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That's a fair point (and worth documenting as part of the library), but I'd be much more likely to implement pow(x, x) carefully than switch to a different language or compiler.

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I appreciate the library approach and I basically agree with you. If anything, I wanted to point out that a normal general language is so general that adding differentiation into it would be highly costly - just this feature would require that every loop and every conditional return be watched (relative to pow(x,x), an even more challenging example is the Newton's method implementation of a continuous function using a loop).

An alternative would be creating a general purpose language just for this feature - an interesting though rather specialized project.

I'm not certain, but I suspect you'll hit the halting problem if you tried to be completely general purpose.

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