Kahan summation is an example (also described in the top level article) of one such “gotcha”. It involves adding a term that - if floats were algebraic in this

Kahan summation is an example (also described in the top level article) of one such “gotcha”. It involves adding a term that - if floats were algebraic in this sense - would always be zero, so ffast-math often deletes it, but this actually completely removes the accuracy improvement of the algorithm