AutoDiff of function inverse?

[roflmaostc]

Just as comment, there was a similar question in the past

Automatic inverse of a function?

I hear you, yes. subpieces of the algorithm might not be invertibles. But what if the global algorithm is, indeed, invertible ? I mean, f(a,b) = (a+b, exp(a+2b)) is invertible, and you could get more creative.