  Using quantum maps we study the accuracy of semiclassical trace formulas. The
role of chaos in improving the semiclassical accuracy, in some systems, is
demonstrated quantitatively. However, our study of the standard map cautions
that this may not be most general. While studying a sawtooth map we demonstrate
the rather remarkable fact that at the level of the time one trace even in the
presence of fixed points on singularities the trace formula may be exact, and
in any case has no logarithmic divergences observed for the quantum bakers map.
As a byproduct we introduce fantastic periodic curves akin to curlicues.
