Average Error: 0.1 → 0.1
Time: 6.2s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\left(\log \left({\left({y}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{y}\right)}^{\frac{1}{3}}\right) \cdot x - y\right) - z\right) + \log t\right)
double f(double x, double y, double z, double t) {
        double r76976 = x;
        double r76977 = y;
        double r76978 = log(r76977);
        double r76979 = r76976 * r76978;
        double r76980 = r76979 - r76977;
        double r76981 = z;
        double r76982 = r76980 - r76981;
        double r76983 = t;
        double r76984 = log(r76983);
        double r76985 = r76982 + r76984;
        return r76985;
}
↓
double f(double x, double y, double z, double t) {
        double r76986 = x;
        double r76987 = y;
        double r76988 = cbrt(r76987);
        double r76989 = r76988 * r76988;
        double r76990 = log(r76989);
        double r76991 = r76986 * r76990;
        double r76992 = 0.3333333333333333;
        double r76993 = pow(r76987, r76992);
        double r76994 = 0.6666666666666666;
        double r76995 = pow(r76993, r76994);
        double r76996 = pow(r76988, r76992);
        double r76997 = r76995 * r76996;
        double r76998 = log(r76997);
        double r76999 = r76998 * r76986;
        double r77000 = r76999 - r76987;
        double r77001 = z;
        double r77002 = r77000 - r77001;
        double r77003 = t;
        double r77004 = log(r77003);
        double r77005 = r77002 + r77004;
        double r77006 = r76991 + r77005;
        return r77006;
}

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 pow1/30.1

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

  13. Applied add-cube-cbrt0.1

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

  14. Simplified0.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2020020 +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)))