diff --git a/docs/guide/OpenXLA_Support_on_GPU.md b/docs/guide/OpenXLA_Support_on_GPU.md
index 711c82923..4c0979c77 100644
--- a/docs/guide/OpenXLA_Support_on_GPU.md
+++ b/docs/guide/OpenXLA_Support_on_GPU.md
@@ -38,41 +38,64 @@ Then we can get the library with xla extension   **./bazel-bin/itex/libitex_xla_
 $ export PJRT_NAMES_AND_LIBRARY_PATHS='xpu:Your_itex_path/bazel-bin/itex/libitex_xla_extension.so'
 $ export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:Your_Python_site-packages/jaxlib # Some functions defined in xla_extension.so are needed by libitex_xla_extension.so
 
-$ export ONEDNN_VERBOSE=1 # Optional variable setting. Enable onednn verbose to check if it runs on GPU.
+$ export ITEX_VERBOSE=1 # Optional variable setting. It shows detailed optimization/compilation/execution info.
 ```
 * **Run the below jax python code.**
 ```python
+import jax
 import jax.numpy as jnp
-from jax import random
-key = random.PRNGKey(0)
-size = 3000
-x = random.normal(key, (size, size), dtype=jnp.float32)
-y = jnp.dot(x, x.T).block_until_ready()
-print(y)
+
+@jax.jit
+def lax_conv():
+  key = jax.random.PRNGKey(0)
+  lhs = jax.random.uniform(key, (2,1,9,9), jnp.float32)
+  rhs = jax.random.uniform(key, (1,1,4,4), jnp.float32)
+  side = jax.random.uniform(key, (1,1,1,1), jnp.float32)
+  out = jax.lax.conv_with_general_padding(lhs, rhs, (1,1), ((0,0),(0,0)), (1,1), (1,1))
+  out = jax.nn.relu(out)
+  out = jnp.multiply(out, side)
+  return out
+
+print(lax_conv())
 ```
 * **Reference result:**
 ```
-onednn_verbose,info,oneDNN v3.1.0 (commit xxxx)
-onednn_verbose,info,cpu,runtime:DPC++,nthr:1
-onednn_verbose,info,cpu,isa:Intel 64
-onednn_verbose,info,gpu,runtime:DPC++
-onednn_verbose,info,cpu,engine,0,backend:OpenCL,name:Intel(R) Xeon(R) Gold 6346 CPU @ 3.10GHz,driver_version:2022.15.12,binary_kernels:disabled
-onednn_verbose,info,gpu,engine,0,backend:Level Zero,name:Intel(R) Data Center GPU Flex Series 170 [0x56c0],driver_version:1.3.25018,binary_kernels:enabled
-onednn_verbose,info,gpu,engine,1,backend:Level Zero,name:Intel(R) Data Center GPU Flex Series 170 [0x56c0],driver_version:1.3.25018,binary_kernels:enabled
-onednn_verbose,info,experimental features are enabled
-onednn_verbose,info,use batch_normalization stats one pass is enabled
-onednn_verbose,info,experimental functionality for sparse domain is enabled
-onednn_verbose,info,prim_template:operation,engine,primitive,implementation,prop_kind,memory_descriptors,attributes,auxiliary,problem_desc,exec_time
-onednn_verbose,exec,gpu:0,matmul,jit:gemm:any,undef,src_f32::blocked:abc:f0 wei_f32::blocked:abc:f0 dst_f32::blocked:abc:f0,attr-scratchpad:user ,,1x3000x3000:1x3000x3000:1x3000x3000,xxxxxxxx
-[[2938.1716   17.388428  36.508217  ...   32.315964  51.31904    -34.432026]
- [17.388428   3031.179   41.194576  ...   47.248768  58.077858   -13.371612]
- [36.508217   41.194576  3000.4697  ...   8.10901    -42.501842  26.495111]
- ...
- [32.315964   47.248768  8.10901    ...   2916.339   34.38107    39.404522]
- [51.31904    58.077858  -42.501842 ...   34.38107   3032.2844   63.69183 ]
- [-34.432026  -13.371612 26.495111  ...   39.404522  63.69183    3033.4866  ]]
+I itex/core/devices/gpu/itex_gpu_runtime.cc:129] Selected platform: Intel(R) Level-Zero
+I itex/core/compiler/xla/service/service.cc:176] XLA service 0x56060b5ae740 initialized for platform sycl (this does not guarantee that XLA will be used). Devices:
+I itex/core/compiler/xla/service/service.cc:184]   StreamExecutor device (0): <undefined>, <undefined>
+I itex/core/compiler/xla/service/service.cc:184]   StreamExecutor device (1): <undefined>, <undefined>
+[[[[2.0449753 2.093208  2.1844783 1.9769732 1.5857391 1.6942389]
+   [1.9218378 2.2862523 2.1549542 1.8367321 1.3978379 1.3860377]
+   [1.9456574 2.062028  2.0365305 1.901286  1.5255247 1.1421617]
+   [2.0621    2.2933435 2.1257985 2.1095486 1.5584903 1.1229166]
+   [1.7746235 2.2446113 1.7870374 1.8216239 1.557919  0.9832508]
+   [2.0887792 2.5433128 1.9749291 2.2580051 1.6096935 1.264905 ]]]
+
+
+ [[[2.175818  2.0094342 2.005763  1.6559253 1.3896458 1.4036925]
+   [2.1342552 1.8239582 1.6091168 1.434404  1.671778  1.7397764]
+   [1.930626  1.659667  1.6508744 1.3305787 1.4061482 2.0829628]
+   [2.130649  1.6637266 1.594426  1.2636002 1.7168686 1.8598001]
+   [1.9009514 1.7938274 1.4870623 1.6193901 1.5297288 2.0247464]
+   [2.0905268 1.7598859 1.9362347 1.9513799 1.9403584 2.1483061]]]]
+```
+If `ITEX_VERBOSE=1` is set, the log looks like this:
+```
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:301] Running HLO pass pipeline on module jit_lax_conv: optimization
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:181]   HLO pass fusion
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:181]   HLO pass fusion_merger
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:181]   HLO pass multi_output_fusion
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:181]   HLO pass gpu-conv-rewriter
+I itex/core/compiler/xla/service/hlo_pass_pipeline.cc:181]   HLO pass onednn-fused-convolution-rewriter
+
+I itex/core/compiler/xla/service/gpu/gpu_compiler.cc:1221] Build kernel via LLVM kernel compilation.
+I itex/core/compiler/xla/service/gpu/spir_compiler.cc:255] CompileTargetBinary - CompileToSpir time: 11 us (cumulative: 99.2 ms, max: 74.9 ms, #called: 8)
+
+I itex/core/compiler/xla/pjrt/pjrt_stream_executor_client.cc:2201] Executing computation jit_lax_conv; num_replicas=1 num_partitions=1 num_addressable_devices=1
+I itex/core/compiler/xla/pjrt/pjrt_stream_executor_client.cc:2268] Replicated execution complete.
+I itex/core/compiler/xla/pjrt/pjrt_stream_executor_client.cc:1208] PjRtStreamExecutorBuffer::Delete
+I itex/core/compiler/xla/pjrt/pjrt_stream_executor_client.cc:1299] PjRtStreamExecutorBuffer::ToLiteral
 ```
-Check it runs on GPU but not CPU. For example, "onednn_verbose,exec,**gpu**:0,matmul, ..." means "matmul" runs on GPU.
 
 **4. More JAX examples.**    
 Get examples from [https://github.com/google/jax](https://github.com/google/jax/tree/jaxlib-v0.4.4/examples) to run.
diff --git a/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.cc b/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.cc
index 661116339..9ee5ae2f3 100644
--- a/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.cc
+++ b/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.cc
@@ -179,7 +179,7 @@ StatusOr<bool> FuseConvertToFloat(HloComputation* comp) {
     if (!Match(instr, pattern)) {
       continue;
     }
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseConvertToFloat: ", conv->ToString());
         })) {
       continue;
@@ -229,7 +229,7 @@ StatusOr<bool> FuseConvAlpha(HloComputation* comp) {
     if (config.conv_result_scale() != 1) {
       continue;
     }
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseConvAlpha: ", conv->ToString());
         })) {
       continue;
@@ -327,7 +327,7 @@ StatusOr<bool> FuseBiasOrSideInput(HloComputation* comp) {
       continue;
     }
 
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseBiasOrSideInput: ", conv->ToString());
         })) {
       continue;
@@ -401,7 +401,7 @@ StatusOr<bool> FuseSideInputAlpha(HloComputation* comp) {
                     }))))) {
       continue;
     }
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseSideInputAlpha: ", conv->ToString());
         })) {
       continue;
@@ -481,7 +481,7 @@ StatusOr<bool> FuseRelu(HloComputation* comp) {
       continue;
     }
 
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseRelu: ", conv->ToString());
         })) {
       continue;
@@ -524,7 +524,7 @@ StatusOr<bool> FuseConvertToF16(HloComputation* comp) {
               0, m::GetTupleElement(m::Op().WithPredicate(IsConvCustomCall))));
       continue;
     }
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseConvertToF16: ", conv->ToString());
         })) {
       continue;
@@ -609,7 +609,7 @@ StatusOr<bool> FuseConvertToS8(HloComputation* comp) {
     } else {
       continue;
     }
-    if (!ConsumeFuel("cudnn-fused-convolution-rewriter", [&] {
+    if (!ConsumeFuel("onednn-fused-convolution-rewriter", [&] {
           return absl::StrCat("FuseConvertToS8: ", conv->ToString());
         })) {
       continue;
diff --git a/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.h b/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.h
index 04411bbb3..7e112b40c 100644
--- a/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.h
+++ b/itex/core/compiler/xla/service/gpu/onednn_fused_conv_rewriter.h
@@ -97,7 +97,7 @@ namespace gpu {
 class CudnnFusedConvRewriter : public HloModulePass {
  public:
   absl::string_view name() const override {
-    return "cudnn-fused-convolution-rewriter";
+    return "onednn-fused-convolution-rewriter";
   }
 
   StatusOr<bool> Run(HloModule* module) override;