Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \sqrt[3]{{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\right)}^{3}}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \sqrt[3]{{\left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\right)}^{3}}
double f(double x) {
        double r125686 = x;
        double r125687 = 2.30753;
        double r125688 = 0.27061;
        double r125689 = r125686 * r125688;
        double r125690 = r125687 + r125689;
        double r125691 = 1.0;
        double r125692 = 0.99229;
        double r125693 = 0.04481;
        double r125694 = r125686 * r125693;
        double r125695 = r125692 + r125694;
        double r125696 = r125695 * r125686;
        double r125697 = r125691 + r125696;
        double r125698 = r125690 / r125697;
        double r125699 = r125686 - r125698;
        return r125699;
}
↓
double f(double x) {
        double r125700 = x;
        double r125701 = 2.30753;
        double r125702 = 0.27061;
        double r125703 = r125700 * r125702;
        double r125704 = r125701 + r125703;
        double r125705 = 1.0;
        double r125706 = 0.99229;
        double r125707 = 0.04481;
        double r125708 = r125700 * r125707;
        double r125709 = r125706 + r125708;
        double r125710 = r125709 * r125700;
        double r125711 = r125705 + r125710;
        double r125712 = r125704 / r125711;
        double r125713 = 3.0;
        double r125714 = pow(r125712, r125713);
        double r125715 = cbrt(r125714);
        double r125716 = r125700 - r125715;
        return r125716;
}

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-cbrt-cube0.0

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

  4. Applied add-cbrt-cube20.7

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

  5. Applied cbrt-undiv20.7

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(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)))))