Average Error: 0.3 → 0.3
Time: 34.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(y + x\right)\right) + \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\left(\log \left(\sqrt[3]{z}\right) + \log \left(y + x\right)\right) + \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r1207855 = x;
        double r1207856 = y;
        double r1207857 = r1207855 + r1207856;
        double r1207858 = log(r1207857);
        double r1207859 = z;
        double r1207860 = log(r1207859);
        double r1207861 = r1207858 + r1207860;
        double r1207862 = t;
        double r1207863 = r1207861 - r1207862;
        double r1207864 = a;
        double r1207865 = 0.5;
        double r1207866 = r1207864 - r1207865;
        double r1207867 = log(r1207862);
        double r1207868 = r1207866 * r1207867;
        double r1207869 = r1207863 + r1207868;
        return r1207869;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1207870 = z;
        double r1207871 = cbrt(r1207870);
        double r1207872 = log(r1207871);
        double r1207873 = y;
        double r1207874 = x;
        double r1207875 = r1207873 + r1207874;
        double r1207876 = log(r1207875);
        double r1207877 = r1207872 + r1207876;
        double r1207878 = r1207877 + r1207872;
        double r1207879 = r1207878 + r1207872;
        double r1207880 = t;
        double r1207881 = r1207879 - r1207880;
        double r1207882 = log(r1207880);
        double r1207883 = a;
        double r1207884 = 0.5;
        double r1207885 = r1207883 - r1207884;
        double r1207886 = r1207882 * r1207885;
        double r1207887 = r1207881 + r1207886;
        return r1207887;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019132 
(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))))