Average Error: 0.3 → 0.3
Time: 26.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\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 r7717849 = x;
        double r7717850 = y;
        double r7717851 = r7717849 + r7717850;
        double r7717852 = log(r7717851);
        double r7717853 = z;
        double r7717854 = log(r7717853);
        double r7717855 = r7717852 + r7717854;
        double r7717856 = t;
        double r7717857 = r7717855 - r7717856;
        double r7717858 = a;
        double r7717859 = 0.5;
        double r7717860 = r7717858 - r7717859;
        double r7717861 = log(r7717856);
        double r7717862 = r7717860 * r7717861;
        double r7717863 = r7717857 + r7717862;
        return r7717863;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r7717864 = x;
        double r7717865 = y;
        double r7717866 = r7717864 + r7717865;
        double r7717867 = log(r7717866);
        double r7717868 = z;
        double r7717869 = cbrt(r7717868);
        double r7717870 = log(r7717869);
        double r7717871 = r7717870 + r7717870;
        double r7717872 = r7717867 + r7717871;
        double r7717873 = r7717872 + r7717870;
        double r7717874 = t;
        double r7717875 = r7717873 - r7717874;
        double r7717876 = log(r7717874);
        double r7717877 = a;
        double r7717878 = 0.5;
        double r7717879 = r7717877 - r7717878;
        double r7717880 = r7717876 * r7717879;
        double r7717881 = r7717875 + r7717880;
        return r7717881;
}

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
Target0.2
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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 
(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))))