I've been thinking recently about the differences between affine arithmetic and error Taylor series. In both, an expression is represented as 1) the answer, plus 2) a number of error terms. But in my experience, tools based on affine arithmetic are less precise than those based on error Taylor series. What gives? And how are the two analyses related? In affine arithmetic, the true answer is modeled as the computed answer plus a series of errors, each of which are a symbolic epsilon times a re...
