Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(\log \left({z}^{\frac{1}{3}}\right) \cdot y + \left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + x \cdot 0.5\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(\log \left({z}^{\frac{1}{3}}\right) \cdot y + \left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + x \cdot 0.5
double f(double x, double y, double z) {
        double r299736 = x;
        double r299737 = 0.5;
        double r299738 = r299736 * r299737;
        double r299739 = y;
        double r299740 = 1.0;
        double r299741 = z;
        double r299742 = r299740 - r299741;
        double r299743 = log(r299741);
        double r299744 = r299742 + r299743;
        double r299745 = r299739 * r299744;
        double r299746 = r299738 + r299745;
        return r299746;
}
↓
double f(double x, double y, double z) {
        double r299747 = z;
        double r299748 = 0.3333333333333333;
        double r299749 = pow(r299747, r299748);
        double r299750 = log(r299749);
        double r299751 = y;
        double r299752 = r299750 * r299751;
        double r299753 = 1.0;
        double r299754 = 2.0;
        double r299755 = cbrt(r299747);
        double r299756 = log(r299755);
        double r299757 = r299754 * r299756;
        double r299758 = r299747 - r299757;
        double r299759 = r299753 - r299758;
        double r299760 = r299759 * r299751;
        double r299761 = r299752 + r299760;
        double r299762 = x;
        double r299763 = 0.5;
        double r299764 = r299762 * r299763;
        double r299765 = r299761 + r299764;
        return r299765;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1 - z\right) + y \cdot \log z\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate-+r+0.1

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

  9. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y} + \log \left(\sqrt[3]{z}\right) \cdot y\right)\]
  10. Using strategy rm

  11. Applied pow10.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot \color{blue}{{y}^{1}}\right)\]

  12. Applied pow10.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \color{blue}{{\left(\log \left(\sqrt[3]{z}\right)\right)}^{1}} \cdot {y}^{1}\right)\]

  13. Applied pow-prod-down0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + \color{blue}{{\left(\log \left(\sqrt[3]{z}\right) \cdot y\right)}^{1}}\right)\]

  14. Simplified0.1

    \[\leadsto x \cdot 0.5 + \left(\left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y + {\color{blue}{\left(\log \left({z}^{\frac{1}{3}}\right) \cdot y\right)}}^{1}\right)\]

  15. Final simplification0.1

    \[\leadsto \left(\log \left({z}^{\frac{1}{3}}\right) \cdot y + \left(1 - \left(z - 2 \cdot \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))