Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}\]
↓
\[x - \frac{1}{\sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x} \cdot \sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}\]
x - \frac{2.30753 + x \cdot 0.27061000000000002}{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}
↓
x - \frac{1}{\sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x} \cdot \sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + \left(0.992290000000000005 + x \cdot 0.044810000000000003\right) \cdot x}}
double f(double x) {
        double r79586 = x;
        double r79587 = 2.30753;
        double r79588 = 0.27061;
        double r79589 = r79586 * r79588;
        double r79590 = r79587 + r79589;
        double r79591 = 1.0;
        double r79592 = 0.99229;
        double r79593 = 0.04481;
        double r79594 = r79586 * r79593;
        double r79595 = r79592 + r79594;
        double r79596 = r79595 * r79586;
        double r79597 = r79591 + r79596;
        double r79598 = r79590 / r79597;
        double r79599 = r79586 - r79598;
        return r79599;
}
↓
double f(double x) {
        double r79600 = x;
        double r79601 = 1.0;
        double r79602 = 1.0;
        double r79603 = 0.99229;
        double r79604 = 0.04481;
        double r79605 = r79600 * r79604;
        double r79606 = r79603 + r79605;
        double r79607 = r79606 * r79600;
        double r79608 = r79602 + r79607;
        double r79609 = cbrt(r79608);
        double r79610 = r79609 * r79609;
        double r79611 = r79601 / r79610;
        double r79612 = 2.30753;
        double r79613 = 0.27061;
        double r79614 = r79600 * r79613;
        double r79615 = r79612 + r79614;
        double r79616 = r79615 / r79609;
        double r79617 = r79611 * r79616;
        double r79618 = r79600 - r79617;
        return r79618;
}

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 add-cube-cbrt0.0

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied times-frac0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(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)))))