Average Error: 0.1 → 0.1
Time: 8.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot {t}^{\frac{1}{3}}\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot {t}^{\frac{1}{3}}\right) \cdot z\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 r416657 = x;
        double r416658 = y;
        double r416659 = r416657 + r416658;
        double r416660 = z;
        double r416661 = r416659 + r416660;
        double r416662 = t;
        double r416663 = log(r416662);
        double r416664 = r416660 * r416663;
        double r416665 = r416661 - r416664;
        double r416666 = a;
        double r416667 = 0.5;
        double r416668 = r416666 - r416667;
        double r416669 = b;
        double r416670 = r416668 * r416669;
        double r416671 = r416665 + r416670;
        return r416671;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r416672 = x;
        double r416673 = y;
        double r416674 = r416672 + r416673;
        double r416675 = z;
        double r416676 = r416674 + r416675;
        double r416677 = t;
        double r416678 = cbrt(r416677);
        double r416679 = 0.3333333333333333;
        double r416680 = pow(r416677, r416679);
        double r416681 = r416678 * r416680;
        double r416682 = log(r416681);
        double r416683 = r416682 * r416675;
        double r416684 = r416676 - r416683;
        double r416685 = log(r416678);
        double r416686 = r416685 * r416675;
        double r416687 = r416684 - r416686;
        double r416688 = a;
        double r416689 = 0.5;
        double r416690 = r416688 - r416689;
        double r416691 = b;
        double r416692 = r416690 * r416691;
        double r416693 = r416687 + r416692;
        return r416693;
}

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. Using strategy rm

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(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)))