We introduce a new idea for enhancing constraint solving engines that
drive many analysis and synthesis techniques that are powerful but
have high complexity. Our insight is that in many cases the engines
are run repeatedly against input constraints that encode problems that
are related but of increasing complexity, and domain-specific
knowledge can reduce the complexity. Moreover, even for one formula
the engine may perform multiple expensive tasks with commonalities
that can be estimated and exploited. We believe these relationships
lay a foundation for making the engines more effective and
scalable. We illustrate the viability of our idea in the context of a
well-known solver for imperative constraints, and discuss how the idea
generalizes to more general purpose methods.