System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Average Error: 0.1 → 0.1

Time: 21.2s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

↓

\[x \cdot 0.5 + \left(y \cdot \left(\left(1.0 - z\right) + \left(\log \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]

C

double f(double x, double y, double z) {
        double r17298641 = x;
        double r17298642 = 0.5;
        double r17298643 = r17298641 * r17298642;
        double r17298644 = y;
        double r17298645 = 1.0;
        double r17298646 = z;
        double r17298647 = r17298645 - r17298646;
        double r17298648 = log(r17298646);
        double r17298649 = r17298647 + r17298648;
        double r17298650 = r17298644 * r17298649;
        double r17298651 = r17298643 + r17298650;
        return r17298651;
}

↓

double f(double x, double y, double z) {
        double r17298652 = x;
        double r17298653 = 0.5;
        double r17298654 = r17298652 * r17298653;
        double r17298655 = y;
        double r17298656 = 1.0;
        double r17298657 = z;
        double r17298658 = r17298656 - r17298657;
        double r17298659 = cbrt(r17298657);
        double r17298660 = cbrt(r17298659);
        double r17298661 = r17298660 * r17298660;
        double r17298662 = r17298661 * r17298660;
        double r17298663 = log(r17298662);
        double r17298664 = log(r17298659);
        double r17298665 = r17298663 + r17298664;
        double r17298666 = r17298658 + r17298665;
        double r17298667 = r17298655 * r17298666;
        double r17298668 = r17298655 * r17298664;
        double r17298669 = r17298667 + r17298668;
        double r17298670 = r17298654 + r17298669;
        return r17298670;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

1. Initial program 0.1

   \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
2. Using strategy rm

3. Applied distribute-lft-in 0.1

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(1.0 - z\right) + y \cdot \log z\right)}\]
4. Using strategy rm

5. Applied add-cube-cbrt 0.1

   \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1.0 - z\right) + y \cdot \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\right)\]

6. Applied log-prod 0.1

   \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1.0 - z\right) + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\right)\]

7. Applied distribute-rgt-in 0.1

   \[\leadsto x \cdot 0.5 + \left(y \cdot \left(1.0 - z\right) + \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot y\right)}\right)\]

8. Applied associate-+r+ 0.1

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(y \cdot \left(1.0 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot y\right) + \log \left(\sqrt[3]{z}\right) \cdot y\right)}\]

9. Simplified 0.1

   \[\leadsto x \cdot 0.5 + \left(\color{blue}{\left(\left(1.0 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) \cdot y} + \log \left(\sqrt[3]{z}\right) \cdot y\right)\]
10. Using strategy rm

11. Applied add-cube-cbrt 0.1

    \[\leadsto x \cdot 0.5 + \left(\left(\left(1.0 - z\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right)}\right)\right) \cdot y + \log \left(\sqrt[3]{z}\right) \cdot y\right)\]

12. Final simplification 0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(\left(1.0 - z\right) + \left(\log \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z}}\right) \cdot \sqrt[3]{\sqrt[3]{z}}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

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

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))