Average Error: 0.3 → 0.3
Time: 39.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2278971 = x;
        double r2278972 = y;
        double r2278973 = r2278971 + r2278972;
        double r2278974 = log(r2278973);
        double r2278975 = z;
        double r2278976 = log(r2278975);
        double r2278977 = r2278974 + r2278976;
        double r2278978 = t;
        double r2278979 = r2278977 - r2278978;
        double r2278980 = a;
        double r2278981 = 0.5;
        double r2278982 = r2278980 - r2278981;
        double r2278983 = log(r2278978);
        double r2278984 = r2278982 * r2278983;
        double r2278985 = r2278979 + r2278984;
        return r2278985;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2278986 = y;
        double r2278987 = x;
        double r2278988 = r2278986 + r2278987;
        double r2278989 = log(r2278988);
        double r2278990 = z;
        double r2278991 = log(r2278990);
        double r2278992 = r2278989 + r2278991;
        double r2278993 = t;
        double r2278994 = r2278992 - r2278993;
        double r2278995 = cbrt(r2278993);
        double r2278996 = log(r2278995);
        double r2278997 = a;
        double r2278998 = 0.5;
        double r2278999 = r2278997 - r2278998;
        double r2279000 = r2278996 * r2278999;
        double r2279001 = r2279000 + r2279000;
        double r2279002 = r2279000 + r2279001;
        double r2279003 = r2278994 + r2279002;
        return r2279003;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\]

  5. Applied distribute-lft-in0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)}\]

  6. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  7. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \color{blue}{\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)}\right)\]

  8. Final simplification0.3

    \[\leadsto \left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)\right)\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))