From 019088400a5ea86caaa2eb0a0416fd832159f6f3 Mon Sep 17 00:00:00 2001
From: Oscar Dowson <o.dowson@gmail.com>
Date: Mon, 7 Sep 2026 11:19:37 +1200
Subject: [PATCH] [Nonlinear.SymbolicAD] fix derivative of atan

---
 src/Nonlinear/SymbolicAD/SymbolicAD.jl |  2 +-
 test/Nonlinear/test_SymbolicAD.jl      | 29 +++++++++++++++++++++++---
 2 files changed, 27 insertions(+), 4 deletions(-)

diff --git a/src/Nonlinear/SymbolicAD/SymbolicAD.jl b/src/Nonlinear/SymbolicAD/SymbolicAD.jl
index 97875bbceb..3c962eabf8 100644
--- a/src/Nonlinear/SymbolicAD/SymbolicAD.jl
+++ b/src/Nonlinear/SymbolicAD/SymbolicAD.jl
@@ -704,7 +704,7 @@ function derivative(f::MOI.ScalarNonlinearFunction, x::MOI.VariableIndex)
         return MOI.ScalarNonlinearFunction(
             :/,
             Any[
-                MOI.ScalarNonlinearFunction(:+, Any[u_dv_dx, v_du_dx]),
+                MOI.ScalarNonlinearFunction(:-, Any[v_du_dx, u_dv_dx]),
                 MOI.ScalarNonlinearFunction(:+, Any[u_2, v_2]),
             ],
         )
diff --git a/test/Nonlinear/test_SymbolicAD.jl b/test/Nonlinear/test_SymbolicAD.jl
index a123100d17..0d2046bcfb 100644
--- a/test/Nonlinear/test_SymbolicAD.jl
+++ b/test/Nonlinear/test_SymbolicAD.jl
@@ -7,10 +7,10 @@ module TestMathOptSymbolicAD
 
 using Test
 
+import ForwardDiff
 import MathOptInterface as MOI
 import MathOptInterface: Nonlinear
-
-const SymbolicAD = Nonlinear.SymbolicAD
+import MathOptInterface.Nonlinear: SymbolicAD
 
 function runtests()
     for name in names(@__MODULE__; all = true)
@@ -100,7 +100,7 @@ function test_derivative()
         # :atan
         op(:atan, x, sin_x)=>op(
             :/,
-            op(:+, op(:*, x, cos_x), sin_x),
+            op(:-, sin_x, op(:*, x, cos_x)),
             op(:+, op(:^, x, 2), op(:^, sin_x, 2)),
         ),
         # :min
@@ -785,6 +785,29 @@ function test_simplify_drops_ones()
     return
 end
 
+function test_atan_derivatives()
+    model = MOI.Utilities.Model{Float64}()
+    u, v = MOI.VariableIndex.(1:2)
+    f = MOI.ScalarNonlinearFunction(:atan, Any[u, v])
+    f_u = MOI.Nonlinear.SymbolicAD.derivative(f, u)
+    f_v = MOI.Nonlinear.SymbolicAD.derivative(f, v)
+    for x in -1.0:0.5:1.0, y in -1.0:0.5:1.0
+        if iszero(x) && iszero(y)
+            continue
+        end
+        point = Dict(u => x, v => y)
+        @test isapprox(
+            MOI.Utilities.eval_variables(xi -> point[xi], model, f_u),
+            ForwardDiff.derivative(a -> atan(a, y), x),
+        )
+        @test isapprox(
+            MOI.Utilities.eval_variables(xi -> point[xi], model, f_v),
+            ForwardDiff.derivative(b -> atan(x, b), y),
+        )
+    end
+    return
+end
+
 end  # module
 
 TestMathOptSymbolicAD.runtests()