Approximating the cumulative distribution function of the normal distribution

Over the years, a number of approximations to the cdf of the Normal distribution
have been proposed. How does one make a choice among them? This paper
compares their performance with a view to identifying the best among them.
Our analysis reveals that a uniformly best approximation formula does not exist.
Locally best are identi ed. Finally we combine the locally best approximations to
obtain a combined formula with a very high accuracy. A subroutine is presented.