Accurate Normal Distribution for the HP67/97

[Albert Chan]

Another 1 Exp method, but correct from direct method: (Revision 2)

Example: Z(z = 20.3333 333333), using Emu48

B = z²/2 = 206.722 222222
D = exp(-B) / √(2 Pi) = 6.64644 886819 e-91, error = -303 ULP

D is very close to true result, only linear correction is enough !

x = z rounded to 5 digits = 20.333
h = z - x = 0.0003 333333

Z(z) = D (B - x²/2 - x h - h²/2 + 1) = D * 1.00000 000046 = 6.64644 887125 e-91, error = +3 ULP

Edit: if correction underflow is not an issue, D + D (B - x²/2 - x h - h²/2) may be more accurate.
We get D + D * 45.5555 555 e-11 = 6.64644 887122 e-91, matched true result.