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A comment on From scratch: reverse-mode automatic differentiation (in Python). Parent comment

Re:From scratch: reverse-mode automatic differentiation (in ... by JadeNB on Sunday June 14, 2020 @07:30PM (#23522365)
> I don't think it makes sense to the same degree. Simple compositions of elementary functions, e.g. exp(x^2), do not have indefinite integrals.

While it's clear what you meant, it's mathematically important to note that functions like yours, and, indeed, all continuous functions, definitely do have indefinite integrals—that of `exp(x^2)` even has a name (https://mathworld.wolfram.com/Erfi.html); those integrals just aren't elementary, in the same technical sense in which you are using the word (https://en.wikipedia.org/wiki/Elementary_function).

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Re:From scratch: reverse-mode automatic differentiation (in ... by ohsonice on Monday June 15, 2020 @01:35AM (#23524124)
Your first link is not working for me on mobile. Thanks for the clarification though.

Exp(x^2) is a finite composition of a polynomial and an exponential function so from what you posted, it does fall into the Wikipedia definition of elementary function.

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Re:From scratch: reverse-mode automatic differentiation (in ... by brewmarche on Monday June 15, 2020 @04:35AM (#23525171)
The first link of your parent should've been https://mathworld.wolfram.com/Erfi.html

They were arguing that the antiderivative F of f: x ↦ exp(x²) is not elementary, whereas f itself is elementary. But both F and f are well-defined functions, which means that f has an indefinite integral, it just happens to be not elementary.

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Re:From scratch: reverse-mode automatic differentiation (in ... by JadeNB on Monday June 15, 2020 @01:55PM (#23530579)
> The first link of your parent should've been https://mathworld.wolfram.com/Erfi.html

Sometimes Markdown eats following parentheses and sometimes it doesn't, and I've never figured out why. When I first viewed the post it showed me the parenthesis not being eaten, but then it did it anyway when I viewed it from the main page (too late for me to edit). Thanks for fixing it up!

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