[AlotOfReading]

"precision" is an ambiguous term here. There's reproducibility (getting the same results every time), accuracy (getting as close as possible to same results computed with infinite precision), and the native format precision.

ffast-math is sacrificing both the first and the second for performance. Compilers usually sacrifice the first for the second by default with things like automation fma contraction. This isn't a necessary trade-off, it's just easier.

There's very few cases where you actually need accuracy down to the ULP though. No robot can do anything meaningful with femtometer+ precision, for example. Instead you choose a development balance between reproducibility (relatively easy) and accuracy (extremely hard). In robotics, that will usually swing a bit towards reproducibility. CAD would swing more towards accuracy.