IEEE 754 defines an exact binary result for the addition of any two floats. That this bit-identical result is not the same operation as addition of real number

IEEE 754 defines an exact binary result for the addition of any two floats. That this bit-identical result is not the same operation as addition of real numbers is irrelevant, because floats aren't reals. f1 + f2 is not an estimation. Even treating it as an approximation will get you into trouble. It's not that either, it's a floating-point result, and algorithms making heavy use of floating point had better understand precisely what f1 + f2 is going to give you if they want to obtain maximum precision and accuracy.