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

Average Error: 0.3 → 0.3

Time: 5.1s

Precision: 64

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

Math

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

↓

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

C

double f(double x, double y) {
        double r815348 = x;
        double r815349 = 3.0;
        double r815350 = r815348 * r815349;
        double r815351 = y;
        double r815352 = r815350 * r815351;
        double r815353 = r815352 * r815351;
        return r815353;
}

↓

double f(double x, double y) {
        double r815354 = 3.0;
        double r815355 = y;
        double r815356 = r815354 * r815355;
        double r815357 = x;
        double r815358 = r815355 * r815357;
        double r815359 = r815356 * r815358;
        return r815359;
}

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 associate-*l* 0.3

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

5. Applied pow1 0.3

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

6. Applied pow1 0.3

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

7. Applied pow-prod-down 0.3

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

8. Applied pow1 0.3

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

9. Applied pow-prod-down 0.3

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

10. Simplified 0.3

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

12. Applied unpow-prod-down 0.3

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

13. Applied associate-*l* 0.3

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

14. Simplified 0.3

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

15. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))