Average Error: 0.3 → 0.3
Time: 40.3s
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 r12861888 = x;
        double r12861889 = y;
        double r12861890 = r12861888 + r12861889;
        double r12861891 = log(r12861890);
        double r12861892 = z;
        double r12861893 = log(r12861892);
        double r12861894 = r12861891 + r12861893;
        double r12861895 = t;
        double r12861896 = r12861894 - r12861895;
        double r12861897 = a;
        double r12861898 = 0.5;
        double r12861899 = r12861897 - r12861898;
        double r12861900 = log(r12861895);
        double r12861901 = r12861899 * r12861900;
        double r12861902 = r12861896 + r12861901;
        return r12861902;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r12861903 = y;
        double r12861904 = x;
        double r12861905 = r12861903 + r12861904;
        double r12861906 = log(r12861905);
        double r12861907 = z;
        double r12861908 = log(r12861907);
        double r12861909 = r12861906 + r12861908;
        double r12861910 = t;
        double r12861911 = r12861909 - r12861910;
        double r12861912 = cbrt(r12861910);
        double r12861913 = log(r12861912);
        double r12861914 = a;
        double r12861915 = 0.5;
        double r12861916 = r12861914 - r12861915;
        double r12861917 = r12861913 * r12861916;
        double r12861918 = r12861917 + r12861917;
        double r12861919 = r12861917 + r12861918;
        double r12861920 = r12861911 + r12861919;
        return r12861920;
}

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

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

  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"

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

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