Update

docs/src/submodules/Nonlinear/SymbolicAD.md

@@ -185,7 +185,7 @@ julia> f = MOI.ScalarNonlinearFunction(:sin, Any[x])
 sin(MOI.VariableIndex(1))
 
 julia> MOI.Nonlinear.SymbolicAD.derivative(f, x)
-*(cos(MOI.VariableIndex(1)), (true))
+cos(MOI.VariableIndex(1)
 ```
 
 Note that the resultant expression can often be simplified. Thus, in most cases
@@ -196,14 +196,14 @@ using it in other places:
 julia> x = MOI.VariableIndex(1)
 MOI.VariableIndex(1)
 
-julia> f = MOI.ScalarNonlinearFunction(:sin, Any[x])
-sin(MOI.VariableIndex(1))
+julia> f = MOI.ScalarNonlinearFunction(:sin, Any[x + 1.0])
+sin(1.0 + 1.0 MOI.VariableIndex(1))
 
 julia> df_dx = MOI.Nonlinear.SymbolicAD.derivative(f, x)
-*(cos(MOI.VariableIndex(1)), (true))
+*(cos(1.0 + 1.0 MOI.VariableIndex(1)), 1.0)
 
 julia> MOI.Nonlinear.SymbolicAD.simplify!(df_dx)
-cos(MOI.VariableIndex(1))
+cos(1.0 + 1.0 MOI.VariableIndex(1))
 ```
 
 ## `gradient_and_hessian`

src/Nonlinear/SymbolicAD/SymbolicAD.jl

@@ -558,6 +558,14 @@ that the user would never write themselves.
 """
 const __DERIVATIVE__ = "__DERIVATIVE__"
 
+# This function helps simplify df_du * du_dx in the commonn case that `du_dx`
+# is `true` (when u = x), or `false` (when x ∉ u).
+function _univariate_chain_rule(df_du, du_dx)
+    return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+end
+
+_univariate_chain_rule(df_du, du_dx::Bool) = ifelse(du_dx, df_du, du_dx)
+
 function derivative(f::MOI.ScalarNonlinearFunction, x::MOI.VariableIndex)
     if length(f.args) == 1
         u = only(f.args)
@@ -571,28 +579,28 @@ function derivative(f::MOI.ScalarNonlinearFunction, x::MOI.VariableIndex)
                 :ifelse,
                 Any[MOI.ScalarNonlinearFunction(:>=, Any[u, 0]), 1, -1],
             )
-            return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+            return _univariate_chain_rule(df_du, du_dx)
         elseif f.head == :sign
             return false
         elseif f.head == :deg2rad
             df_du = deg2rad(1)
-            return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+            return _univariate_chain_rule(df_du, du_dx)
         elseif f.head == :rad2deg
             df_du = rad2deg(1)
-            return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+            return _univariate_chain_rule(df_du, du_dx)
         end
         for (key, df, _) in MOI.Nonlinear.SYMBOLIC_UNIVARIATE_EXPRESSIONS
             if key == f.head
                 # The chain rule: d(f(g(x))) / dx = f'(g(x)) * g'(x)
                 df_du = _replace_expression(copy(df), u)
-                return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+                return _univariate_chain_rule(df_du, du_dx)
             end
         end
         # Delay derivative until evaluation. This may result in a later
         # UnsupportedNonlinearOperator error, but we can't tell just yet.
         d_op = Symbol(__DERIVATIVE__ * "$(f.head)")
         df_du = MOI.ScalarNonlinearFunction(d_op, Any[u])
-        return MOI.ScalarNonlinearFunction(:*, Any[df_du, du_dx])
+        return _univariate_chain_rule(df_du, du_dx)
     end
     if f.head == :+
         # d/dx(+(args...)) = +(d/dx args)

test/Nonlinear/SymbolicAD.jl

@@ -134,6 +134,12 @@ function test_derivative()
     return
 end
 
+function test_derivative_univariate_simplification()
+    x = MOI.VariableIndex(1)
+    @test SymbolicAD.derivative(op(:sin, x), x) ≈ op(:cos, x)
+    return
+end
+
 function test_derivative_error()
     x = MOI.VariableIndex(1)
     f = MOI.ScalarNonlinearFunction(:foo, Any[x, x])