  Recently we developed a new sampling methodology based on incomplete cosine
expansion of the sinc function and applied it in numerical integration in order
to obtain a rational approximation for the complex error function $w\left(z
\right) = e^{- {z^2}}\left(1 + \frac{2i}{\sqrt \pi}\int_0^z e^{t^2}dt\right),$
where $z = x + iy$. As a further development, in this work we show how this
sampling-based rational approximation can be transformed into alternative form
for efficient computation of the complex error function $w\left(z \right)$ at
smaller values of the imaginary argument $y=\operatorname{Im}\left[z \right]$.
Such an approach enables us to avoid poles in implementation and to cover the
entire complex plain with high accuracy in a rapid algorithm. An optimized
Matlab code utilizing only three rapid approximations is presented.
