Approximations for hand calculators using small integer coefficients

Abstract

Methods are presented for deriving approximations containing small integer coefficients. This approach is useful for electronic hand calculators and programmable calculators, where it is important to minimize the number of keystrokes necessary to evaluate the function. For example, the probability P ( x ) P(x) of exceeding x standard deviations of either sign (Gaussian probability integral) is approximated by \[ P ( x ) ≈ EXP [ − ( 83 x + 351 ) x + 562 703 / x + 165 ] P(x) \approx {\text {EXP}}\left [ { - \frac {{(83x + 351)x + 562}}{{703/x + 165}}} \right ] \] with a relative error less than 0.042