[LegionMammal978]

"Multiple times" doesn't have to mean "no modifications". Suppose the software is currently on version A. You think that changing it to a version B might make it more performant, so you implement and profile it. You find no difference, so you figure that your B implementation isn't good enough, and write a slight variation B', perhaps moving around some loops or function calls. If that makes no difference, you keep writing variations B'', B''', B'''', etc., until one of them finally comes out faster than version A. You finally declare that version B (when properly implemented) is better than version A, when you've really just tried a lot more samples.

[starspangled]

Well it does mean "no modifications" to the hypothesis, hypothesis being about performance of code A and B. Code B' would be a change.

It's just semantics, but the point is that the article wasn't saying the same thing OP was worried about. There's nothing wrong with testing B, B', B'', etc. until you find a significant performance improvement. You just wouldn't test B several times and take the last set of data when it looks good. Almost goes without saying really.

[LegionMammal978]

Sure, it may not be precise repetition, but my idea here is that none of B', B'', etc. are really different than B (they may even compile down to the exact same bytecode), they're just the same thing but written differently. And in fact, none of these are really faster than A, even if they're all "changes". But it's the same issue as any other form of p-hacking, where you keep trying more and more trivial B-variations until you eventually get the result that you're looking for, by random chance. (Cf. the example in xkcd 882, which does change the experimental protocol each time, but only trivially.)

There is, in fact, "something wrong" with this, which is what GP was pointing out. It's literally covered under "Playing with multiple comparisons" in TFA.

(Personally, to combat this, I've ignored the fancy p-values and resorted to the eyeball test of whether it very consistently produces a noticable speedup.)