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It is well known that the variable ordering can be critical to the efficiencyor even tractability of the cylindrical algebraic decomposition (CAD)algorithm. We propose new heuristics inspired by complexity analysis of CAD tochoose the variable ordering. These heuristics are evaluated against existingheuristics with experiments on the SMT-LIB benchmarks using both existingperformance metrics and a new metric we propose for the problem at hand. Thebest of these new heuristics chooses orderings that lead to timings on average17% slower than the virtual-best: an improvement compared to the priorstate-of-the-art which achieved timings 25% slower.

New heuristic to choose a cylindrical algebraic decomposition variable ordering motivated by complexity analysis