Graph Transformations for Roundoff Analysis

When analyzing a numerical algorithm, it is often possible to show that a rounding error at one floating-point operation is equivalent to errors at other operations. In such cases, it can be concluded that no generality is lost if certain operations are considered error-free. Sometimes this conclusion can be reached automatically and inexpensively compared to the cost of the ultimate roundoff analysis. It may be advantageous to use a preprocessor which performs this reduction before other automatic techniques are invoked. In this report we consider a class of elementary rounding error reductions which are most naturally interpreted as graph transformations. This leads to questions concerning heuristics and optimal strategies for the application of these transformations.