From e0bde4a08a5253c90d7e142b07724273908d008d Mon Sep 17 00:00:00 2001
From: Herman Sletmoen <hermansletmoen@gmail.com>
Date: Thu, 29 Aug 2024 11:46:55 +0200
Subject: [PATCH 1/3] Resolve isequal(Num, ForwardDiff.Dual) ambiguity

---
 ext/SymbolicsForwardDiffExt.jl | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/ext/SymbolicsForwardDiffExt.jl b/ext/SymbolicsForwardDiffExt.jl
index 480fc83f5..9882bec12 100644
--- a/ext/SymbolicsForwardDiffExt.jl
+++ b/ext/SymbolicsForwardDiffExt.jl
@@ -103,6 +103,25 @@ function binary_dual_definition(M, f, Ts)
     return expr
 end
 
+#####################
+# Generic Functions #
+#####################
+
+# Predicates #
+#------------#
+
+for pred in [:isequal, :(==)]
+    @eval begin
+        @define_binary_dual_op(
+            Base.$(pred),
+            $(pred)(value(x), value(y)) && $(pred)(partials(x), partials(y)),
+            $(pred)(value(x), y)        && iszero(partials(x)),
+            $(pred)(x, value(y))        && iszero(partials(y)),
+            $AMBIGUOUS_TYPES
+        )
+    end
+end
+
 ###################################
 # General Mathematical Operations #
 ###################################

From 3664e2091dd369c99dd7f4550cbe4d4744da4dd3 Mon Sep 17 00:00:00 2001
From: Herman Sletmoen <hermansletmoen@gmail.com>
Date: Thu, 29 Aug 2024 12:03:30 +0200
Subject: [PATCH 2/3] Test isequal(Num, ForwardDiff.Dual) ambiguity

---
 test/forwarddiff_symbolic_dual_ops.jl | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/test/forwarddiff_symbolic_dual_ops.jl b/test/forwarddiff_symbolic_dual_ops.jl
index 1b89c79e6..d5e3d3f47 100644
--- a/test/forwarddiff_symbolic_dual_ops.jl
+++ b/test/forwarddiff_symbolic_dual_ops.jl
@@ -107,3 +107,10 @@ for f ∈ (hypot, muladd)
 end
 
 # fma is not defined for Symbolics.Num
+
+# https://github.com/JuliaSymbolics/Symbolics.jl/issues/1246
+@testset "isequal type ambiguity" begin
+    @variables x
+    xfunc(xval) = isequal(x, xval) ? xval : xval
+    @test ForwardDiff.derivative(xfunc, 0.0) == 1.0
+end

From f0bcc47f9411b7d5aed72cd85db679b4557bc488 Mon Sep 17 00:00:00 2001
From: Herman Sletmoen <hermansletmoen@gmail.com>
Date: Thu, 29 Aug 2024 15:43:08 +0200
Subject: [PATCH 3/3] Improve test

---
 test/forwarddiff_symbolic_dual_ops.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/forwarddiff_symbolic_dual_ops.jl b/test/forwarddiff_symbolic_dual_ops.jl
index d5e3d3f47..e132f9a50 100644
--- a/test/forwarddiff_symbolic_dual_ops.jl
+++ b/test/forwarddiff_symbolic_dual_ops.jl
@@ -110,7 +110,7 @@ end
 
 # https://github.com/JuliaSymbolics/Symbolics.jl/issues/1246
 @testset "isequal type ambiguity" begin
-    @variables x
-    xfunc(xval) = isequal(x, xval) ? xval : xval
-    @test ForwardDiff.derivative(xfunc, 0.0) == 1.0
+    @variables z
+    y(x) = isequal(z, x) ? 0 : x
+    @test ForwardDiff.derivative(y, 0) == 1 # expect ∂(x)/∂x
 end