Average Error: 0.1 → 0.1
Time: 6.2s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right) - z\right)\right) + \log t
double f(double x, double y, double z, double t) {
        double r106983 = x;
        double r106984 = y;
        double r106985 = log(r106984);
        double r106986 = r106983 * r106985;
        double r106987 = r106986 - r106984;
        double r106988 = z;
        double r106989 = r106987 - r106988;
        double r106990 = t;
        double r106991 = log(r106990);
        double r106992 = r106989 + r106991;
        return r106992;
}
↓
double f(double x, double y, double z, double t) {
        double r106993 = x;
        double r106994 = y;
        double r106995 = cbrt(r106994);
        double r106996 = r106995 * r106995;
        double r106997 = log(r106996);
        double r106998 = r106993 * r106997;
        double r106999 = log(r106995);
        double r107000 = r106999 * r106993;
        double r107001 = r107000 - r106994;
        double r107002 = z;
        double r107003 = r107001 - r107002;
        double r107004 = r106998 + r107003;
        double r107005 = t;
        double r107006 = log(r107005);
        double r107007 = r107004 + r107006;
        return r107007;
}

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. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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)))