Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x\]
↓
\[\frac{2.30753 + x \cdot 0.27061000000000002}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} \cdot \sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x\]
\frac{2.30753 + x \cdot 0.27061000000000002}{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)} - x
↓
\frac{2.30753 + x \cdot 0.27061000000000002}{\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{\sqrt[3]{1}}{\sqrt[3]{1 + x \cdot \left(0.992290000000000005 + x \cdot 0.044810000000000003\right)}} - x
double f(double x) {
        double r77858 = 2.30753;
        double r77859 = x;
        double r77860 = 0.27061;
        double r77861 = r77859 * r77860;
        double r77862 = r77858 + r77861;
        double r77863 = 1.0;
        double r77864 = 0.99229;
        double r77865 = 0.04481;
        double r77866 = r77859 * r77865;
        double r77867 = r77864 + r77866;
        double r77868 = r77859 * r77867;
        double r77869 = r77863 + r77868;
        double r77870 = r77862 / r77869;
        double r77871 = r77870 - r77859;
        return r77871;
}
↓
double f(double x) {
        double r77872 = 2.30753;
        double r77873 = x;
        double r77874 = 0.27061;
        double r77875 = r77873 * r77874;
        double r77876 = r77872 + r77875;
        double r77877 = 1.0;
        double r77878 = 0.99229;
        double r77879 = 0.04481;
        double r77880 = r77873 * r77879;
        double r77881 = r77878 + r77880;
        double r77882 = r77873 * r77881;
        double r77883 = r77877 + r77882;
        double r77884 = cbrt(r77883);
        double r77885 = r77884 * r77884;
        double r77886 = r77876 / r77885;
        double r77887 = 1.0;
        double r77888 = cbrt(r77887);
        double r77889 = r77888 / r77884;
        double r77890 = r77886 * r77889;
        double r77891 = r77890 - r77873;
        return r77891;
}

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 div-inv0.0

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

  5. Applied add-cube-cbrt0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied times-frac0.0

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

  8. Applied associate-*r*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(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))