[ogogmad]

I don't think this is a failure of Automatic Differentiation. It's a failure of assuming that the derivative of an approximation is equal to an approximation of the derivative. That's obviously nonsense, as the example f(x) = atan(10000 x)/10000, which is nearly 0, shows you. This was first pointed out here in this comment: https://news.ycombinator.com/item?id=45293066

[adgjlsfhk1]

the part that's really weird is that AD normally produces extremely accurate derivatives so the rare algorithms where it doesn't are very surprising at first.