Average Error: 0.1 → 0.1
Time: 7.6s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[x \cdot \log \left(\sqrt[3]{1} \cdot {y}^{\frac{2}{3}}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
x \cdot \log \left(\sqrt[3]{1} \cdot {y}^{\frac{2}{3}}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r156052 = x;
        double r156053 = y;
        double r156054 = log(r156053);
        double r156055 = r156052 * r156054;
        double r156056 = r156055 - r156053;
        double r156057 = z;
        double r156058 = r156056 - r156057;
        double r156059 = t;
        double r156060 = log(r156059);
        double r156061 = r156058 + r156060;
        return r156061;
}
↓
double f(double x, double y, double z, double t) {
        double r156062 = x;
        double r156063 = 1.0;
        double r156064 = cbrt(r156063);
        double r156065 = y;
        double r156066 = 0.6666666666666666;
        double r156067 = pow(r156065, r156066);
        double r156068 = r156064 * r156067;
        double r156069 = log(r156068);
        double r156070 = r156062 * r156069;
        double r156071 = cbrt(r156065);
        double r156072 = log(r156071);
        double r156073 = r156072 * r156062;
        double r156074 = r156073 - r156065;
        double r156075 = z;
        double r156076 = r156074 - r156075;
        double r156077 = t;
        double r156078 = log(r156077);
        double r156079 = r156076 + r156078;
        double r156080 = r156070 + r156079;
        return r156080;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - z\right) + \log t\]

  4. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  5. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - y\right) - z\right) + \log t\]

  6. Applied associate--l+0.1

    \[\leadsto \left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(x \cdot \log \left(\sqrt[3]{y}\right) - y\right)\right)} - z\right) + \log t\]

  7. Applied associate--l+0.1

    \[\leadsto \color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(x \cdot \log \left(\sqrt[3]{y}\right) - y\right) - z\right)\right)} + \log t\]

  8. Applied associate-+l+0.1

    \[\leadsto \color{blue}{x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\left(x \cdot \log \left(\sqrt[3]{y}\right) - y\right) - z\right) + \log t\right)}\]

  9. Simplified0.1

    \[\leadsto x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \color{blue}{\left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)}\]
  10. Using strategy rm

  11. Applied *-un-lft-identity0.1

    \[\leadsto x \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot y}} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]

  12. Applied cbrt-prod0.1

    \[\leadsto x \cdot \log \left(\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{y}\right)} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]

  13. Applied associate-*l*0.1

    \[\leadsto x \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)} + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]

  14. Simplified0.1

    \[\leadsto x \cdot \log \left(\sqrt[3]{1} \cdot \color{blue}{{y}^{\frac{2}{3}}}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]

  15. Final simplification0.1

    \[\leadsto x \cdot \log \left(\sqrt[3]{1} \cdot {y}^{\frac{2}{3}}\right) + \left(\left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right) + \log t\right)\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))