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

Average Error: 10.4 → 0.3

Time: 10.5s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y) {
        double r757639 = x;
        double r757640 = 3.0;
        double r757641 = r757639 * r757640;
        double r757642 = r757641 * r757639;
        double r757643 = y;
        double r757644 = r757642 * r757643;
        return r757644;
}

↓

double f(double x, double y) {
        double r757645 = y;
        double r757646 = 3.0;
        double r757647 = r757645 * r757646;
        double r757648 = x;
        double r757649 = r757647 * r757648;
        double r757650 = r757649 * r757648;
        return r757650;
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.4
Target	0.2
Herbie	0.3

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

Derivation

1. Initial program 10.4

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

3. Applied associate-*l* 0.2

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

5. Applied associate-*l* 0.2

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

7. Applied pow1 0.2

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

8. Applied pow1 0.2

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

9. Applied pow-prod-down 0.2

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

10. Applied pow1 0.2

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

11. Applied pow-prod-down 0.2

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

12. Simplified 0.3

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

13. Taylor expanded around 0 0.2

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

14. Simplified 0.3

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

15. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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