Error differentiating through complex power due to isinteger

I have a weird case where a complex power is giving me an inexact error because the _cpow helper function determines my object to be an integer.

Truncated error message:

julia> ForwardDiff.gradient(test_func, ptest)
ERROR: InexactError: Int(Int64, Dual{ForwardDiff.Tag{typeof(test_func), Float64}}(1.0,-0.0,-0.8333333333333333,-0.0,-0.0,-0.17599538919114094))
Stacktrace:
  [1] Int64
    @ ~/.julia/packages/ForwardDiff/QdStj/src/dual.jl:364 [inlined]
  [2] convert(#unused#::Type{Int64}, x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_func), Float64}, Float64, 5})                                  
    @ Base ./number.jl:7
  [3] _cpow(z::Complex{ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_func), Float64}, Float64, 5}}, p::ForwardDiff.Dual{ForwardDiff.Tag{typeof(test_func), Float64}, Float64, 5})
    @ Base ./complex.jl:782
  [4] ^
    @ ./complex.jl:851 [inlined]
  [5] ^
    @ ./complex.jl:866 [inlined]

So given that

julia> typeof(test_func)
typeof(test_func) (singleton type of function test_func, subtype of Function)

It seems that we can get the following MWE:

julia> isinteger(Dual{ForwardDiff.Tag{Function, Float64}}(1.0,-0.0,-0.8333333333333333,-0.0,-0.0,-0.17599538919114094))
true

This is the associated culprit line in complex.jl that tries to do this conversion to Int (only the relevant part is shown):

# _cpow helper function to avoid method ambiguity with ^(::Complex,::Real)
function _cpow(z::Union{T,Complex{T}}, p::Union{T,Complex{T}}) where T
    z = float(z)
    p = float(p)
    Tf = float(T)
    if isreal(p)
        pᵣ = real(p)
        if isinteger(pᵣ) && abs(pᵣ) < typemax(Int32) 
            # |p| < typemax(Int32) serves two purposes: it prevents overflow
            # when converting p to Int, and it also turns out to be roughly
            # the crossover point for exp(p*log(z)) or similar to be faster.
            if iszero(pᵣ) # fix signs of imaginary part for z^0
                zer = flipsign(copysign(zero(Tf),pᵣ), imag(z))
                return Complex(one(Tf), zer)
            end
            ip = convert(Int, pᵣ) # <--- HERE!

Admittedly, I am not sure if the partials should be considered for determining if it's an integer or not.

Start by reproducing the supplied MWE with ForwardDiff.Dual values and read the _cpow implementation in Julia's complex.jl, especially the isinteger check and subsequent Int conversion. Determine the expected treatment of Dual partials and verify that complex-power differentiation completes without the reported InexactError.