Average Error: 0.3 → 0.3
Time: 35.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r251888 = x;
        double r251889 = y;
        double r251890 = r251888 + r251889;
        double r251891 = log(r251890);
        double r251892 = z;
        double r251893 = log(r251892);
        double r251894 = r251891 + r251893;
        double r251895 = t;
        double r251896 = r251894 - r251895;
        double r251897 = a;
        double r251898 = 0.5;
        double r251899 = r251897 - r251898;
        double r251900 = log(r251895);
        double r251901 = r251899 * r251900;
        double r251902 = r251896 + r251901;
        return r251902;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r251903 = x;
        double r251904 = y;
        double r251905 = r251903 + r251904;
        double r251906 = log(r251905);
        double r251907 = 2.0;
        double r251908 = z;
        double r251909 = cbrt(r251908);
        double r251910 = log(r251909);
        double r251911 = r251907 * r251910;
        double r251912 = r251906 + r251911;
        double r251913 = r251912 + r251910;
        double r251914 = t;
        double r251915 = r251913 - r251914;
        double r251916 = a;
        double r251917 = 0.5;
        double r251918 = r251916 - r251917;
        double r251919 = log(r251914);
        double r251920 = r251918 * r251919;
        double r251921 = r251915 + r251920;
        return r251921;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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

    \[\leadsto \left(\left(\color{blue}{\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

  7. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + 2 \cdot \log \left(\sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))