That's an approximation formula for the cumulative normal distribution; number 26.2.17 in Abramowitz and Stegun. You may want to try some of A&S's other formulae and their error bounds.
Presumably at http://www.espenhaug.com/black_scholes.html .. may as well give the poor guy proper credit. The rest of the page, B/S in various languages, is also of interest. I remember writing approximation-to-normal code 20+ years ago.. memmorrriiiiieeeeesssss..