Average Error: 0.1 → 0.1
Time: 53.0s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}\right)\right) - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sqrt[3]{y}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}}\right)\right) - y\right)\right) - z\right) + \log t
double f(double x, double y, double z, double t) {
        double r5234040 = x;
        double r5234041 = y;
        double r5234042 = log(r5234041);
        double r5234043 = r5234040 * r5234042;
        double r5234044 = r5234043 - r5234041;
        double r5234045 = z;
        double r5234046 = r5234044 - r5234045;
        double r5234047 = t;
        double r5234048 = log(r5234047);
        double r5234049 = r5234046 + r5234048;
        return r5234049;
}
↓
double f(double x, double y, double z, double t) {
        double r5234050 = y;
        double r5234051 = cbrt(r5234050);
        double r5234052 = r5234051 * r5234051;
        double r5234053 = log(r5234052);
        double r5234054 = x;
        double r5234055 = r5234053 * r5234054;
        double r5234056 = cbrt(r5234051);
        double r5234057 = r5234056 * r5234056;
        double r5234058 = cbrt(r5234056);
        double r5234059 = cbrt(r5234057);
        double r5234060 = r5234058 * r5234059;
        double r5234061 = r5234057 * r5234060;
        double r5234062 = log(r5234061);
        double r5234063 = r5234054 * r5234062;
        double r5234064 = r5234063 - r5234050;
        double r5234065 = r5234055 + r5234064;
        double r5234066 = z;
        double r5234067 = r5234065 - r5234066;
        double r5234068 = t;
        double r5234069 = log(r5234068);
        double r5234070 = r5234067 + r5234069;
        return r5234070;
}

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. Using strategy rm

  8. Applied add-cube-cbrt0.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied cbrt-prod0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  (+ (- (- (* x (log y)) y) z) (log t)))