On the one hand, the ambiguity of FMA is kind of annoying, but on the other, FMA is a godsend for writing accurate arithmatic. One reason for this, is that the error of `ab` is `fma(a, b, -ab)` which makes compensated algorithms much faster to write. Secondly, polynomial evaluations using horner's method converge to .5 ULP (units in last place) with FMA, but to 1.5 ULP without. This is incredibly useful since polynomial approximations are at the heart of pretty much everything else.

I think Julia takes an interesting approach here of never reordering floating point computations unless you explecitly give permission using @fastmath (which acts locally instead of globally like a --fast-math in C/C++). This makes it much easier to use ieee specific tricks and be confident that the compiler won't mess with you, while still making it easy to tell the compiler to do what it wants.