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

Average Error: 10.3 → 0.3

Time: 6.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r679877 = x;
        double r679878 = 3.0;
        double r679879 = r679877 * r679878;
        double r679880 = r679879 * r679877;
        double r679881 = y;
        double r679882 = r679880 * r679881;
        return r679882;
}

↓

double f(double x, double y) {
        double r679883 = x;
        double r679884 = y;
        double r679885 = 3.0;
        double r679886 = r679884 * r679885;
        double r679887 = r679886 * r679883;
        double r679888 = r679883 * r679887;
        return r679888;
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.3
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.3

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

2. Simplified 10.3

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

4. Applied pow1 10.3

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

5. Applied pow1 10.3

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

6. Applied pow1 10.3

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

7. Applied pow-prod-down 10.3

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

8. Applied pow1 10.3

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

9. Applied pow-prod-down 10.3

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

10. Applied pow-prod-down 10.3

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

11. Simplified 0.2

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

12. Taylor expanded around 0 10.3

    \[\leadsto {\color{blue}{\left(3 \cdot \left({x}^{2} \cdot y\right)\right)}}^{1}\]

13. Simplified 0.3

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

15. Applied associate-*r* 0.3

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

16. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019194 
(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))