Arithmetic operations are ambiguous when combining Num:s and ForwardDiff

[asterycs]

Hi!

Arithmetic operations appear to be ambiguous when combining Num:s with ForwardDiff. A minimal example is below (originally reported here):

using Symbolics
using ForwardDiff

@variables a, x

function f(x)
    a*x
end

ForwardDiff.derivative(f, x)

which yields the following error:

ERROR: MethodError: *(::Num, ::ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Num}, Num, 1}) is ambiguous.

Candidates:
  *(x::Real, y::ForwardDiff.Dual{Ty}) where Ty
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/dual.jl:145
  *(a::Num, b::Real)
    @ Symbolics ~/.julia/packages/SymbolicUtils/r1pzW/src/methods.jl:73
  *(a::Num, b::Number)
    @ Symbolics ~/.julia/packages/SymbolicUtils/r1pzW/src/methods.jl:75

Possible fix, define
  *(::Num, ::ForwardDiff.Dual{Ty}) where Ty

Stacktrace:
 [1] f(x::ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Num}, Num, 1})
   @ Main ./REPL[4]:2
 [2] derivative(f::typeof(f), x::Num)
   @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/derivative.jl:14
 [3] top-level scope
   @ REPL[5]:1

I'm trying to come up with a fix for this, but my understanding of Symbolics is still superficial. Would adding the (::Num, ::ForwardDiff.Dual{Ty}) methods to Symbolics similarly as here be a reasonable approach?

[ChrisRackauckas]

Yes. You'd have to copy the ForwardDiff DiffRules loop and add new methods for each operation.

[asterycs]

Closed by #1036