Sound Probabilistic Numerical Error Analysis

Numerical software uses floating-point arithmetic to implement real-valued algorithms which inevitably introduces roundoff errors. Additionally, in an effort to reduce energy consumption, approximate hardware introduces further errors. As errors are propagated through a computation, the result of the approximated floating-point program can be vastly different from the real-valued ideal one. Previous work on soundly bounding (roundoff) errors has focused on worst-case absolute error analysis. However, not all inputs and not all errors are equally likely such that these methods can lead to overly pessimistic error bounds.