"Now that we understand differentiation, let’s move on to programming. So far, we’ve only considered mathematical functions, but we can easily translate our perspective to programs. For simplicity, we’ll only consider pure functions, i.e. functions whose output depends solely on
its parameters (no state)."
I think I've seen this notion that the constraint is pureness also in documentation of autodiff libraries, but this cannot be strong enough, right?
It easy enough to come up with functions that are nowhere differentiable. So my question is, what are the actual requirements a state of the art autodiff library has for the input function and why do people focus on the pureness aspect if that is probably the least of the problems.
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