> restart:
> Digits:=40;
> a:=[-3.969683028665376e+01, 2.209460984245205e+02,
> -2.759285104469687e+02, 1.383577518672690e+02,
> -3.066479806614716e+01, 2.506628277459239e+00];
> b:=[-5.447609879822406e+01, 1.615858368580409e+02,
> 	-1.556989798598866e+02, 6.680131188771972e+01,
> -1.328068155288572e+01];
> c:=[-7.784894002430293e-03, -3.223964580411365e-01,
> -2.400758277161838e+00, -2.549732539343734e+00, 4.374664141464968e+00,
> 2.938163982698783e+00];
> d:=[7.784695709041462e-03, 3.224671290700398e-01,
> 2.445134137142996e+00, 3.754408661907416e+00];
> #u := q - 0.5;
> #t := u * u;
> u := U * (((((a[1] * t + a[2]) * t + a[3]) * t + a[4]) * t + a[5]) * t
> + a[6])
> 	    /(((((b[1] * t + b[2]) * t + b[3]) * t + b[4]) * t + b[5]) * t +
> 1.0);
> t_ := sqrt(2.0)*Q;#sqrt(-2.0 * log(q));
> u_ := (((((c[1] * t_ + c[2]) * t_ + c[3]) * t_ + c[4]) * t_ + c[5]) *
> t_ + c[6])
> 	    /((((d[1] * t_ + d[2]) * t_ + d[3]) * t_ + d[4]) *t_ + 1.0);
> 

                             Digits := 40


  a := [-39.69683028665376, 220.9460984245205, -275.9285104469687,

        138.3577518672690, -30.66479806614716, 2.506628277459239]


  b := [-54.47609879822406, 161.5858368580409, -155.6989798598866,

        66.80131188771972, -13.28068155288572]


  c := [-0.007784894002430293, -0.3223964580411365,

        -2.400758277161838, -2.549732539343734, 4.374664141464968,

        2.938163982698783]


  d := [0.007784695709041462, 0.3224671290700398, 2.445134137142996,

        3.754408661907416]


  u := U (((((-39.69683028665376 t + 220.9460984245205) t

         - 275.9285104469687) t + 138.3577518672690) t

         - 30.66479806614716) t + 2.506628277459239)/((((

        (-54.47609879822406 t + 161.5858368580409) t

         - 155.6989798598866) t + 66.80131188771972) t

         - 13.28068155288572) t + 1.0)


          t_ := 1.414213562373095048801688724209698078570 Q


  u_ := (1.414213562373095048801688724209698078570 (

        1.414213562373095048801688724209698078570 (

        1.414213562373095048801688724209698078570 (

        1.414213562373095048801688724209698078570 (

        -0.01100950267987388672798637002440513580830 Q

         - 0.3223964580411365) Q - 2.400758277161838) Q

         - 2.549732539343734) Q + 4.374664141464968) Q

         + 2.938163982698783)/(

        1.414213562373095048801688724209698078570 (

        1.414213562373095048801688724209698078570 (

        1.414213562373095048801688724209698078570 (

        0.01100922225067407300617876507022233666631 Q

         + 0.3224671290700398) Q + 2.445134137142996) Q

         + 3.754408661907416) Q + 1.0)

> with(numapprox):
> ierf1:=convert(evalf((subs(q=(y+1)/2,normal(expand(sqrt(2.)*u))))),hor
> ner);
> ierf2:=subs(Q=sqrt(-ln((y+1)/2.)),hornerform(factor(evalf(sqrt(2)*u_))
> ,Q));

  ierf1 := U (-3.544907705810765295505665718572722409393 + (

        43.36657331257757109076702467506121353083 + (

        -195.6674091501432358871886667629048566966 + (

        390.2218417195093784004984640943102852344 + (

        -312.4649689453776198212601960895482222640

         + 56.13979577460878582336455957425683612063 t) t) t) t) t)/(

        -1. + (13.28068155288572000000000000000000000000 + (

        -66.80131188771972000000000000000000000000 + (

        155.6989798598866000000000000000000000000 + (

        -161.5858368580409000000000000000000000000

         + 54.47609879822406000000000000000000000000 t) t) t) t) t)


  ierf2 := - 2.000050944416131948227267355243852992704

        (%1 + 22.73777230481436499516779895424500212089)

        (%1 + 5.352510420435462167145102449823247783109)

        (%1 + 1.618888586630886083997843272345593052133)

        (%1 + 0.4067753714160157551643163079786755678642)

        (%1 - 0.8324751754965660964085275823519476015729)/(

        (%1 + 22.70055746612312273302231184873396591411)

        (%1 + 5.213271232693735748366578666495225744200)

        (%1 + 1.138444540257063858241777655664381170080)

        (%1 + 0.2383634405785183657476502235410438313666))

  %1 := (-ln(0.5000000000000000000000000000000000000000 y

                                                       1/2
         + 0.5000000000000000000000000000000000000000))

> yn:=0.1:
> subs(y=yn,ierf1);
> subs(q=(yn+1)/2,u*sqrt(2.));
> evalf(subs(y=yn,ierf2));
> evalf(subs(Q=sqrt(-ln((yn+1)/2.)),u_*sqrt(2.)));

              0.1777119810182547967590368227913735050444


              0.1777119810182547967590368227913735050445


              0.1773549607124649398991024707644887000326


              0.1773549607124649398991024707644887000326

> 
