Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \sqrt[3]{x} + 1}\]
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(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right) \cdot \sqrt[3]{x} + 1}
double f(double x) {
        double r3452612 = x;
        double r3452613 = 2.30753;
        double r3452614 = 0.27061;
        double r3452615 = r3452612 * r3452614;
        double r3452616 = r3452613 + r3452615;
        double r3452617 = 1.0;
        double r3452618 = 0.99229;
        double r3452619 = 0.04481;
        double r3452620 = r3452612 * r3452619;
        double r3452621 = r3452618 + r3452620;
        double r3452622 = r3452621 * r3452612;
        double r3452623 = r3452617 + r3452622;
        double r3452624 = r3452616 / r3452623;
        double r3452625 = r3452612 - r3452624;
        return r3452625;
}
↓
double f(double x) {
        double r3452626 = x;
        double r3452627 = 2.30753;
        double r3452628 = 0.27061;
        double r3452629 = r3452626 * r3452628;
        double r3452630 = r3452627 + r3452629;
        double r3452631 = cbrt(r3452626);
        double r3452632 = r3452631 * r3452631;
        double r3452633 = 0.04481;
        double r3452634 = r3452633 * r3452626;
        double r3452635 = 0.99229;
        double r3452636 = r3452634 + r3452635;
        double r3452637 = r3452632 * r3452636;
        double r3452638 = r3452637 * r3452631;
        double r3452639 = 1.0;
        double r3452640 = r3452638 + r3452639;
        double r3452641 = r3452630 / r3452640;
        double r3452642 = r3452626 - r3452641;
        return r3452642;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(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)))))