Average Error: 0.1 → 0.1
Time: 28.3s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + z\right) + \left(y - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\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) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r281911 = x;
        double r281912 = y;
        double r281913 = r281911 + r281912;
        double r281914 = z;
        double r281915 = r281913 + r281914;
        double r281916 = t;
        double r281917 = log(r281916);
        double r281918 = r281914 * r281917;
        double r281919 = r281915 - r281918;
        double r281920 = a;
        double r281921 = 0.5;
        double r281922 = r281920 - r281921;
        double r281923 = b;
        double r281924 = r281922 * r281923;
        double r281925 = r281919 + r281924;
        return r281925;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r281926 = x;
        double r281927 = z;
        double r281928 = r281926 + r281927;
        double r281929 = y;
        double r281930 = 2.0;
        double r281931 = t;
        double r281932 = cbrt(r281931);
        double r281933 = log(r281932);
        double r281934 = r281930 * r281933;
        double r281935 = r281934 * r281927;
        double r281936 = r281929 - r281935;
        double r281937 = r281928 + r281936;
        double r281938 = r281927 * r281933;
        double r281939 = r281937 - r281938;
        double r281940 = a;
        double r281941 = 0.5;
        double r281942 = r281940 - r281941;
        double r281943 = b;
        double r281944 = r281942 * r281943;
        double r281945 = r281939 + r281944;
        return r281945;
}

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-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

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)))