Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(\sqrt[3]{x} \cdot \left(\left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + 1}\]
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}{\left(\sqrt[3]{x} \cdot \left(\left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + 1}
double f(double x) {
        double r83874 = x;
        double r83875 = 2.30753;
        double r83876 = 0.27061;
        double r83877 = r83874 * r83876;
        double r83878 = r83875 + r83877;
        double r83879 = 1.0;
        double r83880 = 0.99229;
        double r83881 = 0.04481;
        double r83882 = r83874 * r83881;
        double r83883 = r83880 + r83882;
        double r83884 = r83883 * r83874;
        double r83885 = r83879 + r83884;
        double r83886 = r83878 / r83885;
        double r83887 = r83874 - r83886;
        return r83887;
}
↓
double f(double x) {
        double r83888 = x;
        double r83889 = 2.30753;
        double r83890 = 0.27061;
        double r83891 = r83888 * r83890;
        double r83892 = r83889 + r83891;
        double r83893 = cbrt(r83888);
        double r83894 = 0.04481;
        double r83895 = r83888 * r83894;
        double r83896 = 0.99229;
        double r83897 = r83895 + r83896;
        double r83898 = r83897 * r83893;
        double r83899 = r83893 * r83898;
        double r83900 = r83899 * r83893;
        double r83901 = 1.0;
        double r83902 = r83900 + r83901;
        double r83903 = r83892 / r83902;
        double r83904 = r83888 - r83903;
        return r83904;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot \color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)}}\]

  4. Applied associate-*r*0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\left(\left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x}}}\]

  5. Simplified0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \color{blue}{\left(\left(\left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}\]

  6. Final simplification0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(\sqrt[3]{x} \cdot \left(\left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) \cdot \sqrt[3]{x}\right)\right) \cdot \sqrt[3]{x} + 1}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* (+ 0.99229 (* x 0.04481)) x)))))