Incorrect element type when nesting ForwardDiff inside ReverseDiff

[rdeits]

Cross-posted from https://discourse.julialang.org/t/nesting-forwarddiff-inside-reversediff/3684/3

The following (possibly ill-advised) nesting of ForwardDiff inside ReverseDiff fails:

f = (x, w) -> sum(x .* w)
g = (x, w) -> ForwardDiff.gradient(x -> f(x, w), x)
ReverseDiff.jacobian(w -> g(x, w), w)

MethodError: Cannot `convert` an object of type ForwardDiff.Dual{2,Float64} to an object of type Float64
This may have arisen from a call to the constructor Float64(...),
since type constructors fall back to convert methods.

 in increment_deriv! at /Users/rdeits/.julia/v0.5/ReverseDiff/src/derivatives/propagation.jl:34 [inlined]
 in broadcast_increment_deriv!(::ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}}, ::Array{Float64,1}, ::Array{ForwardDiff.Dual{2,Float64},1}, ::CartesianIndex{1}, ::CartesianIndex{1}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/derivatives/propagation.jl:142
 in special_reverse_exec!(::ReverseDiff.SpecialInstruction{Base.#.*,Tuple{Array{ForwardDiff.Dual{2,Float64},1},ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}}},ReverseDiff.TrackedArray{ForwardDiff.Dual{2,Float64},Float64,1,Array{ForwardDiff.Dual{2,Float64},1},Array{Float64,1}},Tuple{CartesianIndex{1},CartesianIndex{1}}}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/derivatives/elementwise.jl:473
 in reverse_exec!(::ReverseDiff.SpecialInstruction{Base.#.*,Tuple{Array{ForwardDiff.Dual{2,Float64},1},ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}}},ReverseDiff.TrackedArray{ForwardDiff.Dual{2,Float64},Float64,1,Array{ForwardDiff.Dual{2,Float64},1},Array{Float64,1}},Tuple{CartesianIndex{1},CartesianIndex{1}}}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/tape.jl:93
 in reverse_pass!(::Array{ReverseDiff.AbstractInstruction,1}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/tape.jl:87
 in seeded_reverse_pass!(::Array{Float64,2}, ::Array{ReverseDiff.TrackedReal{ForwardDiff.Dual{2,Float64},Float64,Void},1}, ::ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}}, ::ReverseDiff.JacobianTape{##137#138,ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}},Array{ReverseDiff.TrackedReal{ForwardDiff.Dual{2,Float64},Float64,Void},1}}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/utils.jl:51
 in seeded_reverse_pass! at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/tape.jl:47 [inlined]
 in jacobian!(::Array{Float64,2}, ::ReverseDiff.JacobianTape{##137#138,ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}},Array{ReverseDiff.TrackedReal{ForwardDiff.Dual{2,Float64},Float64,Void},1}}, ::Array{Float64,1}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/jacobians.jl:122
 in jacobian! at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/jacobians.jl:106 [inlined]
 in jacobian(::Function, ::Array{Float64,1}, ::ReverseDiff.JacobianConfig{ReverseDiff.TrackedArray{Float64,Float64,1,Array{Float64,1},Array{Float64,1}},Void}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/jacobians.jl:25
 in jacobian(::Function, ::Array{Float64,1}) at /Users/rdeits/.julia/v0.5/ReverseDiff/src/api/jacobians.jl:23