diff --git a/optimistix/_ad.py b/optimistix/_ad.py
index 38d6bcd..6b2f108 100644
--- a/optimistix/_ad.py
+++ b/optimistix/_ad.py
@@ -5,6 +5,7 @@
 import equinox as eqx
 import equinox.internal as eqxi
 import jax
+import jax.custom_derivatives
 import jax.numpy as jnp
 import jax.tree_util as jtu
 import lineax as lx
@@ -107,6 +108,11 @@ def _for_jvp(_diff):
     _, jvp_diff = jax.jvp(_for_jvp, (diff,), (t_inputs,))
 
     t_root = (-(lx.linear_solve(operator, jvp_diff, linear_solver).value ** ω)).ω
-    t_residual = tree_full_like(residual, 0)
+    if hasattr(jax.custom_derivatives, "zero_from_primal"):
+        t_residual = jax.custom_derivatives.zero_from_primal(  # pyright: ignore[reportGeneralTypeIssues]
+            residual, symbolic_zeros=True
+        )
+    else:
+        t_residual = tree_full_like(residual, 0)
 
     return (root, residual), (t_root, t_residual)
diff --git a/pyproject.toml b/pyproject.toml
index e22ee43..833ace3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [project]
 name = "optimistix"
-version = "0.0.8"
+version = "0.0.9"
 description = "Nonlinear optimisation in JAX and Equinox."
 readme = "README.md"
 requires-python ="~=3.9"