FPU-Supported Running Error Analysis

A-posteriori forward rounding error analyses tend to give sharper error estimates than a-priori ones, as they use actual data quantities. One of such a-posteriori analysis – running error analysis – uses expressions consisting of two parts; one generates the error and the other propagates input errors to the output. This paper suggests replacing the error generating term with an FPU-extracted rounding error estimate, which produces a sharper error bound.