Synthesizing accurate floating-point formulas

Many critical embedded systems perform floating-point computations yet their accuracy is difficult to assert and strongly depends on how formulas are written in programs. In this article, we focus on the synthesis of accurate formulas mathematically equal to the original formulas occurring in source codes. In general, an expression may be rewritten in many ways. To avoid any combinatorial explosion, we use an intermediate representation, called APEG, enabling us to represent many equivalent expressions in the same structure. In this article, we specifically address the problem of selecting an accurate formula among all the expressions of an APEG. To validate our approach, we present experimental results showing how APEGs, combined with profitability analysis, make it possible to significantly improve the accuracy of floating-point computations.