Average Error: 0.3 → 0.3
Time: 10.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\frac{\left(\log \left(x + y\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot \left(\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)\right)}{\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)} + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\frac{\left(\log \left(x + y\right) + \log \left({z}^{\frac{2}{3}}\right)\right) \cdot \left(\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\right)\right)}{\log \left(x + y\right) - \log \left({z}^{\frac{2}{3}}\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 r460058 = x;
        double r460059 = y;
        double r460060 = r460058 + r460059;
        double r460061 = log(r460060);
        double r460062 = z;
        double r460063 = log(r460062);
        double r460064 = r460061 + r460063;
        double r460065 = t;
        double r460066 = r460064 - r460065;
        double r460067 = a;
        double r460068 = 0.5;
        double r460069 = r460067 - r460068;
        double r460070 = log(r460065);
        double r460071 = r460069 * r460070;
        double r460072 = r460066 + r460071;
        return r460072;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r460073 = x;
        double r460074 = y;
        double r460075 = r460073 + r460074;
        double r460076 = log(r460075);
        double r460077 = z;
        double r460078 = 0.6666666666666666;
        double r460079 = pow(r460077, r460078);
        double r460080 = log(r460079);
        double r460081 = r460076 + r460080;
        double r460082 = r460076 - r460080;
        double r460083 = r460081 * r460082;
        double r460084 = r460083 / r460082;
        double r460085 = cbrt(r460077);
        double r460086 = log(r460085);
        double r460087 = r460084 + r460086;
        double r460088 = t;
        double r460089 = r460087 - r460088;
        double r460090 = a;
        double r460091 = 0.5;
        double r460092 = r460090 - r460091;
        double r460093 = log(r460088);
        double r460094 = r460092 * r460093;
        double r460095 = r460089 + r460094;
        return r460095;
}

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. Using strategy rm

  7. Applied flip-+0.3

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

  8. Simplified0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020057 
(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))))