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

Average Error: 0.3 → 0.3

Time: 8.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y) {
        double r668908 = x;
        double r668909 = 3.0;
        double r668910 = r668908 * r668909;
        double r668911 = y;
        double r668912 = r668910 * r668911;
        double r668913 = r668912 * r668911;
        return r668913;
}

↓

double f(double x, double y) {
        double r668914 = 3.0;
        double r668915 = y;
        double r668916 = r668914 * r668915;
        double r668917 = x;
        double r668918 = r668917 * r668915;
        double r668919 = r668916 * r668918;
        return r668919;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.3
Herbie	0.3

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

Derivation

1. Initial program 0.3

   \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
2. Using strategy rm

3. Applied pow1 0.3

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

4. Applied pow1 0.3

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

5. Applied pow1 0.3

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

6. Applied pow-prod-down 0.3

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

7. Applied pow-prod-down 0.3

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

8. Simplified 0.3

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

10. Applied unpow-prod-down 0.3

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

11. Applied associate-*l* 0.3

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

12. Simplified 0.3

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

14. Applied associate-*r* 0.3

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

15. Simplified 0.3

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

16. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (* (* x (* 3 y)) y)

  (* (* (* x 3) y) y))