[stephencanon]

There are multiple ways to analyze computations; condition number is one of them. It is relevant when inputs are assumed to be approximations to some hidden "correct" value. However, this assumption is not always warranted when dealing with floating-point numbers; sometimes, we would instead like to analyze errors under the assumption that the inputs are exact values. When this is the case, fma(x,x,-1) produces a correctly rounded result, whereas (x-1)(x+1) does not, and the ill-conditioning of the function x^2 - 1 does not enter into the analysis anywhere.

If you are used to working with complex computations (most of what is usually referred to as numerical analysis, for example), you likely do not find yourself in the latter situation very often. However, for those of us who work on low-level details of floating-point on a regular basis, the latter analysis is often critical.

[conistonwater]

Okay, I agree, that is completely reasonable. I do usually work with fairly complex algorithms, so I care about individual operations less than about the final result.