The best way to obtain the inversion from U[0, 1] to Normal distribution is by using an algorithm presented in a famous short paper of Moro (1995). Moro presented a hybrid algorithm: he uses the Beasley & Springer algorithm for the central part of the Normal distribution and another algorithm for the tails of the distribution.
He modeled the distribution tails using truncated Chebyschev series..... .................. http://marcoagd.usuarios.rdc.puc-rio.br/quasi_mc.html