How Operator Fusion Affects Error

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…