Average Error: 0.0 → 0.0
Time: 11.3s
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 r100760 = x;
        double r100761 = 2.30753;
        double r100762 = 0.27061;
        double r100763 = r100760 * r100762;
        double r100764 = r100761 + r100763;
        double r100765 = 1.0;
        double r100766 = 0.99229;
        double r100767 = 0.04481;
        double r100768 = r100760 * r100767;
        double r100769 = r100766 + r100768;
        double r100770 = r100769 * r100760;
        double r100771 = r100765 + r100770;
        double r100772 = r100764 / r100771;
        double r100773 = r100760 - r100772;
        return r100773;
}
↓
double f(double x) {
        double r100774 = x;
        double r100775 = 162377988252285.0;
        double r100776 = 70368744177664.0;
        double r100777 = r100775 / r100776;
        double r100778 = 609359547581365.0;
        double r100779 = 2251799813685248.0;
        double r100780 = r100778 / r100779;
        double r100781 = r100774 * r100780;
        double r100782 = r100777 + r100781;
        double r100783 = 1.0;
        double r100784 = 8937753748486939.0;
        double r100785 = 9007199254740992.0;
        double r100786 = r100784 / r100785;
        double r100787 = 3228900788839551.0;
        double r100788 = 7.205759403792794e+16;
        double r100789 = r100787 / r100788;
        double r100790 = r100774 * r100789;
        double r100791 = r100786 + r100790;
        double r100792 = r100791 * r100774;
        double r100793 = r100783 + r100792;
        double r100794 = r100782 / r100793;
        double r100795 = r100774 - r100794;
        return r100795;
}

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 2019303 
(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)))))