Average Error: 0.2 → 0.3
Time: 29.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\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) + \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
double f(double x, double y, double z, double t, double a) {
        double r24779916 = x;
        double r24779917 = y;
        double r24779918 = r24779916 + r24779917;
        double r24779919 = log(r24779918);
        double r24779920 = z;
        double r24779921 = log(r24779920);
        double r24779922 = r24779919 + r24779921;
        double r24779923 = t;
        double r24779924 = r24779922 - r24779923;
        double r24779925 = a;
        double r24779926 = 0.5;
        double r24779927 = r24779925 - r24779926;
        double r24779928 = log(r24779923);
        double r24779929 = r24779927 * r24779928;
        double r24779930 = r24779924 + r24779929;
        return r24779930;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r24779931 = x;
        double r24779932 = y;
        double r24779933 = r24779931 + r24779932;
        double r24779934 = log(r24779933);
        double r24779935 = z;
        double r24779936 = cbrt(r24779935);
        double r24779937 = r24779936 * r24779936;
        double r24779938 = log(r24779937);
        double r24779939 = r24779934 + r24779938;
        double r24779940 = log(r24779936);
        double r24779941 = r24779939 + r24779940;
        double r24779942 = t;
        double r24779943 = r24779941 - r24779942;
        double r24779944 = a;
        double r24779945 = 0.5;
        double r24779946 = r24779944 - r24779945;
        double r24779947 = log(r24779942);
        double r24779948 = r24779946 * r24779947;
        double r24779949 = r24779943 + r24779948;
        return r24779949;
}

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

Original0.2
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 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019174 
(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))))