Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right) \cdot x}
double f(double x) {
        double r52714 = x;
        double r52715 = 2.30753;
        double r52716 = 0.27061;
        double r52717 = r52714 * r52716;
        double r52718 = r52715 + r52717;
        double r52719 = 1.0;
        double r52720 = 0.99229;
        double r52721 = 0.04481;
        double r52722 = r52714 * r52721;
        double r52723 = r52720 + r52722;
        double r52724 = r52723 * r52714;
        double r52725 = r52719 + r52724;
        double r52726 = r52718 / r52725;
        double r52727 = r52714 - r52726;
        return r52727;
}
↓
double f(double x) {
        double r52728 = x;
        double r52729 = 162377988252285.0;
        double r52730 = 70368744177664.0;
        double r52731 = r52729 / r52730;
        double r52732 = 609359547581365.0;
        double r52733 = 2251799813685248.0;
        double r52734 = r52732 / r52733;
        double r52735 = r52728 * r52734;
        double r52736 = r52731 + r52735;
        double r52737 = 1.0;
        double r52738 = 8937753748486939.0;
        double r52739 = 9007199254740992.0;
        double r52740 = r52738 / r52739;
        double r52741 = 3228900788839551.0;
        double r52742 = 7.205759403792794e+16;
        double r52743 = r52741 / r52742;
        double r52744 = r52728 * r52743;
        double r52745 = r52740 + r52744;
        double r52746 = r52745 * r52728;
        double r52747 = r52737 + r52746;
        double r52748 = r52736 / r52747;
        double r52749 = r52728 - r52748;
        return r52749;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x - \frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right) \cdot x}}\]

  3. Final simplification0.0

    \[\leadsto x - \frac{\frac{162377988252285}{70368744177664} + x \cdot \frac{609359547581365}{2251799813685248}}{1 + \left(\frac{8937753748486939}{9007199254740992} + x \cdot \frac{3228900788839551}{72057594037927936}\right) \cdot x}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* (+ 0.992290000000000005 (* x 0.044810000000000003)) x)))))