Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A

Average Error: 10.6 → 0.3

Time: 7.6s

Precision: 64

Math

\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]

↓

\[\left(3 \cdot x\right) \cdot \left(x \cdot y\right)\]

C

double f(double x, double y) {
        double r812928 = x;
        double r812929 = 3.0;
        double r812930 = r812928 * r812929;
        double r812931 = r812930 * r812928;
        double r812932 = y;
        double r812933 = r812931 * r812932;
        return r812933;
}

↓

double f(double x, double y) {
        double r812934 = 3.0;
        double r812935 = x;
        double r812936 = r812934 * r812935;
        double r812937 = y;
        double r812938 = r812935 * r812937;
        double r812939 = r812936 * r812938;
        return r812939;
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.6
Target	0.3
Herbie	0.3

\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

1. Initial program 10.6

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]

2. Simplified 10.6

   \[\leadsto \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right) \cdot y}\]
3. Using strategy rm

4. Applied associate-*l* 0.2

   \[\leadsto \color{blue}{x \cdot \left(\left(x \cdot 3\right) \cdot y\right)}\]

5. Simplified 0.3

   \[\leadsto x \cdot \color{blue}{\left(x \cdot \left(3 \cdot y\right)\right)}\]
6. Using strategy rm

7. Applied associate-*r* 0.2

   \[\leadsto x \cdot \color{blue}{\left(\left(x \cdot 3\right) \cdot y\right)}\]
8. Using strategy rm

9. Applied pow1 0.2

   \[\leadsto x \cdot \left(\left(x \cdot 3\right) \cdot \color{blue}{{y}^{1}}\right)\]

10. Applied pow1 0.2

    \[\leadsto x \cdot \left(\left(x \cdot \color{blue}{{3}^{1}}\right) \cdot {y}^{1}\right)\]

11. Applied pow1 0.2

    \[\leadsto x \cdot \left(\left(\color{blue}{{x}^{1}} \cdot {3}^{1}\right) \cdot {y}^{1}\right)\]

12. Applied pow-prod-down 0.2

    \[\leadsto x \cdot \left(\color{blue}{{\left(x \cdot 3\right)}^{1}} \cdot {y}^{1}\right)\]

13. Applied pow-prod-down 0.2

    \[\leadsto x \cdot \color{blue}{{\left(\left(x \cdot 3\right) \cdot y\right)}^{1}}\]

14. Applied pow1 0.2

    \[\leadsto \color{blue}{{x}^{1}} \cdot {\left(\left(x \cdot 3\right) \cdot y\right)}^{1}\]

15. Applied pow-prod-down 0.2

    \[\leadsto \color{blue}{{\left(x \cdot \left(\left(x \cdot 3\right) \cdot y\right)\right)}^{1}}\]

16. Simplified 0.2

    \[\leadsto {\color{blue}{\left(\left(\left(x \cdot y\right) \cdot 3\right) \cdot x\right)}}^{1}\]
17. Using strategy rm

18. Applied associate-*l* 0.3

    \[\leadsto {\color{blue}{\left(\left(x \cdot y\right) \cdot \left(3 \cdot x\right)\right)}}^{1}\]

19. Final simplification 0.3

    \[\leadsto \left(3 \cdot x\right) \cdot \left(x \cdot y\right)\]

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* (* x 3.0) (* x y))

  (* (* (* x 3.0) x) y))