diff --git a/AGENTS.md b/AGENTS.md
index e0d82d61..c393617f 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -5,3 +5,7 @@ Preserve the existing `GPUTsit5` PI-controller behavior. Alternative controllers
 # Differentiation validation
 
 Gradient tests must use the package and its loaded extensions without adding differentiation rules in test code. Keep CPU Enzyme coverage alongside CUDA coverage. Exercise all active problem fields when validating transfer rules, including times and captured function values; parameter-only losses cannot detect discarded sensitivities. Keep initialization regressions enabled across backends and fix their owning dependencies rather than gating the tests.
+
+# Kernel stepper inlining
+
+Keep `@inline` on the `step!` methods in `src/ensemblegpukernel/perform_step/`. Without it the mutable integrator escapes into a call and is heap-allocated in device code: on OpenCL the resulting `gpu_malloc` fails and the kernel exits without writing output, and on Julia 1.12 Enzyme returns an incorrect adaptive Float64 gradient (the primal is unchanged). Scope `@muladd` to arithmetic blocks rather than removing the inline annotation.
diff --git a/src/ensemblegpukernel/perform_step/gpu_tsit5_perform_step.jl b/src/ensemblegpukernel/perform_step/gpu_tsit5_perform_step.jl
index e0a67e63..c093d4f4 100644
--- a/src/ensemblegpukernel/perform_step/gpu_tsit5_perform_step.jl
+++ b/src/ensemblegpukernel/perform_step/gpu_tsit5_perform_step.jl
@@ -101,23 +101,27 @@ end
     while EEst > T(1.0)
         dt < T(1.0e-14) && error("dt<dtmin")
 
-        tmp = uprev + dt * a21 * k1
-        k2 = f(tmp, p, t + c1 * dt)
-        tmp = uprev + dt * (a31 * k1 + a32 * k2)
-        k3 = f(tmp, p, t + c2 * dt)
-        tmp = uprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)
-        k4 = f(tmp, p, t + c3 * dt)
-        tmp = uprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)
-        k5 = f(tmp, p, t + c4 * dt)
-        tmp = uprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)
-        k6 = f(tmp, p, t + dt)
-        u = uprev + dt * (a71 * k1 + a72 * k2 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)
-        k7 = f(u, p, t + dt)
-
-        tmp = dt * (
-            btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 +
-                btilde5 * k5 + btilde6 * k6 + btilde7 * k7
-        )
+        # Fuse only the stage and error-estimate arithmetic; the step-size
+        # controller and endpoint logic below keep unfused rounding.
+        @muladd begin
+            tmp = uprev + dt * a21 * k1
+            k2 = f(tmp, p, t + c1 * dt)
+            tmp = uprev + dt * (a31 * k1 + a32 * k2)
+            k3 = f(tmp, p, t + c2 * dt)
+            tmp = uprev + dt * (a41 * k1 + a42 * k2 + a43 * k3)
+            k4 = f(tmp, p, t + c3 * dt)
+            tmp = uprev + dt * (a51 * k1 + a52 * k2 + a53 * k3 + a54 * k4)
+            k5 = f(tmp, p, t + c4 * dt)
+            tmp = uprev + dt * (a61 * k1 + a62 * k2 + a63 * k3 + a64 * k4 + a65 * k5)
+            k6 = f(tmp, p, t + dt)
+            u = uprev + dt * (a71 * k1 + a72 * k2 + a73 * k3 + a74 * k4 + a75 * k5 + a76 * k6)
+            k7 = f(u, p, t + dt)
+
+            tmp = dt * (
+                btilde1 * k1 + btilde2 * k2 + btilde3 * k3 + btilde4 * k4 +
+                    btilde5 * k5 + btilde6 * k6 + btilde7 * k7
+            )
+        end
         tmp = tmp ./ (abstol .+ max.(abs.(uprev), abs.(u)) * reltol)
         EEst = DiffEqBase.ODE_DEFAULT_NORM(tmp, t)