Perturbation Confusion II: The Tag Wars

@vtjnash was able to rewrite the classic perturbation confusion example into a form that thwarts ForwardDiff's tag generation:

julia> using ForwardDiff

julia> const D = ForwardDiff.derivative
derivative (generic function with 4 methods)

julia> struct Confuse
                whoami::Bool
                x
              end

julia> function (c::Confuse)(xy)
                if c.whoami
                  return xy * D(Confuse(false, xy), 1)
                else
                  return c.x + xy
                end
              end

julia> D(Confuse(true, 0), 1) # this should be 1
2

Essentially, since the function type is constant whether or not the function recursively differentiates itself, ForwardDiff generates the same tag for the nested call that it generates for the outer call.

So it seems that sufficiently unique tags cannot be generated from local type information alone...

Start by reproducing the Julia REPL example in the issue and trace how ForwardDiff generates tags for the outer and nested derivative calls. The work is done when this recursive case produces the expected derivative of 1 and the tag collision is covered by a regression test.