Accurate Normal Distribution for the HP67/97

[Albert Chan]

(06-26-2016 09:34 PM)Dieter Wrote:  The algorithm for the inverse (quantile function) first calculates a rough estimate by means of a simple rational approximation with an error of about ±0,002. The error of this first approximation is taylored for the following correction step that provides the final result. This is a very effective third order extrapolation due to Abramovitz & Stegun (1972) p. 954.

What is the formula for the inverse cdf guess ? Is it this one ?

https://www.johndcook.com/blog/normal_cdf_inverse/

I do not have access to the Abramovitz & Stegun book.
Is third order correction faster than simple Newton's method ?

Newton iteration: x = x - (CDF(x) - p) / PDF(x)