check for iszero(partials(x)) in pow (#592)

src/dual.jl

@@ -534,7 +534,7 @@ for f in (:(Base.:^), :(NaNMath.pow))
             begin
                 v = value(x)
                 expv = ($f)(v, y)
-                if y == zero(y)
+                if y == zero(y) || iszero(partials(x))
                     new_partials = zero(partials(x))
                 else
                     new_partials = partials(x) * y * ($f)(v, y - 1)

test/DualTest.jl

@@ -12,6 +12,7 @@ using DiffRules
 import Calculus
 
 struct TestTag end
+struct OuterTestTag end
 
 samerng() = MersenneTwister(1)
 
@@ -26,6 +27,8 @@ dual_isapprox(a::Dual{T,T1,T2}, b::Dual{T3,T4,T5}) where {T,T1,T2,T3,T4,T5} = er
 
 ForwardDiff.:≺(::Type{TestTag()}, ::Int) = true
 ForwardDiff.:≺(::Int, ::Type{TestTag()}) = false
+ForwardDiff.:≺(::Type{TestTag}, ::Type{OuterTestTag}) = true
+ForwardDiff.:≺(::Type{OuterTestTag}, ::Type{TestTag}) = false
 
 for N in (0,3), M in (0,4), V in (Int, Float32)
     println("  ...testing Dual{TestTag(),$V,$N} and Dual{TestTag(),Dual{TestTag(),$V,$M},$N}")
@@ -574,6 +577,9 @@ end
     @test pow(x3, 2) === x3^2 === x3 * x3
     @test pow(x2, 1) === x2^1 === x2
     @test pow(x1, 0) === x1^0 === Dual{:t1}(1.0, 0.0)
+    y = Dual{typeof(TestTag())}(1.0, 0.0, 1.0);
+    x = Dual{typeof(OuterTestTag())}(0*y, 0*y);
+    @test iszero(ForwardDiff.partials(ForwardDiff.partials(x^y)[1]))
 end
 
 @testset "Type min/max" begin