By having knowledge baked into it about its properties (which it can validly do because the behaviour of the float_abs operation is specified by the language; it's not calling an arbitrary external function). The blog post sketches out one approach to this: as the optimizer is working on a tree of expressions, it has attached to the nodes extra information about the values in it (e.g. "this is a constant X" or "this value is definitely in the range A..B"); then as it simplifies the tree, it can say "abs of a value that's already definitely not negative is a no-op, don't do anything", in the same way it can say "multiplying X by 1 is a no-op".

The actual bug-fix linked to in the footnote does it in a slightly different way: it says "as I'm walking through optimizing my tree of expressions, if I see 'abs(abs(X))' then simplify the tree to just 'abs(X)'".

That fix has limited applicability. x * x is also a non-negative float. But abs(x * x) is not optimized. Or abs(abs(x)+1). GCC, for example, does know that.

The real fix felt more complicated when I drafted this. Seems like it isn't; I'll think about updating the post

Where'd you get that patch from? I can't find it in the blog post.

EDIT: Ah, other comment mentions article was edited.

That shouldn't mean that it doesn't return a NaN. Things are generally not optimized away because of NaNs. E.g. in GCC, abs(c) > -1.0 is not folded, unless building with -ffast-math