Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{1}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{1}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r55706 = 2.30753;
        double r55707 = x;
        double r55708 = 0.27061;
        double r55709 = r55707 * r55708;
        double r55710 = r55706 + r55709;
        double r55711 = 1.0;
        double r55712 = 0.99229;
        double r55713 = 0.04481;
        double r55714 = r55707 * r55713;
        double r55715 = r55712 + r55714;
        double r55716 = r55707 * r55715;
        double r55717 = r55711 + r55716;
        double r55718 = r55710 / r55717;
        double r55719 = r55718 - r55707;
        return r55719;
}
↓
double f(double x) {
        double r55720 = 1.0;
        double r55721 = 1.0;
        double r55722 = x;
        double r55723 = 0.99229;
        double r55724 = 0.04481;
        double r55725 = r55722 * r55724;
        double r55726 = r55723 + r55725;
        double r55727 = r55722 * r55726;
        double r55728 = r55721 + r55727;
        double r55729 = cbrt(r55728);
        double r55730 = r55729 * r55729;
        double r55731 = r55720 / r55730;
        double r55732 = 2.30753;
        double r55733 = 0.27061;
        double r55734 = r55722 * r55733;
        double r55735 = r55732 + r55734;
        double r55736 = r55735 / r55729;
        double r55737 = r55731 * r55736;
        double r55738 = r55737 - r55722;
        return r55738;
}

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

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

  3. Applied add-cube-cbrt0.0

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

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

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

  5. Applied times-frac0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))