Average Error: 0.0 → 0.0
Time: 14.8s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
↓
\[x - \sqrt[3]{\frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(\left(\frac{1}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0}\right)}\]
x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}
↓
x - \sqrt[3]{\frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(\left(\frac{1}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0}\right)}
double f(double x) {
        double r5000764 = x;
        double r5000765 = 2.30753;
        double r5000766 = 0.27061;
        double r5000767 = r5000764 * r5000766;
        double r5000768 = r5000765 + r5000767;
        double r5000769 = 1.0;
        double r5000770 = 0.99229;
        double r5000771 = 0.04481;
        double r5000772 = r5000764 * r5000771;
        double r5000773 = r5000770 + r5000772;
        double r5000774 = r5000773 * r5000764;
        double r5000775 = r5000769 + r5000774;
        double r5000776 = r5000768 / r5000775;
        double r5000777 = r5000764 - r5000776;
        return r5000777;
}
↓
double f(double x) {
        double r5000778 = x;
        double r5000779 = 2.30753;
        double r5000780 = 0.27061;
        double r5000781 = r5000778 * r5000780;
        double r5000782 = r5000779 + r5000781;
        double r5000783 = 0.04481;
        double r5000784 = r5000778 * r5000783;
        double r5000785 = 0.99229;
        double r5000786 = r5000784 + r5000785;
        double r5000787 = r5000786 * r5000778;
        double r5000788 = 1.0;
        double r5000789 = r5000787 + r5000788;
        double r5000790 = r5000782 / r5000789;
        double r5000791 = 1.0;
        double r5000792 = r5000791 / r5000789;
        double r5000793 = r5000792 * r5000782;
        double r5000794 = r5000793 * r5000790;
        double r5000795 = r5000790 * r5000794;
        double r5000796 = cbrt(r5000795);
        double r5000797 = r5000778 - r5000796;
        return r5000797;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061}{1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto x - \frac{2.30753 + x \cdot 0.27061}{\color{blue}{\sqrt[3]{\left(\left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)}}}\]

  4. Applied add-cbrt-cube21.1

    \[\leadsto x - \frac{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061\right) \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \left(2.30753 + x \cdot 0.27061\right)}}}{\sqrt[3]{\left(\left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)}}\]

  5. Applied cbrt-undiv21.1

    \[\leadsto x - \color{blue}{\sqrt[3]{\frac{\left(\left(2.30753 + x \cdot 0.27061\right) \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \left(2.30753 + x \cdot 0.27061\right)}{\left(\left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)\right) \cdot \left(1.0 + \left(0.99229 + x \cdot 0.04481\right) \cdot x\right)}}}\]

  6. Simplified0.0

    \[\leadsto x - \sqrt[3]{\color{blue}{\left(\frac{2.30753 + 0.27061 \cdot x}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)} \cdot \frac{2.30753 + 0.27061 \cdot x}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)}\right) \cdot \frac{2.30753 + 0.27061 \cdot x}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)}}}\]
  7. Using strategy rm

  8. Applied div-inv0.0

    \[\leadsto x - \sqrt[3]{\left(\frac{2.30753 + 0.27061 \cdot x}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)} \cdot \color{blue}{\left(\left(2.30753 + 0.27061 \cdot x\right) \cdot \frac{1}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)}\right)}\right) \cdot \frac{2.30753 + 0.27061 \cdot x}{1.0 + x \cdot \left(0.04481 \cdot x + 0.99229\right)}}\]

  9. Final simplification0.0

    \[\leadsto x - \sqrt[3]{\frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(\left(\frac{1}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0} \cdot \left(2.30753 + x \cdot 0.27061\right)\right) \cdot \frac{2.30753 + x \cdot 0.27061}{\left(x \cdot 0.04481 + 0.99229\right) \cdot x + 1.0}\right)}\]

Reproduce

herbie shell --seed 2019163 
(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)))))