OUP accepted manuscript

We present a computationally efficient and fast semi-numerical technique for simulating the Lyman-$\alpha$ (Ly$\alpha$) absorption optical depth in presence of neutral hydrogen "islands" left over from reionization at redshifts $5 \lesssim z 6$. The main inputs to analysis are (i) photon-conserving model ionized regions during (named SCRIPT) along with prescription shadowing by islands (ii) fluctuating Gunn-Peterson approximation Ly$\alpha$ absorption. Our is then used large-scale fluctuations effective as observed sight lines towards high$-z$ quasars. fully described five parameters. By setting two them default values varying other three, we obtain constraints on history 6$ allowed data. confirm that \emph{not} complete before $z \sim 5.6$ $\gtrsim 2\sigma$ confidence, exact confidence limits depending how non-detections flux data treated. also completion can be late 5.2$. With further improvements more 6$, take advantage computational efficiency our stringent ionization fraction tail-end reionization.