Average Error: 0.1 → 0.1
Time: 22.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(x + y\right) + z\right) - \left(\log \left({t}^{\frac{1}{3}} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(x + y\right) + z\right) - \left(\log \left({t}^{\frac{1}{3}} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r27918796 = x;
        double r27918797 = y;
        double r27918798 = r27918796 + r27918797;
        double r27918799 = z;
        double r27918800 = r27918798 + r27918799;
        double r27918801 = t;
        double r27918802 = log(r27918801);
        double r27918803 = r27918799 * r27918802;
        double r27918804 = r27918800 - r27918803;
        double r27918805 = a;
        double r27918806 = 0.5;
        double r27918807 = r27918805 - r27918806;
        double r27918808 = b;
        double r27918809 = r27918807 * r27918808;
        double r27918810 = r27918804 + r27918809;
        return r27918810;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r27918811 = x;
        double r27918812 = y;
        double r27918813 = r27918811 + r27918812;
        double r27918814 = z;
        double r27918815 = r27918813 + r27918814;
        double r27918816 = t;
        double r27918817 = 0.3333333333333333;
        double r27918818 = pow(r27918816, r27918817);
        double r27918819 = cbrt(r27918816);
        double r27918820 = r27918818 * r27918819;
        double r27918821 = log(r27918820);
        double r27918822 = r27918821 * r27918814;
        double r27918823 = log(r27918819);
        double r27918824 = r27918823 * r27918814;
        double r27918825 = r27918822 + r27918824;
        double r27918826 = r27918815 - r27918825;
        double r27918827 = a;
        double r27918828 = 0.5;
        double r27918829 = r27918827 - r27918828;
        double r27918830 = b;
        double r27918831 = r27918829 * r27918830;
        double r27918832 = r27918826 + r27918831;
        return r27918832;
}

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
Target0.5
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. Using strategy rm

  7. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\log \left(\color{blue}{{t}^{\frac{1}{3}}} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

  8. Final simplification0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\log \left({t}^{\frac{1}{3}} \cdot \sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

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