Average Error: 0.1 → 0.1
Time: 28.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r262878 = x;
        double r262879 = y;
        double r262880 = r262878 + r262879;
        double r262881 = z;
        double r262882 = r262880 + r262881;
        double r262883 = t;
        double r262884 = log(r262883);
        double r262885 = r262881 * r262884;
        double r262886 = r262882 - r262885;
        double r262887 = a;
        double r262888 = 0.5;
        double r262889 = r262887 - r262888;
        double r262890 = b;
        double r262891 = r262889 * r262890;
        double r262892 = r262886 + r262891;
        return r262892;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r262893 = x;
        double r262894 = z;
        double r262895 = r262893 + r262894;
        double r262896 = y;
        double r262897 = 2.0;
        double r262898 = t;
        double r262899 = cbrt(r262898);
        double r262900 = log(r262899);
        double r262901 = r262897 * r262900;
        double r262902 = r262901 * r262894;
        double r262903 = r262896 - r262902;
        double r262904 = r262895 + r262903;
        double r262905 = r262900 * r262894;
        double r262906 = r262904 - r262905;
        double r262907 = a;
        double r262908 = 0.5;
        double r262909 = r262907 - r262908;
        double r262910 = b;
        double r262911 = r262909 * r262910;
        double r262912 = r262906 + r262911;
        return r262912;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

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