4.12 Polynomial approximation

Handbook of Mathematical Functions by Abramowitz and Stegun, 26.2.16 & 26.2.17, p932

Practice script

PolyNom3

## function (x) 
## {
##     CO1 = 0.4361836
##     CO2 = -0.1201676
##     CO3 = 0.937298
##     CO4 = 0.33267
##     TMP1 = exp(-x * x/2)/sqrt(2 * pi)
##     TMP2 = 1/(1 + abs(x) * CO4)
##     y = TMP1 * (CO1 * TMP2 + CO2 * TMP2^2 + CO3 * TMP2^3)
##     if (x > 0) 
##         y = 1 - y
##     return(y)
## }
## <bytecode: 0x000001e2a443f2b0>
## <environment: namespace:math>

format(PolyNom3(2), digits=22)

## [1] "0.9772411898846421474119"

format(pnorm(2), digits=22) # Compare with the above

## [1] "0.9772498680518207914147"