Average Error: 0.1 → 0.1
Time: 24.5s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\log t + \left(\left(\log \left(\left(\sqrt[3]{{y}^{\frac{1}{3}}} \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{{y}^{\frac{1}{3}}}\right) \cdot x - y\right) - z\right)\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\log t + \left(\left(\log \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)\right) + \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x
double f(double x, double y, double z, double t) {
        double r4908910 = x;
        double r4908911 = y;
        double r4908912 = log(r4908911);
        double r4908913 = r4908910 * r4908912;
        double r4908914 = r4908913 - r4908911;
        double r4908915 = z;
        double r4908916 = r4908914 - r4908915;
        double r4908917 = t;
        double r4908918 = log(r4908917);
        double r4908919 = r4908916 + r4908918;
        return r4908919;
}
↓
double f(double x, double y, double z, double t) {
        double r4908920 = t;
        double r4908921 = log(r4908920);
        double r4908922 = y;
        double r4908923 = 0.3333333333333333;
        double r4908924 = pow(r4908922, r4908923);
        double r4908925 = cbrt(r4908924);
        double r4908926 = r4908925 * r4908925;
        double r4908927 = r4908926 * r4908925;
        double r4908928 = log(r4908927);
        double r4908929 = x;
        double r4908930 = r4908928 * r4908929;
        double r4908931 = r4908930 - r4908922;
        double r4908932 = z;
        double r4908933 = r4908931 - r4908932;
        double r4908934 = r4908921 + r4908933;
        double r4908935 = cbrt(r4908922);
        double r4908936 = r4908935 * r4908935;
        double r4908937 = log(r4908936);
        double r4908938 = r4908937 * r4908929;
        double r4908939 = r4908934 + r4908938;
        return r4908939;
}

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-rgt-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  10. Applied pow1/30.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))