Average Error: 0.1 → 0.1
Time: 16.4s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[b \cdot \left(a - 0.5\right) + \left(\left(\left(z + \left(y + x\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
b \cdot \left(a - 0.5\right) + \left(\left(\left(z + \left(y + x\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r6966853 = x;
        double r6966854 = y;
        double r6966855 = r6966853 + r6966854;
        double r6966856 = z;
        double r6966857 = r6966855 + r6966856;
        double r6966858 = t;
        double r6966859 = log(r6966858);
        double r6966860 = r6966856 * r6966859;
        double r6966861 = r6966857 - r6966860;
        double r6966862 = a;
        double r6966863 = 0.5;
        double r6966864 = r6966862 - r6966863;
        double r6966865 = b;
        double r6966866 = r6966864 * r6966865;
        double r6966867 = r6966861 + r6966866;
        return r6966867;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r6966868 = b;
        double r6966869 = a;
        double r6966870 = 0.5;
        double r6966871 = r6966869 - r6966870;
        double r6966872 = r6966868 * r6966871;
        double r6966873 = z;
        double r6966874 = y;
        double r6966875 = x;
        double r6966876 = r6966874 + r6966875;
        double r6966877 = r6966873 + r6966876;
        double r6966878 = t;
        double r6966879 = sqrt(r6966878);
        double r6966880 = log(r6966879);
        double r6966881 = r6966873 * r6966880;
        double r6966882 = r6966877 - r6966881;
        double r6966883 = r6966882 - r6966881;
        double r6966884 = r6966872 + r6966883;
        return r6966884;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--r+0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :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)))