  A set of analytical benchmarks for tracking programs is required for
precision storage ring experiments. To determine the accuracy of precision
tracking programs in electric and magnetic rings, a variety of analytical
estimates of particle and spin dynamics in the rings were developed and
compared to the numerical results of tracking simulations. Initial
discrepancies in the comparisons indicated the need for improvement of several
of the analytical estimates. As an example, we found that the fourth-order
Runge-Kutta/Predictor-Corrector method was slow but accurate, and that it
passed all the benchmarks it was tested against, often to the sub-part per
billion level. Thus, high precision analytical estimates and tracking programs
based on fourth-order Runge-Kutta/Predictor-Corrector integration can be used
to benchmark faster tracking programs for accuracy.
