For the normal distribution, expressed here as $$\begin{equation*} g(x,y)=\exp{(-(x^2+y^2)/2)}dxdy. \end{equation*}$$ it is rather difficult to find an inverse since the cumulative distribution is given by the error function $erf(x)$ $$\begin{equation*} \mathrm{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt. \end{equation*}$$ Both c++ and Fortran have this function as intrinsic ones.