Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r72766 = x;
        double r72767 = 2.30753;
        double r72768 = 0.27061;
        double r72769 = r72766 * r72768;
        double r72770 = r72767 + r72769;
        double r72771 = 1.0;
        double r72772 = 0.99229;
        double r72773 = 0.04481;
        double r72774 = r72766 * r72773;
        double r72775 = r72772 + r72774;
        double r72776 = r72775 * r72766;
        double r72777 = r72771 + r72776;
        double r72778 = r72770 / r72777;
        double r72779 = r72766 - r72778;
        return r72779;
}
↓
double f(double x) {
        double r72780 = x;
        double r72781 = 2.30753;
        double r72782 = 0.27061;
        double r72783 = r72780 * r72782;
        double r72784 = r72781 + r72783;
        double r72785 = 1.0;
        double r72786 = 0.99229;
        double r72787 = 0.04481;
        double r72788 = r72780 * r72787;
        double r72789 = r72786 + r72788;
        double r72790 = r72789 * r72780;
        double r72791 = r72785 + r72790;
        double r72792 = r72784 / r72791;
        double r72793 = r72780 - r72792;
        return r72793;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))