feat: derivative speed hack for no dependence on variable

src/ComposableExpression.jl

@@ -283,12 +283,17 @@ function _symbolic_derivative(
     tree::N, ctx::SymbolicDerivativeContext
 ) where {T,N<:AbstractExpressionNode{T}}
     # NOTE: We cannot mutate the tree here! Since we use it twice.
-    if tree.degree == 0
-        if !tree.constant && tree.feature == ctx.feature
-            return constructorof(N)(; val=one(T))
-        else
-            return constructorof(N)(; val=zero(T))
-        end
+
+    # Quick test to see if we have any dependence on the feature, so
+    # we can return 0 for the branch
+    any_dependence = any(tree) do node
+        node.degree == 0 && !node.constant && node.feature == ctx.feature
+    end
+
+    if !any_dependence
+        return constructorof(N)(; val=zero(T))
+    elseif tree.degree == 0
+        return constructorof(N)(; val=one(T))
     elseif tree.degree == 1
         # f(g(x)) => f'(g(x)) * g'(x)
         f_prime = constructorof(N)(; op=tree.op + ctx.nuna, l=tree.l)

test/test_composable_expression.jl

@@ -349,6 +349,15 @@ end
     @test D(cos(x1), 1)([1.0]) ≈ [-sin(1.0)]
     @test D(sin(x1) * cos(x2), 1)([1.0], [2.0]) ≈ [cos(1.0) * cos(2.0)]
     @test D(D(sin(x1) * cos(x2), 1), 2)([1.0], [2.0]) ≈ [cos(1.0) * -sin(2.0)]
+
+    # Printing should also be nice:
+    @test repr(D(x1 * x2, 1)) == "(∂₁*(x1, x2) * 1.0) + (∂₂*(x1, x2) * 0.0)"
+
+    # We also have special behavior when there is no dependence:
+    @test repr(D(sin(x2), 1)) == "0.0"
+    @test repr(D(x2 + sin(x2), 1)) == "0.0"
+    @test repr(D(x2 + sin(x2) - x1, 1)) ==
+        "(∂₁-(x2 + sin(x2), x1) * 0.0) + (∂₂-(x2 + sin(x2), x1) * 1.0)"
 end
 
 @testitem "Test template structure with derivatives" tags = [:part2] begin