  We consider suspension semiflows of an angle multiplying map on the circle
and study the distributions of periods of their periodic orbits. Under generic
conditions on the roof function, we give an asymptotic formula on the number
$\pi(T)$ of prime periodic orbits with period $\le T$. The error term is
bounded, at least, by \[ \exp((1-\frac{1}{4\lceil
\chi_{\max}/h_{\mathrm{top}}\rceil}+\varepsilon) h_{\top} T)\qquad {in the
limit $T\to \infty$} \] for arbitrarily small $\varepsilon>0$, where
$h_{\mathrm{top}}$ and $\chi_{\max}$ are respectively the topological entropy
and the maximal Lyapunov exponent of the semiflow.
