Modeling of reionization history ${\overline{x}}_{\mathrm{HI}}(z)$ using Eq. (6). The top panel shows the evolution of the neutral fraction as a function of redshift for different reionization scenarios generated using GRIZZLY code. The bold black curve corresponds to our GRIZZLY fiducial reionization scenario. The bottom panel shows fitting error $\mathrm{\Delta }{\overline{x}}_{\mathrm{HI}}={\overline{x}}_{\mathrm{HI}}-{\overline{x}}_{\mathrm{HI},\mathrm{f}}$ on the redshift evolution of ${\overline{x}}_{\mathrm{HI}}$. We have used an asymmetric tanh function (see Eq. (6)) to model the redshift evolution of ${\overline{x}}_{\mathrm{HI}}$.