Résumé
Static analysis by abstract interpretation is one of the most successful techniques used to over-approximate the roundoff errors in numerical programs. In our case, we are inter- ested in using this method to improve the accuracy of pro- grams which perform floating-point computations, known for their sensitivity to the way formulas are written. We are interested in transforming automatically pieces of code by applying to them several rewriting rules. In this arti- cle, we demonstrate the effectiveness of our approach on a non-trivial numerical simulation code.