Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}
double f(double x) {
        double r83633 = x;
        double r83634 = 2.30753;
        double r83635 = 0.27061;
        double r83636 = r83633 * r83635;
        double r83637 = r83634 + r83636;
        double r83638 = 1.0;
        double r83639 = 0.99229;
        double r83640 = 0.04481;
        double r83641 = r83633 * r83640;
        double r83642 = r83639 + r83641;
        double r83643 = r83642 * r83633;
        double r83644 = r83638 + r83643;
        double r83645 = r83637 / r83644;
        double r83646 = r83633 - r83645;
        return r83646;
}
↓
double f(double x) {
        double r83647 = x;
        double r83648 = 1.0;
        double r83649 = 1.0;
        double r83650 = 0.99229;
        double r83651 = 0.04481;
        double r83652 = r83647 * r83651;
        double r83653 = r83650 + r83652;
        double r83654 = r83653 * r83647;
        double r83655 = r83649 + r83654;
        double r83656 = 2.30753;
        double r83657 = 0.27061;
        double r83658 = r83647 * r83657;
        double r83659 = r83656 + r83658;
        double r83660 = r83655 / r83659;
        double r83661 = 3.0;
        double r83662 = pow(r83660, r83661);
        double r83663 = cbrt(r83662);
        double r83664 = r83648 / r83663;
        double r83665 = r83647 - r83664;
        return r83665;
}

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

    \[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto x - \color{blue}{\frac{1}{\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube21.8

    \[\leadsto x - \frac{1}{\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{\color{blue}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}}\]

  6. Applied add-cbrt-cube21.8

    \[\leadsto x - \frac{1}{\frac{\color{blue}{\sqrt[3]{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}}}{\sqrt[3]{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}\]

  7. Applied cbrt-undiv21.8

    \[\leadsto x - \frac{1}{\color{blue}{\sqrt[3]{\frac{\left(\left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)\right) \cdot \left(1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x\right)}{\left(\left(2.30753 + x \cdot 0.27061000000000002\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)\right) \cdot \left(2.30753 + x \cdot 0.27061000000000002\right)}}}}\]

  8. Simplified0.0

    \[\leadsto x - \frac{1}{\sqrt[3]{\color{blue}{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}}\]

  9. Final simplification0.0

    \[\leadsto x - \frac{1}{\sqrt[3]{{\left(\frac{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}{2.30753 + x \cdot 0.27061000000000002}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020060 
(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)))))