I have recently become a big fan of the condition number formalism for floating-point error; it is a simple mental model that explains a lot about floating point. In this blog post I want to use that mental model to investigate "operator fusion": basically, why library functions like log1p, cospi, or hypot improve error.1 [1 Actually, one of the big effects of hypot is to avoid overflow, which condition numbers don't address, so, uhh, it's only part of the story.] The condition number formali...
