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

Average Error: 0.1 → 0.1

Time: 17.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r14507616 = x;
        double r14507617 = 0.5;
        double r14507618 = r14507616 * r14507617;
        double r14507619 = y;
        double r14507620 = 1.0;
        double r14507621 = z;
        double r14507622 = r14507620 - r14507621;
        double r14507623 = log(r14507621);
        double r14507624 = r14507622 + r14507623;
        double r14507625 = r14507619 * r14507624;
        double r14507626 = r14507618 + r14507625;
        return r14507626;
}

↓

double f(double x, double y, double z) {
        double r14507627 = y;
        double r14507628 = z;
        double r14507629 = sqrt(r14507628);
        double r14507630 = cbrt(r14507629);
        double r14507631 = log(r14507630);
        double r14507632 = r14507627 * r14507631;
        double r14507633 = r14507630 * r14507630;
        double r14507634 = log(r14507633);
        double r14507635 = 1.0;
        double r14507636 = r14507635 - r14507628;
        double r14507637 = log(r14507629);
        double r14507638 = r14507636 + r14507637;
        double r14507639 = r14507634 + r14507638;
        double r14507640 = r14507627 * r14507639;
        double r14507641 = 0.5;
        double r14507642 = x;
        double r14507643 = r14507641 * r14507642;
        double r14507644 = r14507640 + r14507643;
        double r14507645 = r14507632 + r14507644;
        return r14507645;
}

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. Applied associate-+r+ 0.1

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

6. Applied add-sqr-sqrt 0.1

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

7. Applied log-prod 0.1

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

8. Applied distribute-lft-in 0.1

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

9. Applied associate-+r+ 0.1

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

11. Applied add-cube-cbrt 0.1

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

12. Applied log-prod 0.1

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

13. Applied distribute-rgt-in 0.1

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

14. Applied associate-+r+ 0.1

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

15. Simplified 0.1

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

16. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019164 
(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)))))