https://gcc.godbolt.org/z/fGaP6roe9
I see the same behavior on clang 17 as well
I deal with a lot of floating point professionally day to day, and I use fast math all the time, since the tradeoff for higher performance and the relatively small loss of accuracy are acceptable. Maybe the biggest issue I run into is lack of denorms with CUDA fast-math, and it’s pretty rare for me to care about numbers smaller than 10^-38. Heck, I’d say I can tolerate 8 or 16 bits of mantissa most of the time, and fast-math floats are way more accurate than that. And we know a lot of neural network training these days can tolerate less than 8 bits of mantissa.
* It links in an object file that enables denormal flushing globally, so that it affects all libraries linked into your application, even if said library explicitly doesn't want fast-math. This is seriously one of the most user-hostile things a compiler can do.
* The results of your program will vary depending on the exact make of your compiler and other random attributes of your compile environment, which can wreak havoc if you have code that absolutely wants bit-identical results. This doesn't matter for everybody, but there are some domains where this can be a non-starter (e.g., multiplayer game code).
* Fast-math precludes you from being able to use NaN or infinities, and often even being able to defensively test for NaN or infinity. Sure, there are times where this is useful, but an option you might generally prefer to suggest for an uninformed programmer would rather be a "floating-point code can't overflow" option rather than "infinity doesn't exist and it's UB if it does exist".
* Fast-math can cause hard range guarantees to fail. Maybe you've got code that you can prove that, even with rounding error, the result will still be >= 0. With fast-math, the code might be adjusted so that the result is instead, say, -1e-10. And if you pass that to a function with a hard domain error at 0 (like sqrt), you now go from the result being 0 to the result being NaN. And see above about what happens when you get NaN.
Fast-math is a tradeoff, and if you're willing to except the tradeoff it offers, it's a fine option to use. But most programmers don't even know what the tradeoffs are, and the failure mode can be absolutely catastrophic. It's definitely an option that is in the "you must be this knowledgeable to use" camp.