In this example, yes. But floating point commutativity isn't guaranteed for multiple operations. a + b = b + a, but a * b * c is not guaranteed to equal b * a * c due to the rounding effects in the registers, which means commutativity fails for numbers that are at the rounding edges of floating point dynamic range.
That's a useful detail, but can you be a bit more specific, or point me to a paper that describes this effect in more detail? The discussions I've had in the past, and the papers I've read in the past, have left me with the impression that every "odd" effect of this type was an interaction with associativity, and not with commutativity.
