Approximate computing, a technique that forgoes quantifiable output accuracy in favor of performance gains, is useful in improving the energy efficiency of error-resilient software, especially in the embedded setting. The identification of program components that can tolerate error plays a crucial role in balancing the energy vs. accuracy trade off in approximate computing. Manual analysis for approximability is not scalable and therefore automated tools which employ static or dynamic analysis have been proposed. However, static techniques are often coarse in their approximations while dynamic efforts incur high overhead. In this work we present ApproxSymate, a framework for automatically identifying program approximations using symbolic execution. ApproxSymate first statically computes symbolic error expressions for program components, and then uses a dynamic sensitivity analysis to compute their approximability. A unique feature of this tool is that it explores the previously not considered dimension of program path for approximation which enables safer transformations. Our evaluation shows that ApproxSymate averages about 96% accuracy in identifying the same approximations found in manually annotated benchmarks, outperforming existing automated techniques.