File:Derivation of speedup with non sequential base.png

\begin{align*}
& \frac{t_{seq}}{t_p}\cdot np =  \\
& \frac{t_{seq} \cdot np }{ t_{over} + t'_{p}} =
\frac{t_{seq}}{ \frac{t_{over}}{np} + \frac{t'_{p}}{np}} \\
& \text{ For } p_0 \leq q \\
& S_{w_{p_0}} =
\frac{ t_{over_{p_0}} + t'_{p_0}}
{\frac{t_{over}}{nq} + \frac{t'_{q}}{nq}} \cdot {np_0}
\end{align*}