Fall back on AD?

[cscherrer]

This bit me today:

julia> with_logabsdet_jacobian(cbrt, 2.0)
NoLogAbsDetJacobian{typeof(cbrt), Float64}()

I could add a method for this, but there are so many other functions out there, maybe this could be automated?

This seems possible, since it's invertible:

julia> inverse(cbrt)
(::Base.Fix2{typeof(^), Int64}) (generic function with 1 method)

and AD-friendly:

julia> ForwardDiff.derivative(cbrt, 2.0)
0.2099868416491455

[oschulz]

maybe this could be automated

I don't think so (without heavy dependencies). But since inverse is already specialized for it we should specialize with_logabsdet_jacobian for it as well.