Sure, but I don't think theoretical guarantees are that important in practice. When I solve math problems, I don't personally use methods with such guarantees.

Sure, but I don't think theoretical guarantees are that important in practice. When I solve math problems, I don't personally use methods with such guarantees. Mathematica has certain guarantees for evaluating integrals, but that really doesn't help when it chokes for an hour on one. In practice what matters is computational complexity, and how well heuristics can help you narrow down your search space. And here IMO geometry problems have the enormous advantage that one knows there exists a short, purely synthetic solution.