Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{\left(\sqrt[3]{x} \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + 1} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{\left(\sqrt[3]{x} \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + 1} - x
double f(double x) {
        double r58905 = 2.30753;
        double r58906 = x;
        double r58907 = 0.27061;
        double r58908 = r58906 * r58907;
        double r58909 = r58905 + r58908;
        double r58910 = 1.0;
        double r58911 = 0.99229;
        double r58912 = 0.04481;
        double r58913 = r58906 * r58912;
        double r58914 = r58911 + r58913;
        double r58915 = r58906 * r58914;
        double r58916 = r58910 + r58915;
        double r58917 = r58909 / r58916;
        double r58918 = r58917 - r58906;
        return r58918;
}
↓
double f(double x) {
        double r58919 = 2.30753;
        double r58920 = 0.27061;
        double r58921 = x;
        double r58922 = r58920 * r58921;
        double r58923 = r58919 + r58922;
        double r58924 = cbrt(r58921);
        double r58925 = 0.04481;
        double r58926 = r58921 * r58925;
        double r58927 = 0.99229;
        double r58928 = r58926 + r58927;
        double r58929 = r58924 * r58928;
        double r58930 = r58924 * r58924;
        double r58931 = r58929 * r58930;
        double r58932 = 1.0;
        double r58933 = r58931 + r58932;
        double r58934 = r58923 / r58933;
        double r58935 = r58934 - r58921;
        return r58935;
}

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

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) + 1} - x}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.0

    \[\leadsto \frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right) + 1} - x\]

  5. Applied associate-*l*0.0

    \[\leadsto \frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)\right)} + 1} - x\]

  6. Simplified0.0

    \[\leadsto \frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\left(\sqrt[3]{x} \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)\right)} + 1} - x\]

  7. Final simplification0.0

    \[\leadsto \frac{2.307529999999999859028321225196123123169 + 0.2706100000000000171951342053944244980812 \cdot x}{\left(\sqrt[3]{x} \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) + 1} - x\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))