Global search theory is based on operations:
Ideal filter: &exist (z:R) (Satisfies(z,r) &and O(x,z))
Necessary filter:
&exist (z:R) (Satisfies(z,r) &and O(x,z)) &rArr &Phi(x,r)
Any necessary filter &Phi will do (even True). Skill is needed to make a good necessary filter &Phi. A stronger &Phi can prune more branches, but may be more expensive to compute.