Average Error: 0.0 → 0.0
Time: 10.5s
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 r73702 = x;
        double r73703 = 2.30753;
        double r73704 = 0.27061;
        double r73705 = r73702 * r73704;
        double r73706 = r73703 + r73705;
        double r73707 = 1.0;
        double r73708 = 0.99229;
        double r73709 = 0.04481;
        double r73710 = r73702 * r73709;
        double r73711 = r73708 + r73710;
        double r73712 = r73711 * r73702;
        double r73713 = r73707 + r73712;
        double r73714 = r73706 / r73713;
        double r73715 = r73702 - r73714;
        return r73715;
}
↓
double f(double x) {
        double r73716 = x;
        double r73717 = 2.30753;
        double r73718 = 0.27061;
        double r73719 = r73716 * r73718;
        double r73720 = r73717 + r73719;
        double r73721 = cbrt(r73716);
        double r73722 = 0.04481;
        double r73723 = r73716 * r73722;
        double r73724 = 0.99229;
        double r73725 = r73723 + r73724;
        double r73726 = r73725 * r73721;
        double r73727 = r73721 * r73726;
        double r73728 = r73727 * r73721;
        double r73729 = 1.0;
        double r73730 = r73728 + r73729;
        double r73731 = r73720 / r73730;
        double r73732 = r73716 - r73731;
        return r73732;
}

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)))))