Average Error: 0.3 → 0.3
Time: 34.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r16959963 = x;
        double r16959964 = y;
        double r16959965 = r16959963 + r16959964;
        double r16959966 = log(r16959965);
        double r16959967 = z;
        double r16959968 = log(r16959967);
        double r16959969 = r16959966 + r16959968;
        double r16959970 = t;
        double r16959971 = r16959969 - r16959970;
        double r16959972 = a;
        double r16959973 = 0.5;
        double r16959974 = r16959972 - r16959973;
        double r16959975 = log(r16959970);
        double r16959976 = r16959974 * r16959975;
        double r16959977 = r16959971 + r16959976;
        return r16959977;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r16959978 = y;
        double r16959979 = x;
        double r16959980 = r16959978 + r16959979;
        double r16959981 = log(r16959980);
        double r16959982 = z;
        double r16959983 = cbrt(r16959982);
        double r16959984 = r16959983 * r16959983;
        double r16959985 = log(r16959984);
        double r16959986 = log(r16959983);
        double r16959987 = t;
        double r16959988 = r16959986 - r16959987;
        double r16959989 = r16959985 + r16959988;
        double r16959990 = log(r16959987);
        double r16959991 = a;
        double r16959992 = 0.5;
        double r16959993 = r16959991 - r16959992;
        double r16959994 = r16959990 * r16959993;
        double r16959995 = r16959989 + r16959994;
        double r16959996 = r16959981 + r16959995;
        return r16959996;
}

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

    \[\leadsto \color{blue}{\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.3

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

  7. Applied log-prod0.3

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

  8. Applied associate--l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(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))))