Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\sqrt[3]{{\left(\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) + 1}\right)}^{3}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\sqrt[3]{{\left(\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right) + 1}\right)}^{3}} - x
double f(double x) {
        double r62858 = 2.30753;
        double r62859 = x;
        double r62860 = 0.27061;
        double r62861 = r62859 * r62860;
        double r62862 = r62858 + r62861;
        double r62863 = 1.0;
        double r62864 = 0.99229;
        double r62865 = 0.04481;
        double r62866 = r62859 * r62865;
        double r62867 = r62864 + r62866;
        double r62868 = r62859 * r62867;
        double r62869 = r62863 + r62868;
        double r62870 = r62862 / r62869;
        double r62871 = r62870 - r62859;
        return r62871;
}
↓
double f(double x) {
        double r62872 = 0.27061;
        double r62873 = x;
        double r62874 = r62872 * r62873;
        double r62875 = 2.30753;
        double r62876 = r62874 + r62875;
        double r62877 = 0.04481;
        double r62878 = r62877 * r62873;
        double r62879 = 0.99229;
        double r62880 = r62878 + r62879;
        double r62881 = r62873 * r62880;
        double r62882 = 1.0;
        double r62883 = r62881 + r62882;
        double r62884 = r62876 / r62883;
        double r62885 = 3.0;
        double r62886 = pow(r62884, r62885);
        double r62887 = cbrt(r62886);
        double r62888 = r62887 - r62873;
        return r62888;
}

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-cbrt-cube0.0

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

  5. Applied add-cbrt-cube21.0

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

  6. Applied cbrt-undiv21.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(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))