Résumé
It is acknowledged that the. symbolic form of the equations is crucial for interval-based solving techniques to efficiently handle systems of equations over the reals. However, only a few automatic transformations: dons of the system have been proposed so far. Vu, Schichl, Sam-Haroud. Neumaier have exploited common subexpressions by transforming the equation system into a unique directed acyclic graph. They claim that the impact of common subexpressions elimination oil the gain in CPU time would he only clue to a reduction in the number of operations.
This paper brings two main contributions. First; we prove theoretically and experimentally that, due to interval arithmetics, exploiting certain common subexpressions might also bring additional filtering/contraction during propagation. Second, based oil a. better exploitation of n-ary phis and times operators, we propose a new algorithm I-CSE taut identifies and exploits all the "useful" common subexpressions. We show oil a sample of benchmarks that I-CSE detects more useful common subexpressions than traditional approaches and leads generally tea significant gains in performance. of sometimes several orders of magnitude.