This program is by Karl Bédard and is used here by permission.

This program is supplied without representation or warranty of any kind. Karl Bédard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

erf(z)=1-(a1*T+a2*T^2+a3*T^3+a4*T^4+a5*T^5)*e(-z^2) where T=1/(1+Pz) and other numerical values are:

P = 0.3275911, a1 = 0.254829592, a2 = - 0.284496736, a3 = 1.421413741, a4 = -1.453152027, a5 =1.061405429.

Example: 0.19 XEQ R (running...) answer = 0.211839… Main Label: 01 LBL R 02 is x not = 0? 03 GTO U 04 0 05 RTN CK D4FD 7.5 bytes (similarly in HP33s, CK=059D LN=27) because T is not behaving properly when z is negative: 01 LBL U 02 is x >0? 03 GTO Q 04 +/- 05 XEQ Q 06 +/- 07 RTN CK AD1D 10.5 bytes (similarly in HP33s, CK=00E0 LN=21) Polynomial using Horner: 01 LBL Q 02 STO Z 03 0.3275911 04 * 05 1 06 + 07 1/X 08 STO T 09 1.061405429 10 * 11 1.453152027 12 - 13 RCL*T 14 1.421413741 15 + 16 RCL*T 17 0.284496736 18 - 19 RCL*T 20 0.254829592 21 + 22 RCL*T 23 RCL Z 24 X^2 25 +/- 26 e^X 27 * 28 +/- 29 1 30 + 31 RTN CK C48E 94.5 bytes (similarly in HP33s, CK=AB42 LN=189)

Example: 1 XEQ Z (running...) answer = DIVIDE BY ZERO (what we want to see) Also, 0.9999 will return something like 2,75. Let’s not forget that erf(z) is close enough to 1 when z=2,4. Main Label: 01 LBL Z 02 STO I 03 1 04 STO C 05 STO D 06 STO i 06 0 07 STO N 08 STO O 10 GTO C 11 RTN CK AE92 16.5 bytes (similarly in HP33s, CK=865E LN=57) The inverse of erf requires the use of a program for linear intrapolation. From points (STO C,STO D) and (STO N,STO O), will give value of J for a point on the same line (STO I, J?). It comes as a bonus with the error fonction... 01 LBL J 02 RCL I 03 RCL -C 04 RCL O 05 RCL-D 06 * 07 RCL N 08 RCL-C 09 / 10 RCL+D 11 RTN CK 8012 16.5 bytes (similarly in HP33s, CK=DF86 LN=33) Output 01 LBL O 02 XEQ J 03 RTN CK 796B 4.5 bytes (similarly in HP33s, CK=0C10 LN=9) 01 LBL A 02 STO O 03 XEQ R 04 STO N 05 22 06 STO i 07 GTO C 08 RTN CK 3637 12 bytes (similarly in HP33s, CK=6E35 LN=36) 01 LBL V 02 STO D 03 XEQ R 04 STO C 05 1 06 STO i 07 GTO C 08 RTN CK 2453 12 bytes (similarly in HP33s, CK=7131 LN=36) Convergence test: (squared is for negative values of N) 01 LBL C 02 RCL I 03 RCL -N 04 X^2 05 1E-12 06 is x >y? 07 GTO O 08 XEQ J 09 GTO (i) 10 RTN CK BBFD 23 bytes (similarly in HP33s, CK=CB53 LN=42)The convergence should take under 10 seconds.

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