa46_14.get_m31(1);
                 *row[45] = op0_limb_1_col45;
-                let op0_limb_2_col46 = memory_id_to_big_value_tmp_f459d_14.get_m31(2);
+                let op0_limb_2_col46 = memory_id_to_big_value_tmp_3fa46_14.get_m31(2);
                 *row[46] = op0_limb_2_col46;
-                let op0_limb_3_col47 = memory_id_to_big_value_tmp_f459d_14.get_m31(3);
+                let op0_limb_3_col47 = memory_id_to_big_value_tmp_3fa46_14.get_m31(3);
                 *row[47] = op0_limb_3_col47;
-                let op0_limb_4_col48 = memory_id_to_big_value_tmp_f459d_14.get_m31(4);
+                let op0_limb_4_col48 = memory_id_to_big_value_tmp_3fa46_14.get_m31(4);
                 *row[48] = op0_limb_4_col48;
-                let op0_limb_5_col49 = memory_id_to_big_value_tmp_f459d_14.get_m31(5);
+                let op0_limb_5_col49 = memory_id_to_big_value_tmp_3fa46_14.get_m31(5);
                 *row[49] = op0_limb_5_col49;
-                let op0_limb_6_col50 = memory_id_to_big_value_tmp_f459d_14.get_m31(6);
+                let op0_limb_6_col50 = memory_id_to_big_value_tmp_3fa46_14.get_m31(6);
                 *row[50] = op0_limb_6_col50;
-                let op0_limb_7_col51 = memory_id_to_big_value_tmp_f459d_14.get_m31(7);
+                let op0_limb_7_col51 = memory_id_to_big_value_tmp_3fa46_14.get_m31(7);
                 *row[51] = op0_limb_7_col51;
-                let op0_limb_8_col52 = memory_id_to_big_value_tmp_f459d_14.get_m31(8);
+                let op0_limb_8_col52 = memory_id_to_big_value_tmp_3fa46_14.get_m31(8);
                 *row[52] = op0_limb_8_col52;
-                let op0_limb_9_col53 = memory_id_to_big_value_tmp_f459d_14.get_m31(9);
+                let op0_limb_9_col53 = memory_id_to_big_value_tmp_3fa46_14.get_m31(9);
                 *row[53] = op0_limb_9_col53;
-                let op0_limb_10_col54 = memory_id_to_big_value_tmp_f459d_14.get_m31(10);
+                let op0_limb_10_col54 = memory_id_to_big_value_tmp_3fa46_14.get_m31(10);
                 *row[54] = op0_limb_10_col54;
-                let op0_limb_11_col55 = memory_id_to_big_value_tmp_f459d_14.get_m31(11);
+                let op0_limb_11_col55 = memory_id_to_big_value_tmp_3fa46_14.get_m31(11);
                 *row[55] = op0_limb_11_col55;
-                let op0_limb_12_col56 = memory_id_to_big_value_tmp_f459d_14.get_m31(12);
+                let op0_limb_12_col56 = memory_id_to_big_value_tmp_3fa46_14.get_m31(12);
                 *row[56] = op0_limb_12_col56;
-                let op0_limb_13_col57 = memory_id_to_big_value_tmp_f459d_14.get_m31(13);
+                let op0_limb_13_col57 = memory_id_to_big_value_tmp_3fa46_14.get_m31(13);
                 *row[57] = op0_limb_13_col57;
-                let op0_limb_14_col58 = memory_id_to_big_value_tmp_f459d_14.get_m31(14);
+                let op0_limb_14_col58 = memory_id_to_big_value_tmp_3fa46_14.get_m31(14);
                 *row[58] = op0_limb_14_col58;
-                let op0_limb_15_col59 = memory_id_to_big_value_tmp_f459d_14.get_m31(15);
+                let op0_limb_15_col59 = memory_id_to_big_value_tmp_3fa46_14.get_m31(15);
                 *row[59] = op0_limb_15_col59;
-                let op0_limb_16_col60 = memory_id_to_big_value_tmp_f459d_14.get_m31(16);
+                let op0_limb_16_col60 = memory_id_to_big_value_tmp_3fa46_14.get_m31(16);
                 *row[60] = op0_limb_16_col60;
-                let op0_limb_17_col61 = memory_id_to_big_value_tmp_f459d_14.get_m31(17);
+                let op0_limb_17_col61 = memory_id_to_big_value_tmp_3fa46_14.get_m31(17);
                 *row[61] = op0_limb_17_col61;
-                let op0_limb_18_col62 = memory_id_to_big_value_tmp_f459d_14.get_m31(18);
+                let op0_limb_18_col62 = memory_id_to_big_value_tmp_3fa46_14.get_m31(18);
                 *row[62] = op0_limb_18_col62;
-                let op0_limb_19_col63 = memory_id_to_big_value_tmp_f459d_14.get_m31(19);
+                let op0_limb_19_col63 = memory_id_to_big_value_tmp_3fa46_14.get_m31(19);
                 *row[63] = op0_limb_19_col63;
-                let op0_limb_20_col64 = memory_id_to_big_value_tmp_f459d_14.get_m31(20);
+                let op0_limb_20_col64 = memory_id_to_big_value_tmp_3fa46_14.get_m31(20);
                 *row[64] = op0_limb_20_col64;
-                let op0_limb_21_col65 = memory_id_to_big_value_tmp_f459d_14.get_m31(21);
+                let op0_limb_21_col65 = memory_id_to_big_value_tmp_3fa46_14.get_m31(21);
                 *row[65] = op0_limb_21_col65;
-                let op0_limb_22_col66 = memory_id_to_big_value_tmp_f459d_14.get_m31(22);
+                let op0_limb_22_col66 = memory_id_to_big_value_tmp_3fa46_14.get_m31(22);
                 *row[66] = op0_limb_22_col66;
-                let op0_limb_23_col67 = memory_id_to_big_value_tmp_f459d_14.get_m31(23);
+                let op0_limb_23_col67 = memory_id_to_big_value_tmp_3fa46_14.get_m31(23);
                 *row[67] = op0_limb_23_col67;
-                let op0_limb_24_col68 = memory_id_to_big_value_tmp_f459d_14.get_m31(24);
+                let op0_limb_24_col68 = memory_id_to_big_value_tmp_3fa46_14.get_m31(24);
                 *row[68] = op0_limb_24_col68;
-                let op0_limb_25_col69 = memory_id_to_big_value_tmp_f459d_14.get_m31(25);
+                let op0_limb_25_col69 = memory_id_to_big_value_tmp_3fa46_14.get_m31(25);
                 *row[69] = op0_limb_25_col69;
-                let op0_limb_26_col70 = memory_id_to_big_value_tmp_f459d_14.get_m31(26);
+                let op0_limb_26_col70 = memory_id_to_big_value_tmp_3fa46_14.get_m31(26);
                 *row[70] = op0_limb_26_col70;
-                let op0_limb_27_col71 = memory_id_to_big_value_tmp_f459d_14.get_m31(27);
+                let op0_limb_27_col71 = memory_id_to_big_value_tmp_3fa46_14.get_m31(27);
                 *row[71] = op0_limb_27_col71;
                 for (i, &input) in op0_id_col43.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[1] = input;
@@ -544,11 +547,11 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f459d_15 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_3fa46_15 = memory_address_to_id_state
                     .deduce_output(((mem1_base_col13) + ((offset2_col5) - (M31_32768))));
-                let memory_id_to_big_value_tmp_f459d_16 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f459d_15);
-                let op1_id_col72 = memory_address_to_id_value_tmp_f459d_15;
+                let memory_id_to_big_value_tmp_3fa46_16 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_3fa46_15);
+                let op1_id_col72 = memory_address_to_id_value_tmp_3fa46_15;
                 *row[72] = op1_id_col72;
                 for (i, &input) in ((mem1_base_col13) + ((offset2_col5) - (M31_32768)))
                     .unpack()
@@ -561,61 +564,61 @@ fn write_trace_simd(
                     ((mem1_base_col13) + ((offset2_col5) - (M31_32768))),
                     op1_id_col72,
                 ];
-                let op1_limb_0_col73 = memory_id_to_big_value_tmp_f459d_16.get_m31(0);
+                let op1_limb_0_col73 = memory_id_to_big_value_tmp_3fa46_16.get_m31(0);
                 *row[73] = op1_limb_0_col73;
-                let op1_limb_1_col74 = memory_id_to_big_value_tmp_f459d_16.get_m31(1);
+                let op1_limb_1_col74 = memory_id_to_big_value_tmp_3fa46_16.get_m31(1);
                 *row[74] = op1_limb_1_col74;
-                let op1_limb_2_col75 = memory_id_to_big_value_tmp_f459d_16.get_m31(2);
+                let op1_limb_2_col75 = memory_id_to_big_value_tmp_3fa46_16.get_m31(2);
                 *row[75] = op1_limb_2_col75;
-                let op1_limb_3_col76 = memory_id_to_big_value_tmp_f459d_16.get_m31(3);
+                let op1_limb_3_col76 = memory_id_to_big_value_tmp_3fa46_16.get_m31(3);
                 *row[76] = op1_limb_3_col76;
-                let op1_limb_4_col77 = memory_id_to_big_value_tmp_f459d_16.get_m31(4);
+                let op1_limb_4_col77 = memory_id_to_big_value_tmp_3fa46_16.get_m31(4);
                 *row[77] = op1_limb_4_col77;
-                let op1_limb_5_col78 = memory_id_to_big_value_tmp_f459d_16.get_m31(5);
+                let op1_limb_5_col78 = memory_id_to_big_value_tmp_3fa46_16.get_m31(5);
                 *row[78] = op1_limb_5_col78;
-                let op1_limb_6_col79 = memory_id_to_big_value_tmp_f459d_16.get_m31(6);
+                let op1_limb_6_col79 = memory_id_to_big_value_tmp_3fa46_16.get_m31(6);
                 *row[79] = op1_limb_6_col79;
-                let op1_limb_7_col80 = memory_id_to_big_value_tmp_f459d_16.get_m31(7);
+                let op1_limb_7_col80 = memory_id_to_big_value_tmp_3fa46_16.get_m31(7);
                 *row[80] = op1_limb_7_col80;
-                let op1_limb_8_col81 = memory_id_to_big_value_tmp_f459d_16.get_m31(8);
+                let op1_limb_8_col81 = memory_id_to_big_value_tmp_3fa46_16.get_m31(8);
                 *row[81] = op1_limb_8_col81;
-                let op1_limb_9_col82 = memory_id_to_big_value_tmp_f459d_16.get_m31(9);
+                let op1_limb_9_col82 = memory_id_to_big_value_tmp_3fa46_16.get_m31(9);
                 *row[82] = op1_limb_9_col82;
-                let op1_limb_10_col83 = memory_id_to_big_value_tmp_f459d_16.get_m31(10);
+                let op1_limb_10_col83 = memory_id_to_big_value_tmp_3fa46_16.get_m31(10);
                 *row[83] = op1_limb_10_col83;
-                let op1_limb_11_col84 = memory_id_to_big_value_tmp_f459d_16.get_m31(11);
+                let op1_limb_11_col84 = memory_id_to_big_value_tmp_3fa46_16.get_m31(11);
                 *row[84] = op1_limb_11_col84;
-                let op1_limb_12_col85 = memory_id_to_big_value_tmp_f459d_16.get_m31(12);
+                let op1_limb_12_col85 = memory_id_to_big_value_tmp_3fa46_16.get_m31(12);
                 *row[85] = op1_limb_12_col85;
-                let op1_limb_13_col86 = memory_id_to_big_value_tmp_f459d_16.get_m31(13);
+                let op1_limb_13_col86 = memory_id_to_big_value_tmp_3fa46_16.get_m31(13);
                 *row[86] = op1_limb_13_col86;
-                let op1_limb_14_col87 = memory_id_to_big_value_tmp_f459d_16.get_m31(14);
+                let op1_limb_14_col87 = memory_id_to_big_value_tmp_3fa46_16.get_m31(14);
                 *row[87] = op1_limb_14_col87;
-                let op1_limb_15_col88 = memory_id_to_big_value_tmp_f459d_16.get_m31(15);
+                let op1_limb_15_col88 = memory_id_to_big_value_tmp_3fa46_16.get_m31(15);
                 *row[88] = op1_limb_15_col88;
-                let op1_limb_16_col89 = memory_id_to_big_value_tmp_f459d_16.get_m31(16);
+                let op1_limb_16_col89 = memory_id_to_big_value_tmp_3fa46_16.get_m31(16);
                 *row[89] = op1_limb_16_col89;
-                let op1_limb_17_col90 = memory_id_to_big_value_tmp_f459d_16.get_m31(17);
+                let op1_limb_17_col90 = memory_id_to_big_value_tmp_3fa46_16.get_m31(17);
                 *row[90] = op1_limb_17_col90;
-                let op1_limb_18_col91 = memory_id_to_big_value_tmp_f459d_16.get_m31(18);
+                let op1_limb_18_col91 = memory_id_to_big_value_tmp_3fa46_16.get_m31(18);
                 *row[91] = op1_limb_18_col91;
-                let op1_limb_19_col92 = memory_id_to_big_value_tmp_f459d_16.get_m31(19);
+                let op1_limb_19_col92 = memory_id_to_big_value_tmp_3fa46_16.get_m31(19);
                 *row[92] = op1_limb_19_col92;
-                let op1_limb_20_col93 = memory_id_to_big_value_tmp_f459d_16.get_m31(20);
+                let op1_limb_20_col93 = memory_id_to_big_value_tmp_3fa46_16.get_m31(20);
                 *row[93] = op1_limb_20_col93;
-                let op1_limb_21_col94 = memory_id_to_big_value_tmp_f459d_16.get_m31(21);
+                let op1_limb_21_col94 = memory_id_to_big_value_tmp_3fa46_16.get_m31(21);
                 *row[94] = op1_limb_21_col94;
-                let op1_limb_22_col95 = memory_id_to_big_value_tmp_f459d_16.get_m31(22);
+                let op1_limb_22_col95 = memory_id_to_big_value_tmp_3fa46_16.get_m31(22);
                 *row[95] = op1_limb_22_col95;
-                let op1_limb_23_col96 = memory_id_to_big_value_tmp_f459d_16.get_m31(23);
+                let op1_limb_23_col96 = memory_id_to_big_value_tmp_3fa46_16.get_m31(23);
                 *row[96] = op1_limb_23_col96;
-                let op1_limb_24_col97 = memory_id_to_big_value_tmp_f459d_16.get_m31(24);
+                let op1_limb_24_col97 = memory_id_to_big_value_tmp_3fa46_16.get_m31(24);
                 *row[97] = op1_limb_24_col97;
-                let op1_limb_25_col98 = memory_id_to_big_value_tmp_f459d_16.get_m31(25);
+                let op1_limb_25_col98 = memory_id_to_big_value_tmp_3fa46_16.get_m31(25);
                 *row[98] = op1_limb_25_col98;
-                let op1_limb_26_col99 = memory_id_to_big_value_tmp_f459d_16.get_m31(26);
+                let op1_limb_26_col99 = memory_id_to_big_value_tmp_3fa46_16.get_m31(26);
                 *row[99] = op1_limb_26_col99;
-                let op1_limb_27_col100 = memory_id_to_big_value_tmp_f459d_16.get_m31(27);
+                let op1_limb_27_col100 = memory_id_to_big_value_tmp_3fa46_16.get_m31(27);
                 *row[100] = op1_limb_27_col100;
                 for (i, &input) in op1_id_col72.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[2] = input;
@@ -654,11 +657,11 @@ fn write_trace_simd(
 
                 // Verify Add 252.
 
-                let sub_p_bit_tmp_f459d_17 = ((UInt16_1)
+                let sub_p_bit_tmp_3fa46_17 = ((UInt16_1)
                     & (((PackedUInt16::from_m31(op0_limb_0_col44))
                         ^ (PackedUInt16::from_m31(op1_limb_0_col73)))
                         ^ (PackedUInt16::from_m31(dst_limb_0_col15))));
-                let sub_p_bit_col101 = sub_p_bit_tmp_f459d_17.as_m31();
+                let sub_p_bit_col101 = sub_p_bit_tmp_3fa46_17.as_m31();
                 *row[101] = sub_p_bit_col101;
 
                 *lookup_data.opcodes_0 = [input_pc_col0, input_ap_col1, input_fp_col2];
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/component.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/component.rs
similarity index 81%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/component.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/component.rs
index f47b85c1..315c14ca 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/component.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/component.rs
@@ -4,6 +4,7 @@ use num_traits::{One, Zero};
 use serde::{Deserialize, Serialize};
 use stwo_cairo_serialize::CairoSerialize;
 use stwo_prover::constraint_framework::logup::{LogupAtRow, LogupSums, LookupElements};
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::{
     EvalAtRow, FrameworkComponent, FrameworkEval, RelationEntry,
 };
@@ -369,305 +370,305 @@ impl FrameworkEval for Eval {
 
         // sub_p_bit is a bit.
         eval.add_constraint((sub_p_bit_col97.clone() * (sub_p_bit_col97.clone() - M31_1.clone())));
-        let carry_tmp_f0ae3_15 = eval.add_intermediate(
+        let carry_tmp_7e965_15 = eval.add_intermediate(
             (((((op0_limb_0_col40.clone() + op1_limb_0_col69.clone()) + M31_0.clone())
                 - dst_limb_0_col11.clone())
                 - (M31_1.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_15.clone()
-                * ((carry_tmp_f0ae3_15.clone() * carry_tmp_f0ae3_15.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_15.clone()
+                * ((carry_tmp_7e965_15.clone() * carry_tmp_7e965_15.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_16 = eval.add_intermediate(
+        let carry_tmp_7e965_16 = eval.add_intermediate(
             (((((op0_limb_1_col41.clone() + op1_limb_1_col70.clone())
-                + carry_tmp_f0ae3_15.clone())
+                + carry_tmp_7e965_15.clone())
                 - dst_limb_1_col12.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_16.clone()
-                * ((carry_tmp_f0ae3_16.clone() * carry_tmp_f0ae3_16.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_16.clone()
+                * ((carry_tmp_7e965_16.clone() * carry_tmp_7e965_16.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_17 = eval.add_intermediate(
+        let carry_tmp_7e965_17 = eval.add_intermediate(
             (((((op0_limb_2_col42.clone() + op1_limb_2_col71.clone())
-                + carry_tmp_f0ae3_16.clone())
+                + carry_tmp_7e965_16.clone())
                 - dst_limb_2_col13.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_17.clone()
-                * ((carry_tmp_f0ae3_17.clone() * carry_tmp_f0ae3_17.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_17.clone()
+                * ((carry_tmp_7e965_17.clone() * carry_tmp_7e965_17.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_18 = eval.add_intermediate(
+        let carry_tmp_7e965_18 = eval.add_intermediate(
             (((((op0_limb_3_col43.clone() + op1_limb_3_col72.clone())
-                + carry_tmp_f0ae3_17.clone())
+                + carry_tmp_7e965_17.clone())
                 - dst_limb_3_col14.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_18.clone()
-                * ((carry_tmp_f0ae3_18.clone() * carry_tmp_f0ae3_18.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_18.clone()
+                * ((carry_tmp_7e965_18.clone() * carry_tmp_7e965_18.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_19 = eval.add_intermediate(
+        let carry_tmp_7e965_19 = eval.add_intermediate(
             (((((op0_limb_4_col44.clone() + op1_limb_4_col73.clone())
-                + carry_tmp_f0ae3_18.clone())
+                + carry_tmp_7e965_18.clone())
                 - dst_limb_4_col15.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_19.clone()
-                * ((carry_tmp_f0ae3_19.clone() * carry_tmp_f0ae3_19.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_19.clone()
+                * ((carry_tmp_7e965_19.clone() * carry_tmp_7e965_19.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_20 = eval.add_intermediate(
+        let carry_tmp_7e965_20 = eval.add_intermediate(
             (((((op0_limb_5_col45.clone() + op1_limb_5_col74.clone())
-                + carry_tmp_f0ae3_19.clone())
+                + carry_tmp_7e965_19.clone())
                 - dst_limb_5_col16.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_20.clone()
-                * ((carry_tmp_f0ae3_20.clone() * carry_tmp_f0ae3_20.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_20.clone()
+                * ((carry_tmp_7e965_20.clone() * carry_tmp_7e965_20.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_21 = eval.add_intermediate(
+        let carry_tmp_7e965_21 = eval.add_intermediate(
             (((((op0_limb_6_col46.clone() + op1_limb_6_col75.clone())
-                + carry_tmp_f0ae3_20.clone())
+                + carry_tmp_7e965_20.clone())
                 - dst_limb_6_col17.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_21.clone()
-                * ((carry_tmp_f0ae3_21.clone() * carry_tmp_f0ae3_21.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_21.clone()
+                * ((carry_tmp_7e965_21.clone() * carry_tmp_7e965_21.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_22 = eval.add_intermediate(
+        let carry_tmp_7e965_22 = eval.add_intermediate(
             (((((op0_limb_7_col47.clone() + op1_limb_7_col76.clone())
-                + carry_tmp_f0ae3_21.clone())
+                + carry_tmp_7e965_21.clone())
                 - dst_limb_7_col18.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_22.clone()
-                * ((carry_tmp_f0ae3_22.clone() * carry_tmp_f0ae3_22.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_22.clone()
+                * ((carry_tmp_7e965_22.clone() * carry_tmp_7e965_22.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_23 = eval.add_intermediate(
+        let carry_tmp_7e965_23 = eval.add_intermediate(
             (((((op0_limb_8_col48.clone() + op1_limb_8_col77.clone())
-                + carry_tmp_f0ae3_22.clone())
+                + carry_tmp_7e965_22.clone())
                 - dst_limb_8_col19.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_23.clone()
-                * ((carry_tmp_f0ae3_23.clone() * carry_tmp_f0ae3_23.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_23.clone()
+                * ((carry_tmp_7e965_23.clone() * carry_tmp_7e965_23.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_24 = eval.add_intermediate(
+        let carry_tmp_7e965_24 = eval.add_intermediate(
             (((((op0_limb_9_col49.clone() + op1_limb_9_col78.clone())
-                + carry_tmp_f0ae3_23.clone())
+                + carry_tmp_7e965_23.clone())
                 - dst_limb_9_col20.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_24.clone()
-                * ((carry_tmp_f0ae3_24.clone() * carry_tmp_f0ae3_24.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_24.clone()
+                * ((carry_tmp_7e965_24.clone() * carry_tmp_7e965_24.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_25 = eval.add_intermediate(
+        let carry_tmp_7e965_25 = eval.add_intermediate(
             (((((op0_limb_10_col50.clone() + op1_limb_10_col79.clone())
-                + carry_tmp_f0ae3_24.clone())
+                + carry_tmp_7e965_24.clone())
                 - dst_limb_10_col21.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_25.clone()
-                * ((carry_tmp_f0ae3_25.clone() * carry_tmp_f0ae3_25.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_25.clone()
+                * ((carry_tmp_7e965_25.clone() * carry_tmp_7e965_25.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_26 = eval.add_intermediate(
+        let carry_tmp_7e965_26 = eval.add_intermediate(
             (((((op0_limb_11_col51.clone() + op1_limb_11_col80.clone())
-                + carry_tmp_f0ae3_25.clone())
+                + carry_tmp_7e965_25.clone())
                 - dst_limb_11_col22.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_26.clone()
-                * ((carry_tmp_f0ae3_26.clone() * carry_tmp_f0ae3_26.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_26.clone()
+                * ((carry_tmp_7e965_26.clone() * carry_tmp_7e965_26.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_27 = eval.add_intermediate(
+        let carry_tmp_7e965_27 = eval.add_intermediate(
             (((((op0_limb_12_col52.clone() + op1_limb_12_col81.clone())
-                + carry_tmp_f0ae3_26.clone())
+                + carry_tmp_7e965_26.clone())
                 - dst_limb_12_col23.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_27.clone()
-                * ((carry_tmp_f0ae3_27.clone() * carry_tmp_f0ae3_27.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_27.clone()
+                * ((carry_tmp_7e965_27.clone() * carry_tmp_7e965_27.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_28 = eval.add_intermediate(
+        let carry_tmp_7e965_28 = eval.add_intermediate(
             (((((op0_limb_13_col53.clone() + op1_limb_13_col82.clone())
-                + carry_tmp_f0ae3_27.clone())
+                + carry_tmp_7e965_27.clone())
                 - dst_limb_13_col24.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_28.clone()
-                * ((carry_tmp_f0ae3_28.clone() * carry_tmp_f0ae3_28.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_28.clone()
+                * ((carry_tmp_7e965_28.clone() * carry_tmp_7e965_28.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_29 = eval.add_intermediate(
+        let carry_tmp_7e965_29 = eval.add_intermediate(
             (((((op0_limb_14_col54.clone() + op1_limb_14_col83.clone())
-                + carry_tmp_f0ae3_28.clone())
+                + carry_tmp_7e965_28.clone())
                 - dst_limb_14_col25.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_29.clone()
-                * ((carry_tmp_f0ae3_29.clone() * carry_tmp_f0ae3_29.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_29.clone()
+                * ((carry_tmp_7e965_29.clone() * carry_tmp_7e965_29.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_30 = eval.add_intermediate(
+        let carry_tmp_7e965_30 = eval.add_intermediate(
             (((((op0_limb_15_col55.clone() + op1_limb_15_col84.clone())
-                + carry_tmp_f0ae3_29.clone())
+                + carry_tmp_7e965_29.clone())
                 - dst_limb_15_col26.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_30.clone()
-                * ((carry_tmp_f0ae3_30.clone() * carry_tmp_f0ae3_30.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_30.clone()
+                * ((carry_tmp_7e965_30.clone() * carry_tmp_7e965_30.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_31 = eval.add_intermediate(
+        let carry_tmp_7e965_31 = eval.add_intermediate(
             (((((op0_limb_16_col56.clone() + op1_limb_16_col85.clone())
-                + carry_tmp_f0ae3_30.clone())
+                + carry_tmp_7e965_30.clone())
                 - dst_limb_16_col27.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_31.clone()
-                * ((carry_tmp_f0ae3_31.clone() * carry_tmp_f0ae3_31.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_31.clone()
+                * ((carry_tmp_7e965_31.clone() * carry_tmp_7e965_31.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_32 = eval.add_intermediate(
+        let carry_tmp_7e965_32 = eval.add_intermediate(
             (((((op0_limb_17_col57.clone() + op1_limb_17_col86.clone())
-                + carry_tmp_f0ae3_31.clone())
+                + carry_tmp_7e965_31.clone())
                 - dst_limb_17_col28.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_32.clone()
-                * ((carry_tmp_f0ae3_32.clone() * carry_tmp_f0ae3_32.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_32.clone()
+                * ((carry_tmp_7e965_32.clone() * carry_tmp_7e965_32.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_33 = eval.add_intermediate(
+        let carry_tmp_7e965_33 = eval.add_intermediate(
             (((((op0_limb_18_col58.clone() + op1_limb_18_col87.clone())
-                + carry_tmp_f0ae3_32.clone())
+                + carry_tmp_7e965_32.clone())
                 - dst_limb_18_col29.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_33.clone()
-                * ((carry_tmp_f0ae3_33.clone() * carry_tmp_f0ae3_33.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_33.clone()
+                * ((carry_tmp_7e965_33.clone() * carry_tmp_7e965_33.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_34 = eval.add_intermediate(
+        let carry_tmp_7e965_34 = eval.add_intermediate(
             (((((op0_limb_19_col59.clone() + op1_limb_19_col88.clone())
-                + carry_tmp_f0ae3_33.clone())
+                + carry_tmp_7e965_33.clone())
                 - dst_limb_19_col30.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_34.clone()
-                * ((carry_tmp_f0ae3_34.clone() * carry_tmp_f0ae3_34.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_34.clone()
+                * ((carry_tmp_7e965_34.clone() * carry_tmp_7e965_34.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_35 = eval.add_intermediate(
+        let carry_tmp_7e965_35 = eval.add_intermediate(
             (((((op0_limb_20_col60.clone() + op1_limb_20_col89.clone())
-                + carry_tmp_f0ae3_34.clone())
+                + carry_tmp_7e965_34.clone())
                 - dst_limb_20_col31.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_35.clone()
-                * ((carry_tmp_f0ae3_35.clone() * carry_tmp_f0ae3_35.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_35.clone()
+                * ((carry_tmp_7e965_35.clone() * carry_tmp_7e965_35.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_36 = eval.add_intermediate(
+        let carry_tmp_7e965_36 = eval.add_intermediate(
             (((((op0_limb_21_col61.clone() + op1_limb_21_col90.clone())
-                + carry_tmp_f0ae3_35.clone())
+                + carry_tmp_7e965_35.clone())
                 - dst_limb_21_col32.clone())
                 - (M31_136.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_36.clone()
-                * ((carry_tmp_f0ae3_36.clone() * carry_tmp_f0ae3_36.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_36.clone()
+                * ((carry_tmp_7e965_36.clone() * carry_tmp_7e965_36.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_37 = eval.add_intermediate(
+        let carry_tmp_7e965_37 = eval.add_intermediate(
             (((((op0_limb_22_col62.clone() + op1_limb_22_col91.clone())
-                + carry_tmp_f0ae3_36.clone())
+                + carry_tmp_7e965_36.clone())
                 - dst_limb_22_col33.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_37.clone()
-                * ((carry_tmp_f0ae3_37.clone() * carry_tmp_f0ae3_37.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_37.clone()
+                * ((carry_tmp_7e965_37.clone() * carry_tmp_7e965_37.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_38 = eval.add_intermediate(
+        let carry_tmp_7e965_38 = eval.add_intermediate(
             (((((op0_limb_23_col63.clone() + op1_limb_23_col92.clone())
-                + carry_tmp_f0ae3_37.clone())
+                + carry_tmp_7e965_37.clone())
                 - dst_limb_23_col34.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_38.clone()
-                * ((carry_tmp_f0ae3_38.clone() * carry_tmp_f0ae3_38.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_38.clone()
+                * ((carry_tmp_7e965_38.clone() * carry_tmp_7e965_38.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_39 = eval.add_intermediate(
+        let carry_tmp_7e965_39 = eval.add_intermediate(
             (((((op0_limb_24_col64.clone() + op1_limb_24_col93.clone())
-                + carry_tmp_f0ae3_38.clone())
+                + carry_tmp_7e965_38.clone())
                 - dst_limb_24_col35.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_39.clone()
-                * ((carry_tmp_f0ae3_39.clone() * carry_tmp_f0ae3_39.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_39.clone()
+                * ((carry_tmp_7e965_39.clone() * carry_tmp_7e965_39.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_40 = eval.add_intermediate(
+        let carry_tmp_7e965_40 = eval.add_intermediate(
             (((((op0_limb_25_col65.clone() + op1_limb_25_col94.clone())
-                + carry_tmp_f0ae3_39.clone())
+                + carry_tmp_7e965_39.clone())
                 - dst_limb_25_col36.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_40.clone()
-                * ((carry_tmp_f0ae3_40.clone() * carry_tmp_f0ae3_40.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_40.clone()
+                * ((carry_tmp_7e965_40.clone() * carry_tmp_7e965_40.clone()) - M31_1.clone())),
         );
-        let carry_tmp_f0ae3_41 = eval.add_intermediate(
+        let carry_tmp_7e965_41 = eval.add_intermediate(
             (((((op0_limb_26_col66.clone() + op1_limb_26_col95.clone())
-                + carry_tmp_f0ae3_40.clone())
+                + carry_tmp_7e965_40.clone())
                 - dst_limb_26_col37.clone())
                 - (M31_0.clone() * sub_p_bit_col97.clone()))
                 * M31_4194304.clone()),
         );
         eval.add_constraint(
-            (carry_tmp_f0ae3_41.clone()
-                * ((carry_tmp_f0ae3_41.clone() * carry_tmp_f0ae3_41.clone()) - M31_1.clone())),
+            (carry_tmp_7e965_41.clone()
+                * ((carry_tmp_7e965_41.clone() * carry_tmp_7e965_41.clone()) - M31_1.clone())),
         );
         eval.add_constraint(
             ((((op0_limb_27_col67.clone() + op1_limb_27_col96.clone())
-                + carry_tmp_f0ae3_41.clone())
+                + carry_tmp_7e965_41.clone())
                 - dst_limb_27_col38.clone())
                 - (M31_256.clone() * sub_p_bit_col97.clone())),
         );
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/mod.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/mod.rs
similarity index 100%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/mod.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/mod.rs
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/prover.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/prover.rs
similarity index 86%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/prover.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/prover.rs
index 564cf4be..8023ecee 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_f_is_imm_t/prover.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_imm/prover.rs
@@ -7,10 +7,13 @@ use itertools::{chain, zip_eq, Itertools};
 use num_traits::{One, Zero};
 use prover_types::cpu::*;
 use prover_types::simd::*;
-use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
+use rayon::iter::{
+    IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator, ParallelIterator,
+};
 use stwo_air_utils::trace::component_trace::ComponentTrace;
 use stwo_air_utils_derive::{IterMut, ParIterMut, Uninitialized};
 use stwo_prover::constraint_framework::logup::LogupTraceGenerator;
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::Relation;
 use stwo_prover::core::air::Component;
 use stwo_prover::core::backend::simd::column::BaseColumn;
@@ -21,6 +24,7 @@ use stwo_prover::core::backend::simd::SimdBackend;
 use stwo_prover::core::backend::{BackendForChannel, Col, Column};
 use stwo_prover::core::channel::{Channel, MerkleChannel};
 use stwo_prover::core::fields::m31::M31;
+use stwo_prover::core::fields::FieldExpOps;
 use stwo_prover::core::pcs::TreeBuilder;
 use stwo_prover::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use stwo_prover::core::poly::BitReversedOrder;
@@ -66,6 +70,7 @@ impl ClaimGenerator {
 
         let packed_inputs = pack_values(&self.inputs);
         let (trace, mut sub_components_inputs, lookup_data) = write_trace_simd(
+            n_rows,
             packed_inputs,
             memory_address_to_id_state,
             memory_id_to_big_state,
@@ -104,8 +109,8 @@ impl ClaimGenerator {
         )
     }
 
-    pub fn add_inputs(&mut self, inputs: &[InputType]) {
-        self.inputs.extend(inputs);
+    pub fn add_inputs(&self, _inputs: &[InputType]) {
+        unimplemented!("Implement manually");
     }
 }
 
@@ -121,6 +126,7 @@ pub struct SubComponentInputs {
 #[allow(clippy::double_parens)]
 #[allow(non_snake_case)]
 fn write_trace_simd(
+    n_rows: usize,
     inputs: Vec<PackedInputType>,
     memory_address_to_id_state: &memory_address_to_id::ClaimGenerator,
     memory_id_to_big_state: &memory_id_to_big::ClaimGenerator,
@@ -157,79 +163,79 @@ fn write_trace_simd(
 
     trace
         .par_iter_mut()
-        .zip(inputs.par_iter())
+        .enumerate()
+        .zip(inputs.into_par_iter())
         .zip(lookup_data.par_iter_mut())
         .zip(sub_components_inputs.par_iter_mut().chunks(N_LANES))
         .for_each(
             |(
-                ((row, add_opcode_is_small_f_is_imm_t_input), lookup_data),
+                (((row_index, row), add_opcode_imm_input), lookup_data),
                 mut sub_components_inputs,
             )| {
-                let input_tmp_f0ae3_0 = add_opcode_is_small_f_is_imm_t_input;
-                let input_pc_col0 = input_tmp_f0ae3_0.pc;
+                let input_tmp_7e965_0 = add_opcode_imm_input;
+                let input_pc_col0 = input_tmp_7e965_0.pc;
                 *row[0] = input_pc_col0;
-                let input_ap_col1 = input_tmp_f0ae3_0.ap;
+                let input_ap_col1 = input_tmp_7e965_0.ap;
                 *row[1] = input_ap_col1;
-                let input_fp_col2 = input_tmp_f0ae3_0.fp;
+                let input_fp_col2 = input_tmp_7e965_0.fp;
                 *row[2] = input_fp_col2;
 
                 // Decode Instruction.
 
-                let memory_address_to_id_value_tmp_f0ae3_1 =
+                let memory_address_to_id_value_tmp_7e965_1 =
                     memory_address_to_id_state.deduce_output(input_pc_col0);
-                let memory_id_to_big_value_tmp_f0ae3_2 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f0ae3_1);
-                let offset0_tmp_f0ae3_3 =
-                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f0ae3_2.get_m31(0)))
+                let memory_id_to_big_value_tmp_7e965_2 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_7e965_1);
+                let offset0_tmp_7e965_3 =
+                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_7e965_2.get_m31(0)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(1),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(1),
                         )) & (UInt16_127))
                             << (UInt16_9)));
-                let offset0_col3 = offset0_tmp_f0ae3_3.as_m31();
+                let offset0_col3 = offset0_tmp_7e965_3.as_m31();
                 *row[3] = offset0_col3;
-                let offset1_tmp_f0ae3_4 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f0ae3_2.get_m31(1)))
+                let offset1_tmp_7e965_4 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_7e965_2.get_m31(1)))
                         >> (UInt16_7))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(2),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(2),
                         )) << (UInt16_2)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(3),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(3),
                         )) & (UInt16_31))
                             << (UInt16_11)));
-                let offset1_col4 = offset1_tmp_f0ae3_4.as_m31();
+                let offset1_col4 = offset1_tmp_7e965_4.as_m31();
                 *row[4] = offset1_col4;
-                let dst_base_fp_tmp_f0ae3_5 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f0ae3_2.get_m31(5)))
+                let dst_base_fp_tmp_7e965_5 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_7e965_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(6),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_0))
                         & (UInt16_1));
-                let dst_base_fp_col5 = dst_base_fp_tmp_f0ae3_5.as_m31();
+                let dst_base_fp_col5 = dst_base_fp_tmp_7e965_5.as_m31();
                 *row[5] = dst_base_fp_col5;
-                let op0_base_fp_tmp_f0ae3_6 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f0ae3_2.get_m31(5)))
+                let op0_base_fp_tmp_7e965_6 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_7e965_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(6),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_1))
                         & (UInt16_1));
-                let op0_base_fp_col6 = op0_base_fp_tmp_f0ae3_6.as_m31();
+                let op0_base_fp_col6 = op0_base_fp_tmp_7e965_6.as_m31();
                 *row[6] = op0_base_fp_col6;
-                let ap_update_add_1_tmp_f0ae3_7 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_f0ae3_2.get_m31(5)))
+                let ap_update_add_1_tmp_7e965_7 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_7e965_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_f0ae3_2.get_m31(6),
+                            memory_id_to_big_value_tmp_7e965_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_11))
                         & (UInt16_1));
-                let ap_update_add_1_col7 = ap_update_add_1_tmp_f0ae3_7.as_m31();
+                let ap_update_add_1_col7 = ap_update_add_1_tmp_7e965_7.as_m31();
                 *row[7] = ap_update_add_1_col7;
-
                 for (i, &input) in (
                     input_pc_col0,
                     [offset0_col3, offset1_col4, M31_32769],
@@ -288,11 +294,11 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f0ae3_8 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_7e965_8 = memory_address_to_id_state
                     .deduce_output(((mem_dst_base_col8) + ((offset0_col3) - (M31_32768))));
-                let memory_id_to_big_value_tmp_f0ae3_9 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f0ae3_8);
-                let dst_id_col10 = memory_address_to_id_value_tmp_f0ae3_8;
+                let memory_id_to_big_value_tmp_7e965_9 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_7e965_8);
+                let dst_id_col10 = memory_address_to_id_value_tmp_7e965_8;
                 *row[10] = dst_id_col10;
                 for (i, &input) in ((mem_dst_base_col8) + ((offset0_col3) - (M31_32768)))
                     .unpack()
@@ -305,61 +311,61 @@ fn write_trace_simd(
                     ((mem_dst_base_col8) + ((offset0_col3) - (M31_32768))),
                     dst_id_col10,
                 ];
-                let dst_limb_0_col11 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(0);
+                let dst_limb_0_col11 = memory_id_to_big_value_tmp_7e965_9.get_m31(0);
                 *row[11] = dst_limb_0_col11;
-                let dst_limb_1_col12 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(1);
+                let dst_limb_1_col12 = memory_id_to_big_value_tmp_7e965_9.get_m31(1);
                 *row[12] = dst_limb_1_col12;
-                let dst_limb_2_col13 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(2);
+                let dst_limb_2_col13 = memory_id_to_big_value_tmp_7e965_9.get_m31(2);
                 *row[13] = dst_limb_2_col13;
-                let dst_limb_3_col14 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(3);
+                let dst_limb_3_col14 = memory_id_to_big_value_tmp_7e965_9.get_m31(3);
                 *row[14] = dst_limb_3_col14;
-                let dst_limb_4_col15 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(4);
+                let dst_limb_4_col15 = memory_id_to_big_value_tmp_7e965_9.get_m31(4);
                 *row[15] = dst_limb_4_col15;
-                let dst_limb_5_col16 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(5);
+                let dst_limb_5_col16 = memory_id_to_big_value_tmp_7e965_9.get_m31(5);
                 *row[16] = dst_limb_5_col16;
-                let dst_limb_6_col17 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(6);
+                let dst_limb_6_col17 = memory_id_to_big_value_tmp_7e965_9.get_m31(6);
                 *row[17] = dst_limb_6_col17;
-                let dst_limb_7_col18 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(7);
+                let dst_limb_7_col18 = memory_id_to_big_value_tmp_7e965_9.get_m31(7);
                 *row[18] = dst_limb_7_col18;
-                let dst_limb_8_col19 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(8);
+                let dst_limb_8_col19 = memory_id_to_big_value_tmp_7e965_9.get_m31(8);
                 *row[19] = dst_limb_8_col19;
-                let dst_limb_9_col20 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(9);
+                let dst_limb_9_col20 = memory_id_to_big_value_tmp_7e965_9.get_m31(9);
                 *row[20] = dst_limb_9_col20;
-                let dst_limb_10_col21 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(10);
+                let dst_limb_10_col21 = memory_id_to_big_value_tmp_7e965_9.get_m31(10);
                 *row[21] = dst_limb_10_col21;
-                let dst_limb_11_col22 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(11);
+                let dst_limb_11_col22 = memory_id_to_big_value_tmp_7e965_9.get_m31(11);
                 *row[22] = dst_limb_11_col22;
-                let dst_limb_12_col23 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(12);
+                let dst_limb_12_col23 = memory_id_to_big_value_tmp_7e965_9.get_m31(12);
                 *row[23] = dst_limb_12_col23;
-                let dst_limb_13_col24 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(13);
+                let dst_limb_13_col24 = memory_id_to_big_value_tmp_7e965_9.get_m31(13);
                 *row[24] = dst_limb_13_col24;
-                let dst_limb_14_col25 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(14);
+                let dst_limb_14_col25 = memory_id_to_big_value_tmp_7e965_9.get_m31(14);
                 *row[25] = dst_limb_14_col25;
-                let dst_limb_15_col26 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(15);
+                let dst_limb_15_col26 = memory_id_to_big_value_tmp_7e965_9.get_m31(15);
                 *row[26] = dst_limb_15_col26;
-                let dst_limb_16_col27 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(16);
+                let dst_limb_16_col27 = memory_id_to_big_value_tmp_7e965_9.get_m31(16);
                 *row[27] = dst_limb_16_col27;
-                let dst_limb_17_col28 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(17);
+                let dst_limb_17_col28 = memory_id_to_big_value_tmp_7e965_9.get_m31(17);
                 *row[28] = dst_limb_17_col28;
-                let dst_limb_18_col29 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(18);
+                let dst_limb_18_col29 = memory_id_to_big_value_tmp_7e965_9.get_m31(18);
                 *row[29] = dst_limb_18_col29;
-                let dst_limb_19_col30 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(19);
+                let dst_limb_19_col30 = memory_id_to_big_value_tmp_7e965_9.get_m31(19);
                 *row[30] = dst_limb_19_col30;
-                let dst_limb_20_col31 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(20);
+                let dst_limb_20_col31 = memory_id_to_big_value_tmp_7e965_9.get_m31(20);
                 *row[31] = dst_limb_20_col31;
-                let dst_limb_21_col32 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(21);
+                let dst_limb_21_col32 = memory_id_to_big_value_tmp_7e965_9.get_m31(21);
                 *row[32] = dst_limb_21_col32;
-                let dst_limb_22_col33 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(22);
+                let dst_limb_22_col33 = memory_id_to_big_value_tmp_7e965_9.get_m31(22);
                 *row[33] = dst_limb_22_col33;
-                let dst_limb_23_col34 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(23);
+                let dst_limb_23_col34 = memory_id_to_big_value_tmp_7e965_9.get_m31(23);
                 *row[34] = dst_limb_23_col34;
-                let dst_limb_24_col35 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(24);
+                let dst_limb_24_col35 = memory_id_to_big_value_tmp_7e965_9.get_m31(24);
                 *row[35] = dst_limb_24_col35;
-                let dst_limb_25_col36 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(25);
+                let dst_limb_25_col36 = memory_id_to_big_value_tmp_7e965_9.get_m31(25);
                 *row[36] = dst_limb_25_col36;
-                let dst_limb_26_col37 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(26);
+                let dst_limb_26_col37 = memory_id_to_big_value_tmp_7e965_9.get_m31(26);
                 *row[37] = dst_limb_26_col37;
-                let dst_limb_27_col38 = memory_id_to_big_value_tmp_f0ae3_9.get_m31(27);
+                let dst_limb_27_col38 = memory_id_to_big_value_tmp_7e965_9.get_m31(27);
                 *row[38] = dst_limb_27_col38;
                 for (i, &input) in dst_id_col10.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[0] = input;
@@ -398,11 +404,11 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f0ae3_10 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_7e965_10 = memory_address_to_id_state
                     .deduce_output(((mem0_base_col9) + ((offset1_col4) - (M31_32768))));
-                let memory_id_to_big_value_tmp_f0ae3_11 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f0ae3_10);
-                let op0_id_col39 = memory_address_to_id_value_tmp_f0ae3_10;
+                let memory_id_to_big_value_tmp_7e965_11 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_7e965_10);
+                let op0_id_col39 = memory_address_to_id_value_tmp_7e965_10;
                 *row[39] = op0_id_col39;
                 for (i, &input) in ((mem0_base_col9) + ((offset1_col4) - (M31_32768)))
                     .unpack()
@@ -415,61 +421,61 @@ fn write_trace_simd(
                     ((mem0_base_col9) + ((offset1_col4) - (M31_32768))),
                     op0_id_col39,
                 ];
-                let op0_limb_0_col40 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(0);
+                let op0_limb_0_col40 = memory_id_to_big_value_tmp_7e965_11.get_m31(0);
                 *row[40] = op0_limb_0_col40;
-                let op0_limb_1_col41 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(1);
+                let op0_limb_1_col41 = memory_id_to_big_value_tmp_7e965_11.get_m31(1);
                 *row[41] = op0_limb_1_col41;
-                let op0_limb_2_col42 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(2);
+                let op0_limb_2_col42 = memory_id_to_big_value_tmp_7e965_11.get_m31(2);
                 *row[42] = op0_limb_2_col42;
-                let op0_limb_3_col43 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(3);
+                let op0_limb_3_col43 = memory_id_to_big_value_tmp_7e965_11.get_m31(3);
                 *row[43] = op0_limb_3_col43;
-                let op0_limb_4_col44 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(4);
+                let op0_limb_4_col44 = memory_id_to_big_value_tmp_7e965_11.get_m31(4);
                 *row[44] = op0_limb_4_col44;
-                let op0_limb_5_col45 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(5);
+                let op0_limb_5_col45 = memory_id_to_big_value_tmp_7e965_11.get_m31(5);
                 *row[45] = op0_limb_5_col45;
-                let op0_limb_6_col46 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(6);
+                let op0_limb_6_col46 = memory_id_to_big_value_tmp_7e965_11.get_m31(6);
                 *row[46] = op0_limb_6_col46;
-                let op0_limb_7_col47 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(7);
+                let op0_limb_7_col47 = memory_id_to_big_value_tmp_7e965_11.get_m31(7);
                 *row[47] = op0_limb_7_col47;
-                let op0_limb_8_col48 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(8);
+                let op0_limb_8_col48 = memory_id_to_big_value_tmp_7e965_11.get_m31(8);
                 *row[48] = op0_limb_8_col48;
-                let op0_limb_9_col49 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(9);
+                let op0_limb_9_col49 = memory_id_to_big_value_tmp_7e965_11.get_m31(9);
                 *row[49] = op0_limb_9_col49;
-                let op0_limb_10_col50 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(10);
+                let op0_limb_10_col50 = memory_id_to_big_value_tmp_7e965_11.get_m31(10);
                 *row[50] = op0_limb_10_col50;
-                let op0_limb_11_col51 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(11);
+                let op0_limb_11_col51 = memory_id_to_big_value_tmp_7e965_11.get_m31(11);
                 *row[51] = op0_limb_11_col51;
-                let op0_limb_12_col52 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(12);
+                let op0_limb_12_col52 = memory_id_to_big_value_tmp_7e965_11.get_m31(12);
                 *row[52] = op0_limb_12_col52;
-                let op0_limb_13_col53 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(13);
+                let op0_limb_13_col53 = memory_id_to_big_value_tmp_7e965_11.get_m31(13);
                 *row[53] = op0_limb_13_col53;
-                let op0_limb_14_col54 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(14);
+                let op0_limb_14_col54 = memory_id_to_big_value_tmp_7e965_11.get_m31(14);
                 *row[54] = op0_limb_14_col54;
-                let op0_limb_15_col55 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(15);
+                let op0_limb_15_col55 = memory_id_to_big_value_tmp_7e965_11.get_m31(15);
                 *row[55] = op0_limb_15_col55;
-                let op0_limb_16_col56 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(16);
+                let op0_limb_16_col56 = memory_id_to_big_value_tmp_7e965_11.get_m31(16);
                 *row[56] = op0_limb_16_col56;
-                let op0_limb_17_col57 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(17);
+                let op0_limb_17_col57 = memory_id_to_big_value_tmp_7e965_11.get_m31(17);
                 *row[57] = op0_limb_17_col57;
-                let op0_limb_18_col58 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(18);
+                let op0_limb_18_col58 = memory_id_to_big_value_tmp_7e965_11.get_m31(18);
                 *row[58] = op0_limb_18_col58;
-                let op0_limb_19_col59 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(19);
+                let op0_limb_19_col59 = memory_id_to_big_value_tmp_7e965_11.get_m31(19);
                 *row[59] = op0_limb_19_col59;
-                let op0_limb_20_col60 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(20);
+                let op0_limb_20_col60 = memory_id_to_big_value_tmp_7e965_11.get_m31(20);
                 *row[60] = op0_limb_20_col60;
-                let op0_limb_21_col61 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(21);
+                let op0_limb_21_col61 = memory_id_to_big_value_tmp_7e965_11.get_m31(21);
                 *row[61] = op0_limb_21_col61;
-                let op0_limb_22_col62 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(22);
+                let op0_limb_22_col62 = memory_id_to_big_value_tmp_7e965_11.get_m31(22);
                 *row[62] = op0_limb_22_col62;
-                let op0_limb_23_col63 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(23);
+                let op0_limb_23_col63 = memory_id_to_big_value_tmp_7e965_11.get_m31(23);
                 *row[63] = op0_limb_23_col63;
-                let op0_limb_24_col64 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(24);
+                let op0_limb_24_col64 = memory_id_to_big_value_tmp_7e965_11.get_m31(24);
                 *row[64] = op0_limb_24_col64;
-                let op0_limb_25_col65 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(25);
+                let op0_limb_25_col65 = memory_id_to_big_value_tmp_7e965_11.get_m31(25);
                 *row[65] = op0_limb_25_col65;
-                let op0_limb_26_col66 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(26);
+                let op0_limb_26_col66 = memory_id_to_big_value_tmp_7e965_11.get_m31(26);
                 *row[66] = op0_limb_26_col66;
-                let op0_limb_27_col67 = memory_id_to_big_value_tmp_f0ae3_11.get_m31(27);
+                let op0_limb_27_col67 = memory_id_to_big_value_tmp_7e965_11.get_m31(27);
                 *row[67] = op0_limb_27_col67;
                 for (i, &input) in op0_id_col39.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[1] = input;
@@ -508,71 +514,71 @@ fn write_trace_simd(
 
                 // Read Positive Num Bits 252.
 
-                let memory_address_to_id_value_tmp_f0ae3_12 =
+                let memory_address_to_id_value_tmp_7e965_12 =
                     memory_address_to_id_state.deduce_output(((input_pc_col0) + (M31_1)));
-                let memory_id_to_big_value_tmp_f0ae3_13 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_f0ae3_12);
-                let op1_id_col68 = memory_address_to_id_value_tmp_f0ae3_12;
+                let memory_id_to_big_value_tmp_7e965_13 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_7e965_12);
+                let op1_id_col68 = memory_address_to_id_value_tmp_7e965_12;
                 *row[68] = op1_id_col68;
                 for (i, &input) in ((input_pc_col0) + (M31_1)).unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_address_to_id_inputs[2] = input;
                 }
                 *lookup_data.memory_address_to_id_2 = [((input_pc_col0) + (M31_1)), op1_id_col68];
-                let op1_limb_0_col69 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(0);
+                let op1_limb_0_col69 = memory_id_to_big_value_tmp_7e965_13.get_m31(0);
                 *row[69] = op1_limb_0_col69;
-                let op1_limb_1_col70 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(1);
+                let op1_limb_1_col70 = memory_id_to_big_value_tmp_7e965_13.get_m31(1);
                 *row[70] = op1_limb_1_col70;
-                let op1_limb_2_col71 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(2);
+                let op1_limb_2_col71 = memory_id_to_big_value_tmp_7e965_13.get_m31(2);
                 *row[71] = op1_limb_2_col71;
-                let op1_limb_3_col72 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(3);
+                let op1_limb_3_col72 = memory_id_to_big_value_tmp_7e965_13.get_m31(3);
                 *row[72] = op1_limb_3_col72;
-                let op1_limb_4_col73 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(4);
+                let op1_limb_4_col73 = memory_id_to_big_value_tmp_7e965_13.get_m31(4);
                 *row[73] = op1_limb_4_col73;
-                let op1_limb_5_col74 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(5);
+                let op1_limb_5_col74 = memory_id_to_big_value_tmp_7e965_13.get_m31(5);
                 *row[74] = op1_limb_5_col74;
-                let op1_limb_6_col75 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(6);
+                let op1_limb_6_col75 = memory_id_to_big_value_tmp_7e965_13.get_m31(6);
                 *row[75] = op1_limb_6_col75;
-                let op1_limb_7_col76 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(7);
+                let op1_limb_7_col76 = memory_id_to_big_value_tmp_7e965_13.get_m31(7);
                 *row[76] = op1_limb_7_col76;
-                let op1_limb_8_col77 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(8);
+                let op1_limb_8_col77 = memory_id_to_big_value_tmp_7e965_13.get_m31(8);
                 *row[77] = op1_limb_8_col77;
-                let op1_limb_9_col78 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(9);
+                let op1_limb_9_col78 = memory_id_to_big_value_tmp_7e965_13.get_m31(9);
                 *row[78] = op1_limb_9_col78;
-                let op1_limb_10_col79 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(10);
+                let op1_limb_10_col79 = memory_id_to_big_value_tmp_7e965_13.get_m31(10);
                 *row[79] = op1_limb_10_col79;
-                let op1_limb_11_col80 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(11);
+                let op1_limb_11_col80 = memory_id_to_big_value_tmp_7e965_13.get_m31(11);
                 *row[80] = op1_limb_11_col80;
-                let op1_limb_12_col81 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(12);
+                let op1_limb_12_col81 = memory_id_to_big_value_tmp_7e965_13.get_m31(12);
                 *row[81] = op1_limb_12_col81;
-                let op1_limb_13_col82 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(13);
+                let op1_limb_13_col82 = memory_id_to_big_value_tmp_7e965_13.get_m31(13);
                 *row[82] = op1_limb_13_col82;
-                let op1_limb_14_col83 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(14);
+                let op1_limb_14_col83 = memory_id_to_big_value_tmp_7e965_13.get_m31(14);
                 *row[83] = op1_limb_14_col83;
-                let op1_limb_15_col84 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(15);
+                let op1_limb_15_col84 = memory_id_to_big_value_tmp_7e965_13.get_m31(15);
                 *row[84] = op1_limb_15_col84;
-                let op1_limb_16_col85 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(16);
+                let op1_limb_16_col85 = memory_id_to_big_value_tmp_7e965_13.get_m31(16);
                 *row[85] = op1_limb_16_col85;
-                let op1_limb_17_col86 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(17);
+                let op1_limb_17_col86 = memory_id_to_big_value_tmp_7e965_13.get_m31(17);
                 *row[86] = op1_limb_17_col86;
-                let op1_limb_18_col87 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(18);
+                let op1_limb_18_col87 = memory_id_to_big_value_tmp_7e965_13.get_m31(18);
                 *row[87] = op1_limb_18_col87;
-                let op1_limb_19_col88 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(19);
+                let op1_limb_19_col88 = memory_id_to_big_value_tmp_7e965_13.get_m31(19);
                 *row[88] = op1_limb_19_col88;
-                let op1_limb_20_col89 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(20);
+                let op1_limb_20_col89 = memory_id_to_big_value_tmp_7e965_13.get_m31(20);
                 *row[89] = op1_limb_20_col89;
-                let op1_limb_21_col90 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(21);
+                let op1_limb_21_col90 = memory_id_to_big_value_tmp_7e965_13.get_m31(21);
                 *row[90] = op1_limb_21_col90;
-                let op1_limb_22_col91 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(22);
+                let op1_limb_22_col91 = memory_id_to_big_value_tmp_7e965_13.get_m31(22);
                 *row[91] = op1_limb_22_col91;
-                let op1_limb_23_col92 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(23);
+                let op1_limb_23_col92 = memory_id_to_big_value_tmp_7e965_13.get_m31(23);
                 *row[92] = op1_limb_23_col92;
-                let op1_limb_24_col93 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(24);
+                let op1_limb_24_col93 = memory_id_to_big_value_tmp_7e965_13.get_m31(24);
                 *row[93] = op1_limb_24_col93;
-                let op1_limb_25_col94 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(25);
+                let op1_limb_25_col94 = memory_id_to_big_value_tmp_7e965_13.get_m31(25);
                 *row[94] = op1_limb_25_col94;
-                let op1_limb_26_col95 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(26);
+                let op1_limb_26_col95 = memory_id_to_big_value_tmp_7e965_13.get_m31(26);
                 *row[95] = op1_limb_26_col95;
-                let op1_limb_27_col96 = memory_id_to_big_value_tmp_f0ae3_13.get_m31(27);
+                let op1_limb_27_col96 = memory_id_to_big_value_tmp_7e965_13.get_m31(27);
                 *row[96] = op1_limb_27_col96;
                 for (i, &input) in op1_id_col68.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[2] = input;
@@ -611,11 +617,11 @@ fn write_trace_simd(
 
                 // Verify Add 252.
 
-                let sub_p_bit_tmp_f0ae3_14 = ((UInt16_1)
+                let sub_p_bit_tmp_7e965_14 = ((UInt16_1)
                     & (((PackedUInt16::from_m31(op0_limb_0_col40))
                         ^ (PackedUInt16::from_m31(op1_limb_0_col69)))
                         ^ (PackedUInt16::from_m31(dst_limb_0_col11))));
-                let sub_p_bit_col97 = sub_p_bit_tmp_f0ae3_14.as_m31();
+                let sub_p_bit_col97 = sub_p_bit_tmp_7e965_14.as_m31();
                 *row[97] = sub_p_bit_col97;
 
                 *lookup_data.opcodes_0 = [input_pc_col0, input_ap_col1, input_fp_col2];
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/component.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small/component.rs
similarity index 99%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/component.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small/component.rs
index 44b4d9bf..bbfdf739 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/component.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small/component.rs
@@ -4,6 +4,7 @@ use num_traits::{One, Zero};
 use serde::{Deserialize, Serialize};
 use stwo_cairo_serialize::CairoSerialize;
 use stwo_prover::constraint_framework::logup::{LogupAtRow, LogupSums, LookupElements};
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::{
     EvalAtRow, FrameworkComponent, FrameworkEval, RelationEntry,
 };
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/mod.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small/mod.rs
similarity index 100%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/mod.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small/mod.rs
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/prover.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small/prover.rs
similarity index 84%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/prover.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small/prover.rs
index a1ace6a2..636245ba 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_f/prover.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small/prover.rs
@@ -7,10 +7,13 @@ use itertools::{chain, zip_eq, Itertools};
 use num_traits::{One, Zero};
 use prover_types::cpu::*;
 use prover_types::simd::*;
-use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
+use rayon::iter::{
+    IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator, ParallelIterator,
+};
 use stwo_air_utils::trace::component_trace::ComponentTrace;
 use stwo_air_utils_derive::{IterMut, ParIterMut, Uninitialized};
 use stwo_prover::constraint_framework::logup::LogupTraceGenerator;
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::Relation;
 use stwo_prover::core::air::Component;
 use stwo_prover::core::backend::simd::column::BaseColumn;
@@ -21,6 +24,7 @@ use stwo_prover::core::backend::simd::SimdBackend;
 use stwo_prover::core::backend::{BackendForChannel, Col, Column};
 use stwo_prover::core::channel::{Channel, MerkleChannel};
 use stwo_prover::core::fields::m31::M31;
+use stwo_prover::core::fields::FieldExpOps;
 use stwo_prover::core::pcs::TreeBuilder;
 use stwo_prover::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use stwo_prover::core::poly::BitReversedOrder;
@@ -66,6 +70,7 @@ impl ClaimGenerator {
 
         let packed_inputs = pack_values(&self.inputs);
         let (trace, mut sub_components_inputs, lookup_data) = write_trace_simd(
+            n_rows,
             packed_inputs,
             memory_address_to_id_state,
             memory_id_to_big_state,
@@ -104,8 +109,8 @@ impl ClaimGenerator {
         )
     }
 
-    pub fn add_inputs(&mut self, inputs: &[InputType]) {
-        self.inputs.extend(inputs);
+    pub fn add_inputs(&self, _inputs: &[InputType]) {
+        unimplemented!("Implement manually");
     }
 }
 
@@ -121,6 +126,7 @@ pub struct SubComponentInputs {
 #[allow(clippy::double_parens)]
 #[allow(non_snake_case)]
 fn write_trace_simd(
+    n_rows: usize,
     inputs: Vec<PackedInputType>,
     memory_address_to_id_state: &memory_address_to_id::ClaimGenerator,
     memory_id_to_big_state: &memory_id_to_big::ClaimGenerator,
@@ -161,111 +167,111 @@ fn write_trace_simd(
 
     trace
         .par_iter_mut()
-        .zip(inputs.par_iter())
+        .enumerate()
+        .zip(inputs.into_par_iter())
         .zip(lookup_data.par_iter_mut())
         .zip(sub_components_inputs.par_iter_mut().chunks(N_LANES))
         .for_each(
             |(
-                ((row, add_opcode_is_small_t_is_imm_f_input), lookup_data),
+                (((row_index, row), add_opcode_small_input), lookup_data),
                 mut sub_components_inputs,
             )| {
-                let input_tmp_6202e_0 = add_opcode_is_small_t_is_imm_f_input;
-                let input_pc_col0 = input_tmp_6202e_0.pc;
+                let input_tmp_8d553_0 = add_opcode_small_input;
+                let input_pc_col0 = input_tmp_8d553_0.pc;
                 *row[0] = input_pc_col0;
-                let input_ap_col1 = input_tmp_6202e_0.ap;
+                let input_ap_col1 = input_tmp_8d553_0.ap;
                 *row[1] = input_ap_col1;
-                let input_fp_col2 = input_tmp_6202e_0.fp;
+                let input_fp_col2 = input_tmp_8d553_0.fp;
                 *row[2] = input_fp_col2;
 
                 // Decode Instruction.
 
-                let memory_address_to_id_value_tmp_6202e_1 =
+                let memory_address_to_id_value_tmp_8d553_1 =
                     memory_address_to_id_state.deduce_output(input_pc_col0);
-                let memory_id_to_big_value_tmp_6202e_2 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_6202e_1);
-                let offset0_tmp_6202e_3 =
-                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(0)))
+                let memory_id_to_big_value_tmp_8d553_2 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_8d553_1);
+                let offset0_tmp_8d553_3 =
+                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(0)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(1),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(1),
                         )) & (UInt16_127))
                             << (UInt16_9)));
-                let offset0_col3 = offset0_tmp_6202e_3.as_m31();
+                let offset0_col3 = offset0_tmp_8d553_3.as_m31();
                 *row[3] = offset0_col3;
-                let offset1_tmp_6202e_4 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(1)))
+                let offset1_tmp_8d553_4 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(1)))
                         >> (UInt16_7))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(2),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(2),
                         )) << (UInt16_2)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(3),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(3),
                         )) & (UInt16_31))
                             << (UInt16_11)));
-                let offset1_col4 = offset1_tmp_6202e_4.as_m31();
+                let offset1_col4 = offset1_tmp_8d553_4.as_m31();
                 *row[4] = offset1_col4;
-                let offset2_tmp_6202e_5 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(3)))
+                let offset2_tmp_8d553_5 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(3)))
                         >> (UInt16_5))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(4),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(4),
                         )) << (UInt16_4)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(5),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(5),
                         )) & (UInt16_7))
                             << (UInt16_13)));
-                let offset2_col5 = offset2_tmp_6202e_5.as_m31();
+                let offset2_col5 = offset2_tmp_8d553_5.as_m31();
                 *row[5] = offset2_col5;
-                let dst_base_fp_tmp_6202e_6 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(5)))
+                let dst_base_fp_tmp_8d553_6 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(6),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_0))
                         & (UInt16_1));
-                let dst_base_fp_col6 = dst_base_fp_tmp_6202e_6.as_m31();
+                let dst_base_fp_col6 = dst_base_fp_tmp_8d553_6.as_m31();
                 *row[6] = dst_base_fp_col6;
-                let op0_base_fp_tmp_6202e_7 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(5)))
+                let op0_base_fp_tmp_8d553_7 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(6),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_1))
                         & (UInt16_1));
-                let op0_base_fp_col7 = op0_base_fp_tmp_6202e_7.as_m31();
+                let op0_base_fp_col7 = op0_base_fp_tmp_8d553_7.as_m31();
                 *row[7] = op0_base_fp_col7;
-                let op1_base_fp_tmp_6202e_8 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(5)))
+                let op1_base_fp_tmp_8d553_8 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(6),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_3))
                         & (UInt16_1));
-                let op1_base_fp_col8 = op1_base_fp_tmp_6202e_8.as_m31();
+                let op1_base_fp_col8 = op1_base_fp_tmp_8d553_8.as_m31();
                 *row[8] = op1_base_fp_col8;
-                let op1_base_ap_tmp_6202e_9 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(5)))
+                let op1_base_ap_tmp_8d553_9 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(6),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_4))
                         & (UInt16_1));
-                let op1_base_ap_col9 = op1_base_ap_tmp_6202e_9.as_m31();
+                let op1_base_ap_col9 = op1_base_ap_tmp_8d553_9.as_m31();
                 *row[9] = op1_base_ap_col9;
-                let ap_update_add_1_tmp_6202e_10 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_6202e_2.get_m31(5)))
+                let ap_update_add_1_tmp_8d553_10 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_8d553_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_6202e_2.get_m31(6),
+                            memory_id_to_big_value_tmp_8d553_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_11))
                         & (UInt16_1));
-                let ap_update_add_1_col10 = ap_update_add_1_tmp_6202e_10.as_m31();
+                let ap_update_add_1_col10 = ap_update_add_1_tmp_8d553_10.as_m31();
                 *row[10] = ap_update_add_1_col10;
-
                 for (i, &input) in (
                     input_pc_col0,
                     [offset0_col3, offset1_col4, offset2_col5],
@@ -327,11 +333,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_6202e_11 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_8d553_11 = memory_address_to_id_state
                     .deduce_output(((mem_dst_base_col11) + ((offset0_col3) - (M31_32768))));
-                let memory_id_to_big_value_tmp_6202e_12 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_6202e_11);
-                let dst_id_col14 = memory_address_to_id_value_tmp_6202e_11;
+                let memory_id_to_big_value_tmp_8d553_12 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_8d553_11);
+                let dst_id_col14 = memory_address_to_id_value_tmp_8d553_11;
                 *row[14] = dst_id_col14;
                 for (i, &input) in ((mem_dst_base_col11) + ((offset0_col3) - (M31_32768)))
                     .unpack()
@@ -347,19 +353,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_6202e_13 = memory_id_to_big_value_tmp_6202e_12.get_m31(27).eq(M31_256);
-                let msb_col15 = msb_tmp_6202e_13.as_m31();
+                let msb_tmp_8d553_13 = memory_id_to_big_value_tmp_8d553_12.get_m31(27).eq(M31_256);
+                let msb_col15 = msb_tmp_8d553_13.as_m31();
                 *row[15] = msb_col15;
-                let mid_limbs_set_tmp_6202e_14 =
-                    memory_id_to_big_value_tmp_6202e_12.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col16 = mid_limbs_set_tmp_6202e_14.as_m31();
+                let mid_limbs_set_tmp_8d553_14 =
+                    memory_id_to_big_value_tmp_8d553_12.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col16 = mid_limbs_set_tmp_8d553_14.as_m31();
                 *row[16] = mid_limbs_set_col16;
 
-                let dst_limb_0_col17 = memory_id_to_big_value_tmp_6202e_12.get_m31(0);
+                let dst_limb_0_col17 = memory_id_to_big_value_tmp_8d553_12.get_m31(0);
                 *row[17] = dst_limb_0_col17;
-                let dst_limb_1_col18 = memory_id_to_big_value_tmp_6202e_12.get_m31(1);
+                let dst_limb_1_col18 = memory_id_to_big_value_tmp_8d553_12.get_m31(1);
                 *row[18] = dst_limb_1_col18;
-                let dst_limb_2_col19 = memory_id_to_big_value_tmp_6202e_12.get_m31(2);
+                let dst_limb_2_col19 = memory_id_to_big_value_tmp_8d553_12.get_m31(2);
                 *row[19] = dst_limb_2_col19;
                 for (i, &input) in dst_id_col14.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[0] = input;
@@ -398,11 +404,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_6202e_15 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_8d553_15 = memory_address_to_id_state
                     .deduce_output(((mem0_base_col12) + ((offset1_col4) - (M31_32768))));
-                let memory_id_to_big_value_tmp_6202e_16 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_6202e_15);
-                let op0_id_col20 = memory_address_to_id_value_tmp_6202e_15;
+                let memory_id_to_big_value_tmp_8d553_16 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_8d553_15);
+                let op0_id_col20 = memory_address_to_id_value_tmp_8d553_15;
                 *row[20] = op0_id_col20;
                 for (i, &input) in ((mem0_base_col12) + ((offset1_col4) - (M31_32768)))
                     .unpack()
@@ -418,19 +424,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_6202e_17 = memory_id_to_big_value_tmp_6202e_16.get_m31(27).eq(M31_256);
-                let msb_col21 = msb_tmp_6202e_17.as_m31();
+                let msb_tmp_8d553_17 = memory_id_to_big_value_tmp_8d553_16.get_m31(27).eq(M31_256);
+                let msb_col21 = msb_tmp_8d553_17.as_m31();
                 *row[21] = msb_col21;
-                let mid_limbs_set_tmp_6202e_18 =
-                    memory_id_to_big_value_tmp_6202e_16.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col22 = mid_limbs_set_tmp_6202e_18.as_m31();
+                let mid_limbs_set_tmp_8d553_18 =
+                    memory_id_to_big_value_tmp_8d553_16.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col22 = mid_limbs_set_tmp_8d553_18.as_m31();
                 *row[22] = mid_limbs_set_col22;
 
-                let op0_limb_0_col23 = memory_id_to_big_value_tmp_6202e_16.get_m31(0);
+                let op0_limb_0_col23 = memory_id_to_big_value_tmp_8d553_16.get_m31(0);
                 *row[23] = op0_limb_0_col23;
-                let op0_limb_1_col24 = memory_id_to_big_value_tmp_6202e_16.get_m31(1);
+                let op0_limb_1_col24 = memory_id_to_big_value_tmp_8d553_16.get_m31(1);
                 *row[24] = op0_limb_1_col24;
-                let op0_limb_2_col25 = memory_id_to_big_value_tmp_6202e_16.get_m31(2);
+                let op0_limb_2_col25 = memory_id_to_big_value_tmp_8d553_16.get_m31(2);
                 *row[25] = op0_limb_2_col25;
                 for (i, &input) in op0_id_col20.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[1] = input;
@@ -469,11 +475,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_6202e_19 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_8d553_19 = memory_address_to_id_state
                     .deduce_output(((mem1_base_col13) + ((offset2_col5) - (M31_32768))));
-                let memory_id_to_big_value_tmp_6202e_20 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_6202e_19);
-                let op1_id_col26 = memory_address_to_id_value_tmp_6202e_19;
+                let memory_id_to_big_value_tmp_8d553_20 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_8d553_19);
+                let op1_id_col26 = memory_address_to_id_value_tmp_8d553_19;
                 *row[26] = op1_id_col26;
                 for (i, &input) in ((mem1_base_col13) + ((offset2_col5) - (M31_32768)))
                     .unpack()
@@ -489,19 +495,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_6202e_21 = memory_id_to_big_value_tmp_6202e_20.get_m31(27).eq(M31_256);
-                let msb_col27 = msb_tmp_6202e_21.as_m31();
+                let msb_tmp_8d553_21 = memory_id_to_big_value_tmp_8d553_20.get_m31(27).eq(M31_256);
+                let msb_col27 = msb_tmp_8d553_21.as_m31();
                 *row[27] = msb_col27;
-                let mid_limbs_set_tmp_6202e_22 =
-                    memory_id_to_big_value_tmp_6202e_20.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col28 = mid_limbs_set_tmp_6202e_22.as_m31();
+                let mid_limbs_set_tmp_8d553_22 =
+                    memory_id_to_big_value_tmp_8d553_20.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col28 = mid_limbs_set_tmp_8d553_22.as_m31();
                 *row[28] = mid_limbs_set_col28;
 
-                let op1_limb_0_col29 = memory_id_to_big_value_tmp_6202e_20.get_m31(0);
+                let op1_limb_0_col29 = memory_id_to_big_value_tmp_8d553_20.get_m31(0);
                 *row[29] = op1_limb_0_col29;
-                let op1_limb_1_col30 = memory_id_to_big_value_tmp_6202e_20.get_m31(1);
+                let op1_limb_1_col30 = memory_id_to_big_value_tmp_8d553_20.get_m31(1);
                 *row[30] = op1_limb_1_col30;
-                let op1_limb_2_col31 = memory_id_to_big_value_tmp_6202e_20.get_m31(2);
+                let op1_limb_2_col31 = memory_id_to_big_value_tmp_8d553_20.get_m31(2);
                 *row[31] = op1_limb_2_col31;
                 for (i, &input) in op1_id_col26.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[2] = input;
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/component.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/component.rs
similarity index 99%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/component.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/component.rs
index 84c945ac..77a5e9dd 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/component.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/component.rs
@@ -4,6 +4,7 @@ use num_traits::{One, Zero};
 use serde::{Deserialize, Serialize};
 use stwo_cairo_serialize::CairoSerialize;
 use stwo_prover::constraint_framework::logup::{LogupAtRow, LogupSums, LookupElements};
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::{
     EvalAtRow, FrameworkComponent, FrameworkEval, RelationEntry,
 };
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/mod.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/mod.rs
similarity index 100%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/mod.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/mod.rs
diff --git a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/prover.rs b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/prover.rs
similarity index 85%
rename from stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/prover.rs
rename to stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/prover.rs
index a392c6c6..5d0409e0 100644
--- a/stwo_cairo_prover/crates/prover/src/components/add_opcode_is_small_t_is_imm_t/prover.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/add_opcode_small_imm/prover.rs
@@ -7,10 +7,13 @@ use itertools::{chain, zip_eq, Itertools};
 use num_traits::{One, Zero};
 use prover_types::cpu::*;
 use prover_types::simd::*;
-use rayon::iter::{IndexedParallelIterator, IntoParallelRefIterator, ParallelIterator};
+use rayon::iter::{
+    IndexedParallelIterator, IntoParallelIterator, IntoParallelRefIterator, ParallelIterator,
+};
 use stwo_air_utils::trace::component_trace::ComponentTrace;
 use stwo_air_utils_derive::{IterMut, ParIterMut, Uninitialized};
 use stwo_prover::constraint_framework::logup::LogupTraceGenerator;
+use stwo_prover::constraint_framework::preprocessed_columns::PreprocessedColumn;
 use stwo_prover::constraint_framework::Relation;
 use stwo_prover::core::air::Component;
 use stwo_prover::core::backend::simd::column::BaseColumn;
@@ -21,6 +24,7 @@ use stwo_prover::core::backend::simd::SimdBackend;
 use stwo_prover::core::backend::{BackendForChannel, Col, Column};
 use stwo_prover::core::channel::{Channel, MerkleChannel};
 use stwo_prover::core::fields::m31::M31;
+use stwo_prover::core::fields::FieldExpOps;
 use stwo_prover::core::pcs::TreeBuilder;
 use stwo_prover::core::poly::circle::{CanonicCoset, CircleEvaluation};
 use stwo_prover::core::poly::BitReversedOrder;
@@ -66,6 +70,7 @@ impl ClaimGenerator {
 
         let packed_inputs = pack_values(&self.inputs);
         let (trace, mut sub_components_inputs, lookup_data) = write_trace_simd(
+            n_rows,
             packed_inputs,
             memory_address_to_id_state,
             memory_id_to_big_state,
@@ -104,8 +109,8 @@ impl ClaimGenerator {
         )
     }
 
-    pub fn add_inputs(&mut self, inputs: &[InputType]) {
-        self.inputs.extend(inputs);
+    pub fn add_inputs(&self, _inputs: &[InputType]) {
+        unimplemented!("Implement manually");
     }
 }
 
@@ -121,6 +126,7 @@ pub struct SubComponentInputs {
 #[allow(clippy::double_parens)]
 #[allow(non_snake_case)]
 fn write_trace_simd(
+    n_rows: usize,
     inputs: Vec<PackedInputType>,
     memory_address_to_id_state: &memory_address_to_id::ClaimGenerator,
     memory_id_to_big_state: &memory_id_to_big::ClaimGenerator,
@@ -160,79 +166,79 @@ fn write_trace_simd(
 
     trace
         .par_iter_mut()
-        .zip(inputs.par_iter())
+        .enumerate()
+        .zip(inputs.into_par_iter())
         .zip(lookup_data.par_iter_mut())
         .zip(sub_components_inputs.par_iter_mut().chunks(N_LANES))
         .for_each(
             |(
-                ((row, add_opcode_is_small_t_is_imm_t_input), lookup_data),
+                (((row_index, row), add_opcode_small_imm_input), lookup_data),
                 mut sub_components_inputs,
             )| {
-                let input_tmp_c5e3c_0 = add_opcode_is_small_t_is_imm_t_input;
-                let input_pc_col0 = input_tmp_c5e3c_0.pc;
+                let input_tmp_49e92_0 = add_opcode_small_imm_input;
+                let input_pc_col0 = input_tmp_49e92_0.pc;
                 *row[0] = input_pc_col0;
-                let input_ap_col1 = input_tmp_c5e3c_0.ap;
+                let input_ap_col1 = input_tmp_49e92_0.ap;
                 *row[1] = input_ap_col1;
-                let input_fp_col2 = input_tmp_c5e3c_0.fp;
+                let input_fp_col2 = input_tmp_49e92_0.fp;
                 *row[2] = input_fp_col2;
 
                 // Decode Instruction.
 
-                let memory_address_to_id_value_tmp_c5e3c_1 =
+                let memory_address_to_id_value_tmp_49e92_1 =
                     memory_address_to_id_state.deduce_output(input_pc_col0);
-                let memory_id_to_big_value_tmp_c5e3c_2 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_c5e3c_1);
-                let offset0_tmp_c5e3c_3 =
-                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_c5e3c_2.get_m31(0)))
+                let memory_id_to_big_value_tmp_49e92_2 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_49e92_1);
+                let offset0_tmp_49e92_3 =
+                    ((PackedUInt16::from_m31(memory_id_to_big_value_tmp_49e92_2.get_m31(0)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(1),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(1),
                         )) & (UInt16_127))
                             << (UInt16_9)));
-                let offset0_col3 = offset0_tmp_c5e3c_3.as_m31();
+                let offset0_col3 = offset0_tmp_49e92_3.as_m31();
                 *row[3] = offset0_col3;
-                let offset1_tmp_c5e3c_4 =
-                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_c5e3c_2.get_m31(1)))
+                let offset1_tmp_49e92_4 =
+                    ((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_49e92_2.get_m31(1)))
                         >> (UInt16_7))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(2),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(2),
                         )) << (UInt16_2)))
                         + (((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(3),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(3),
                         )) & (UInt16_31))
                             << (UInt16_11)));
-                let offset1_col4 = offset1_tmp_c5e3c_4.as_m31();
+                let offset1_col4 = offset1_tmp_49e92_4.as_m31();
                 *row[4] = offset1_col4;
-                let dst_base_fp_tmp_c5e3c_5 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_c5e3c_2.get_m31(5)))
+                let dst_base_fp_tmp_49e92_5 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_49e92_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(6),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_0))
                         & (UInt16_1));
-                let dst_base_fp_col5 = dst_base_fp_tmp_c5e3c_5.as_m31();
+                let dst_base_fp_col5 = dst_base_fp_tmp_49e92_5.as_m31();
                 *row[5] = dst_base_fp_col5;
-                let op0_base_fp_tmp_c5e3c_6 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_c5e3c_2.get_m31(5)))
+                let op0_base_fp_tmp_49e92_6 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_49e92_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(6),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_1))
                         & (UInt16_1));
-                let op0_base_fp_col6 = op0_base_fp_tmp_c5e3c_6.as_m31();
+                let op0_base_fp_col6 = op0_base_fp_tmp_49e92_6.as_m31();
                 *row[6] = op0_base_fp_col6;
-                let ap_update_add_1_tmp_c5e3c_7 =
-                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_c5e3c_2.get_m31(5)))
+                let ap_update_add_1_tmp_49e92_7 =
+                    (((((PackedUInt16::from_m31(memory_id_to_big_value_tmp_49e92_2.get_m31(5)))
                         >> (UInt16_3))
                         + ((PackedUInt16::from_m31(
-                            memory_id_to_big_value_tmp_c5e3c_2.get_m31(6),
+                            memory_id_to_big_value_tmp_49e92_2.get_m31(6),
                         )) << (UInt16_6)))
                         >> (UInt16_11))
                         & (UInt16_1));
-                let ap_update_add_1_col7 = ap_update_add_1_tmp_c5e3c_7.as_m31();
+                let ap_update_add_1_col7 = ap_update_add_1_tmp_49e92_7.as_m31();
                 *row[7] = ap_update_add_1_col7;
-
                 for (i, &input) in (
                     input_pc_col0,
                     [offset0_col3, offset1_col4, M31_32769],
@@ -291,11 +297,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_c5e3c_8 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_49e92_8 = memory_address_to_id_state
                     .deduce_output(((mem_dst_base_col8) + ((offset0_col3) - (M31_32768))));
-                let memory_id_to_big_value_tmp_c5e3c_9 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_c5e3c_8);
-                let dst_id_col10 = memory_address_to_id_value_tmp_c5e3c_8;
+                let memory_id_to_big_value_tmp_49e92_9 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_49e92_8);
+                let dst_id_col10 = memory_address_to_id_value_tmp_49e92_8;
                 *row[10] = dst_id_col10;
                 for (i, &input) in ((mem_dst_base_col8) + ((offset0_col3) - (M31_32768)))
                     .unpack()
@@ -311,19 +317,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_c5e3c_10 = memory_id_to_big_value_tmp_c5e3c_9.get_m31(27).eq(M31_256);
-                let msb_col11 = msb_tmp_c5e3c_10.as_m31();
+                let msb_tmp_49e92_10 = memory_id_to_big_value_tmp_49e92_9.get_m31(27).eq(M31_256);
+                let msb_col11 = msb_tmp_49e92_10.as_m31();
                 *row[11] = msb_col11;
-                let mid_limbs_set_tmp_c5e3c_11 =
-                    memory_id_to_big_value_tmp_c5e3c_9.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col12 = mid_limbs_set_tmp_c5e3c_11.as_m31();
+                let mid_limbs_set_tmp_49e92_11 =
+                    memory_id_to_big_value_tmp_49e92_9.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col12 = mid_limbs_set_tmp_49e92_11.as_m31();
                 *row[12] = mid_limbs_set_col12;
 
-                let dst_limb_0_col13 = memory_id_to_big_value_tmp_c5e3c_9.get_m31(0);
+                let dst_limb_0_col13 = memory_id_to_big_value_tmp_49e92_9.get_m31(0);
                 *row[13] = dst_limb_0_col13;
-                let dst_limb_1_col14 = memory_id_to_big_value_tmp_c5e3c_9.get_m31(1);
+                let dst_limb_1_col14 = memory_id_to_big_value_tmp_49e92_9.get_m31(1);
                 *row[14] = dst_limb_1_col14;
-                let dst_limb_2_col15 = memory_id_to_big_value_tmp_c5e3c_9.get_m31(2);
+                let dst_limb_2_col15 = memory_id_to_big_value_tmp_49e92_9.get_m31(2);
                 *row[15] = dst_limb_2_col15;
                 for (i, &input) in dst_id_col10.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[0] = input;
@@ -362,11 +368,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_c5e3c_12 = memory_address_to_id_state
+                let memory_address_to_id_value_tmp_49e92_12 = memory_address_to_id_state
                     .deduce_output(((mem0_base_col9) + ((offset1_col4) - (M31_32768))));
-                let memory_id_to_big_value_tmp_c5e3c_13 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_c5e3c_12);
-                let op0_id_col16 = memory_address_to_id_value_tmp_c5e3c_12;
+                let memory_id_to_big_value_tmp_49e92_13 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_49e92_12);
+                let op0_id_col16 = memory_address_to_id_value_tmp_49e92_12;
                 *row[16] = op0_id_col16;
                 for (i, &input) in ((mem0_base_col9) + ((offset1_col4) - (M31_32768)))
                     .unpack()
@@ -382,19 +388,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_c5e3c_14 = memory_id_to_big_value_tmp_c5e3c_13.get_m31(27).eq(M31_256);
-                let msb_col17 = msb_tmp_c5e3c_14.as_m31();
+                let msb_tmp_49e92_14 = memory_id_to_big_value_tmp_49e92_13.get_m31(27).eq(M31_256);
+                let msb_col17 = msb_tmp_49e92_14.as_m31();
                 *row[17] = msb_col17;
-                let mid_limbs_set_tmp_c5e3c_15 =
-                    memory_id_to_big_value_tmp_c5e3c_13.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col18 = mid_limbs_set_tmp_c5e3c_15.as_m31();
+                let mid_limbs_set_tmp_49e92_15 =
+                    memory_id_to_big_value_tmp_49e92_13.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col18 = mid_limbs_set_tmp_49e92_15.as_m31();
                 *row[18] = mid_limbs_set_col18;
 
-                let op0_limb_0_col19 = memory_id_to_big_value_tmp_c5e3c_13.get_m31(0);
+                let op0_limb_0_col19 = memory_id_to_big_value_tmp_49e92_13.get_m31(0);
                 *row[19] = op0_limb_0_col19;
-                let op0_limb_1_col20 = memory_id_to_big_value_tmp_c5e3c_13.get_m31(1);
+                let op0_limb_1_col20 = memory_id_to_big_value_tmp_49e92_13.get_m31(1);
                 *row[20] = op0_limb_1_col20;
-                let op0_limb_2_col21 = memory_id_to_big_value_tmp_c5e3c_13.get_m31(2);
+                let op0_limb_2_col21 = memory_id_to_big_value_tmp_49e92_13.get_m31(2);
                 *row[21] = op0_limb_2_col21;
                 for (i, &input) in op0_id_col16.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[1] = input;
@@ -433,11 +439,11 @@ fn write_trace_simd(
 
                 // Read Small.
 
-                let memory_address_to_id_value_tmp_c5e3c_16 =
+                let memory_address_to_id_value_tmp_49e92_16 =
                     memory_address_to_id_state.deduce_output(((input_pc_col0) + (M31_1)));
-                let memory_id_to_big_value_tmp_c5e3c_17 =
-                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_c5e3c_16);
-                let op1_id_col22 = memory_address_to_id_value_tmp_c5e3c_16;
+                let memory_id_to_big_value_tmp_49e92_17 =
+                    memory_id_to_big_state.deduce_output(memory_address_to_id_value_tmp_49e92_16);
+                let op1_id_col22 = memory_address_to_id_value_tmp_49e92_16;
                 *row[22] = op1_id_col22;
                 for (i, &input) in ((input_pc_col0) + (M31_1)).unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_address_to_id_inputs[2] = input;
@@ -446,19 +452,19 @@ fn write_trace_simd(
 
                 // Cond Decode Small Sign.
 
-                let msb_tmp_c5e3c_18 = memory_id_to_big_value_tmp_c5e3c_17.get_m31(27).eq(M31_256);
-                let msb_col23 = msb_tmp_c5e3c_18.as_m31();
+                let msb_tmp_49e92_18 = memory_id_to_big_value_tmp_49e92_17.get_m31(27).eq(M31_256);
+                let msb_col23 = msb_tmp_49e92_18.as_m31();
                 *row[23] = msb_col23;
-                let mid_limbs_set_tmp_c5e3c_19 =
-                    memory_id_to_big_value_tmp_c5e3c_17.get_m31(20).eq(M31_511);
-                let mid_limbs_set_col24 = mid_limbs_set_tmp_c5e3c_19.as_m31();
+                let mid_limbs_set_tmp_49e92_19 =
+                    memory_id_to_big_value_tmp_49e92_17.get_m31(20).eq(M31_511);
+                let mid_limbs_set_col24 = mid_limbs_set_tmp_49e92_19.as_m31();
                 *row[24] = mid_limbs_set_col24;
 
-                let op1_limb_0_col25 = memory_id_to_big_value_tmp_c5e3c_17.get_m31(0);
+                let op1_limb_0_col25 = memory_id_to_big_value_tmp_49e92_17.get_m31(0);
                 *row[25] = op1_limb_0_col25;
-                let op1_limb_1_col26 = memory_id_to_big_value_tmp_c5e3c_17.get_m31(1);
+                let op1_limb_1_col26 = memory_id_to_big_value_tmp_49e92_17.get_m31(1);
                 *row[26] = op1_limb_1_col26;
-                let op1_limb_2_col27 = memory_id_to_big_value_tmp_c5e3c_17.get_m31(2);
+                let op1_limb_2_col27 = memory_id_to_big_value_tmp_49e92_17.get_m31(2);
                 *row[27] = op1_limb_2_col27;
                 for (i, &input) in op1_id_col22.unpack().iter().enumerate() {
                     *sub_components_inputs[i].memory_id_to_big_inputs[2] = input;
diff --git a/stwo_cairo_prover/crates/prover/src/components/mod.rs b/stwo_cairo_prover/crates/prover/src/components/mod.rs
index be5e7770..951bd318 100644
--- a/stwo_cairo_prover/crates/prover/src/components/mod.rs
+++ b/stwo_cairo_prover/crates/prover/src/components/mod.rs
@@ -1,10 +1,10 @@
 pub mod add_ap_opcode;
 pub mod add_ap_opcode_imm;
 pub mod add_ap_opcode_op_1_base_fp;
-pub mod add_opcode_is_small_f_is_imm_f;
-pub mod add_opcode_is_small_f_is_imm_t;
-pub mod add_opcode_is_small_t_is_imm_f;
-pub mod add_opcode_is_small_t_is_imm_t;
+pub mod add_opcode;
+pub mod add_opcode_imm;
+pub mod add_opcode_small;
+pub mod add_opcode_small_imm;
 pub mod assert_eq_opcode_is_double_deref_f_is_imm_f;
 pub mod assert_eq_opcode_is_double_deref_f_is_imm_t;
 pub mod assert_eq_opcode_is_double_deref_t_is_imm_f;
diff --git a/stwo_cairo_prover/crates/prover/src/input/state_transitions.rs b/stwo_cairo_prover/crates/prover/src/input/state_transitions.rs
index 2a018794..34b7d294 100644
--- a/stwo_cairo_prover/crates/prover/src/input/state_transitions.rs
+++ b/stwo_cairo_prover/crates/prover/src/input/state_transitions.rs
@@ -26,10 +26,10 @@ pub struct CasmStatesByOpcode {
     pub add_ap_opcode: Vec<CasmState>,
     pub add_ap_opcode_imm: Vec<CasmState>,
     pub add_ap_opcode_op_1_base_fp: Vec<CasmState>,
-    pub add_opcode_is_small_t_is_imm_t: Vec<CasmState>,
-    pub add_opcode_is_small_f_is_imm_f: Vec<CasmState>,
-    pub add_opcode_is_small_t_is_imm_f: Vec<CasmState>,
-    pub add_opcode_is_small_f_is_imm_t: Vec<CasmState>,
+    pub add_opcode_small_imm: Vec<CasmState>,
+    pub add_opcode: Vec<CasmState>,
+    pub add_opcode_small: Vec<CasmState>,
+    pub add_opcode_imm: Vec<CasmState>,
     pub assert_eq_opcode_is_double_deref_f_is_imm_f: Vec<CasmState>,
     pub assert_eq_opcode_is_double_deref_t_is_imm_f: Vec<CasmState>,
     pub assert_eq_opcode_is_double_deref_f_is_imm_t: Vec<CasmState>,
@@ -61,22 +61,10 @@ impl CasmStatesByOpcode {
                 "add_ap_opcode_op_1_base_fp",
                 self.add_ap_opcode_op_1_base_fp.len(),
             ),
-            (
-                "add_opcode_is_small_t_is_imm_t",
-                self.add_opcode_is_small_t_is_imm_t.len(),
-            ),
-            (
-                "add_opcode_is_small_f_is_imm_f",
-                self.add_opcode_is_small_f_is_imm_f.len(),
-            ),
-            (
-                "add_opcode_is_small_t_is_imm_f",
-                self.add_opcode_is_small_t_is_imm_f.len(),
-            ),
-            (
-                "add_opcode_is_small_f_is_imm_t",
-                self.add_opcode_is_small_f_is_imm_t.len(),
-            ),
+            ("add_opcode_small_imm", self.add_opcode_small_imm.len()),
+            ("add_opcode", self.add_opcode.len()),
+            ("add_opcode_small", self.add_opcode_small.len()),
+            ("add_opcode_imm", self.add_opcode_imm.len()),
             (
                 "assert_eq_opcode_is_double_deref_f_is_imm_f",
                 self.assert_eq_opcode_is_double_deref_f_is_imm_f.len(),
@@ -616,25 +604,17 @@ impl StateTransitions {
                     // [ap/fp + offset0] = [ap/fp + offset1] + Imm.
                     assert!(!op_1_base_fp && !op_1_base_ap && offset2 == 1);
                     if is_small_add(dst, op0, op_1) {
-                        self.casm_states_by_opcode
-                            .add_opcode_is_small_t_is_imm_t
-                            .push(state);
+                        self.casm_states_by_opcode.add_opcode_small_imm.push(state);
                     } else {
-                        self.casm_states_by_opcode
-                            .add_opcode_is_small_f_is_imm_t
-                            .push(state);
+                        self.casm_states_by_opcode.add_opcode_imm.push(state);
                     };
                 } else {
                     // [ap/fp + offset0] = [ap/fp + offset1] + [ap/fp + offset2].
                     assert!((op_1_base_fp || op_1_base_ap));
                     if is_small_add(dst, op0, op_1) {
-                        self.casm_states_by_opcode
-                            .add_opcode_is_small_t_is_imm_f
-                            .push(state);
+                        self.casm_states_by_opcode.add_opcode_small.push(state);
                     } else {
-                        self.casm_states_by_opcode
-                            .add_opcode_is_small_f_is_imm_f
-                            .push(state);
+                        self.casm_states_by_opcode.add_opcode.push(state);
                     }
                 }
             }
@@ -710,10 +690,7 @@ mod mappings_tests {
                 .len(),
             1
         );
-        assert_eq!(
-            casm_states_by_opcode.add_opcode_is_small_t_is_imm_t.len(),
-            1
-        );
+        assert_eq!(casm_states_by_opcode.add_opcode_small_imm.len(), 1);
     }
 
     #[test]
@@ -910,20 +887,14 @@ mod mappings_tests {
 
         let input = input_from_plain_casm(instructions, false);
         let casm_states_by_opcode = input.state_transitions.casm_states_by_opcode;
-        assert_eq!(
-            casm_states_by_opcode.add_opcode_is_small_t_is_imm_f.len(),
-            1
-        );
+        assert_eq!(casm_states_by_opcode.add_opcode_small.len(), 1);
         assert_eq!(
             casm_states_by_opcode
                 .assert_eq_opcode_is_double_deref_f_is_imm_t
                 .len(),
             2
         );
-        assert_eq!(
-            casm_states_by_opcode.add_opcode_is_small_t_is_imm_t.len(),
-            1
-        );
+        assert_eq!(casm_states_by_opcode.add_opcode_small_imm.len(), 1);
     }
 
     #[test]
@@ -941,14 +912,8 @@ mod mappings_tests {
 
         let input = input_from_plain_casm(instructions, false);
         let casm_states_by_opcode = input.state_transitions.casm_states_by_opcode;
-        assert_eq!(
-            casm_states_by_opcode.add_opcode_is_small_f_is_imm_f.len(),
-            1
-        );
-        assert_eq!(
-            casm_states_by_opcode.add_opcode_is_small_f_is_imm_t.len(),
-            1
-        );
+        assert_eq!(casm_states_by_opcode.add_opcode.len(), 1);
+        assert_eq!(casm_states_by_opcode.add_opcode_imm.len(), 1);
     }
 
     // TODO(Ohad): un-ignore.
diff --git a/stwo_cairo_prover/crates/prover/src/input/vm_import/mod.rs b/stwo_cairo_prover/crates/prover/src/input/vm_import/mod.rs
index 1f63d892..da713583 100644
--- a/stwo_cairo_prover/crates/prover/src/input/vm_import/mod.rs
+++ b/stwo_cairo_prover/crates/prover/src/input/vm_import/mod.rs
@@ -198,10 +198,10 @@ pub mod tests {
         assert_eq!(components.add_ap_opcode.len(), 0);
         assert_eq!(components.add_ap_opcode_imm.len(), 36895);
         assert_eq!(components.add_ap_opcode_op_1_base_fp.len(), 33);
-        assert_eq!(components.add_opcode_is_small_t_is_imm_t.len(), 84732);
-        assert_eq!(components.add_opcode_is_small_f_is_imm_f.len(), 189425);
-        assert_eq!(components.add_opcode_is_small_t_is_imm_f.len(), 36623);
-        assert_eq!(components.add_opcode_is_small_f_is_imm_t.len(), 22089);
+        assert_eq!(components.add_opcode_small_imm.len(), 84732);
+        assert_eq!(components.add_opcode.len(), 189425);
+        assert_eq!(components.add_opcode_small.len(), 36623);
+        assert_eq!(components.add_opcode_imm.len(), 22089);
         assert_eq!(
             components.assert_eq_opcode_is_double_deref_f_is_imm_f.len(),
             233432
@@ -282,10 +282,10 @@ pub mod tests {
         assert_eq!(components.add_ap_opcode.len(), 0);
         assert_eq!(components.add_ap_opcode_imm.len(), 2);
         assert_eq!(components.add_ap_opcode_op_1_base_fp.len(), 1);
-        assert_eq!(components.add_opcode_is_small_t_is_imm_t.len(), 500);
-        assert_eq!(components.add_opcode_is_small_f_is_imm_f.len(), 0);
-        assert_eq!(components.add_opcode_is_small_t_is_imm_f.len(), 0);
-        assert_eq!(components.add_opcode_is_small_f_is_imm_t.len(), 450);
+        assert_eq!(components.add_opcode_small_imm.len(), 500);
+        assert_eq!(components.add_opcode.len(), 0);
+        assert_eq!(components.add_opcode_small.len(), 0);
+        assert_eq!(components.add_opcode_imm.len(), 450);
         assert_eq!(
             components.assert_eq_opcode_is_double_deref_f_is_imm_f.len(),
             55