  A phase-space semiclassical approximation valid to $O(\hbar)$ at short times
is used to compare semiclassical accuracy for long-time and stationary
observables in chaotic, stable, and mixed systems. Given the same level of
semiclassical accuracy for the short time behavior, the squared semiclassical
error in the chaotic system grows linearly in time, in contrast with quadratic
growth in the classically stable system. In the chaotic system, the relative
squared error at the Heisenberg time scales linearly with $\hbar_{\rm eff}$,
allowing for unambiguous semiclassical determination of the eigenvalues and
wave functions in the high-energy limit, while in the stable case the
eigenvalue error always remains of the order of a mean level spacing. For a
mixed classical phase space, eigenvalues associated with the chaotic sea can be
semiclassically computed with greater accuracy than the ones associated with
stable islands.
