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diff --git a/test.slang b/test.slang
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+#ifndef __CUSTOM31_INC
+#define __CUSTOM31_INC
+
+[Differentiable]
+public float3 cart_to_cyl(uniform float3 xyz) {
+  float radius = length(xyz.xy);
+  float theta = atan2(xyz.y, xyz.x);
+  return float3(radius, theta, xyz.z);
+}
+
+public float3x3 cart_to_cyl_jacobian(uniform float3 xyz, uniform float3 n) {
+  DifferentialPair<float3> dp_x = diffPair(xyz, float3(1, 0, 0));
+  DifferentialPair<float3> dp_y = diffPair(xyz, float3(0, 1, 0));
+  DifferentialPair<float3> dp_z = diffPair(xyz, float3(0, 0, 1));
+
+  DifferentialPair<float3> dp_x_out = fwd_diff(cart_to_cyl)(dp_x);
+  DifferentialPair<float3> dp_y_out = fwd_diff(cart_to_cyl)(dp_y);
+  DifferentialPair<float3> dp_z_out = fwd_diff(cart_to_cyl)(dp_z);
+
+  return float3x3(dp_x_out.d, dp_y_out.d, dp_z_out.d);
+}
+
+#endif  // __CUSTOM31_INC
+