Average Error: 0.1 → 0.1
Time: 16.2s
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 r429836 = x;
        double r429837 = y;
        double r429838 = r429836 + r429837;
        double r429839 = z;
        double r429840 = r429838 + r429839;
        double r429841 = t;
        double r429842 = log(r429841);
        double r429843 = r429839 * r429842;
        double r429844 = r429840 - r429843;
        double r429845 = a;
        double r429846 = 0.5;
        double r429847 = r429845 - r429846;
        double r429848 = b;
        double r429849 = r429847 * r429848;
        double r429850 = r429844 + r429849;
        return r429850;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r429851 = x;
        double r429852 = z;
        double r429853 = r429851 + r429852;
        double r429854 = y;
        double r429855 = 2.0;
        double r429856 = t;
        double r429857 = cbrt(r429856);
        double r429858 = log(r429857);
        double r429859 = r429855 * r429858;
        double r429860 = r429859 * r429852;
        double r429861 = r429854 - r429860;
        double r429862 = r429853 + r429861;
        double r429863 = r429852 * r429858;
        double r429864 = r429862 - r429863;
        double r429865 = a;
        double r429866 = 0.5;
        double r429867 = r429865 - r429866;
        double r429868 = b;
        double r429869 = r429867 * r429868;
        double r429870 = r429864 + r429869;
        return r429870;
}

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
Target0.3
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 2020046 
(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)))