A symbolic execution engine regularly queries a Satisfiability Modulo Theory (SMT) solver to determine reacha- bility of code during execution. Unfortunately, the SMT solver is often the bottleneck of symbolic execution. Inspired by abstract interpretation, we propose an abstract symbolic execution (ASE) engine which aims at querying the SMT solver less often by trying to compute reachability faster through an increasingly weaker abstraction. For this purpose, we have designed and implemented a value set decision procedure based on so-called strided value intervals (SVI) for efficiently determining precise, or under-approximating value sets for variables. Our ASE engine begins reasoning with respect to the SVI abstraction, and then only if needed uses the theory of bit-vectors implemented in SMT solvers. Our ASE engine efficiently detects when the former abstraction becomes incomplete to move on and try the next abstraction. We have designed and implemented a prototype of our engine for a subset of 64-bit RISC-V. Our experimental evaluation shows that our prototype often improves symbolic execution time by significantly reducing the number of SMT queries while, whenever the abstractions do not work, the overhead for trying still remains low.