To determine the accuracy of tracking programs for precision storage ring experiments, analytical estimates of particle and spin dynamics in electric and magnetic rings were developed and compared to the numerical results of a tracking program based on Runge-Kutta/Predictor-Corrector integration. Initial discrepancies in the comparisons indicated the need to improve several of the analytical estimates. In the end, this rather slow program passed all benchmarks, often agreeing with the analytical estimates to the part-per-billion level. Thus, it can in turn be used to benchmark faster tracking programs for accuracy. (C) 2015 Elsevier B.V. All rights reserved.