Methods and apparatuses are described for assigning random values to a set of random variables so that the assigned random values satisfy a set of constraints. A constraint solver can receive a set of constraints that is expected to cause performance problems when the system assigns random values to the set of random variables in a manner that satisfies the set of constraints. For example, modulo constraints and bit-slice constraints can cause the system to perform excessive backtracking when the system attempts to assign random values to the set of random variables in a manner that satisfies the set of constraints. The system can rewrite the set of constraints to obtain a new set of constraints that is expected to reduce and/or avoid the performance problems. The system can then assign random values to the set of random variables based on the new set of constraints.