We investigate reversibility violations in the Hybrid Monte Carlo algorithm. Those violations are inevitable when computers with finite numerical precision are being used. In SU(2) gauge theory, we study the dependence of observables on the size of the reversibility violations. While we cannot find any statistically significant deviation in observables related to the simulated physical model, algorithmic specific observables signal an upper bound for reversibility violations below which simulations appear unproblematic. This empirically derived condition is independent of problem size and parameter values, at least in the range of parameters studied here.

17 pages, 5 figures, typos corrected, comment added, matches published version