Advanced compiler design and implementation
Advanced compiler design and implementation
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Symbolic-interval cooperation in constraint programming
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Analytic Variations on the Common Subexpression Problem
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Introduction to Maple
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Interval Analysis on Directed Acyclic Graphs for Global Optimization
Journal of Global Optimization
Consistency techniques for numeric CSPs
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Constructive interval disjunction
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
On complementary principles of object-oriented constraint programming
Programming and Computing Software
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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 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 on the gain in CPU time would be only due 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 on a better exploitation of n-ary plus and times operators, we propose a new algorithm I-CSE that identifies and exploits allthe "useful" common subexpressions. We show on a sample of benchmarks that I-CSE detects more useful common subexpressions than traditional approaches and leads generally to significant gains in performance, of sometimes several orders of magnitude.