  The inverse of the error function, $\operatorname{inverf}(x),$ has
applications in diffusion problems, chemical potentials, ultrasound imaging,
etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z)
|_{z=0}$, as $n\to \infty$ using nested derivatives and a discrete ray method.
We obtain a very good approximation of $\operatorname{inverf}(x)$ through a
high-order Taylor expansion around $x=0$. We give numerical results showing the
accuracy of our formulas.
