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

Average Error: 10.4 → 0.3

Time: 9.2s

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 r866294 = x;
        double r866295 = 3.0;
        double r866296 = r866294 * r866295;
        double r866297 = r866296 * r866294;
        double r866298 = y;
        double r866299 = r866297 * r866298;
        return r866299;
}

↓

double f(double x, double y) {
        double r866300 = y;
        double r866301 = 3.0;
        double r866302 = r866300 * r866301;
        double r866303 = x;
        double r866304 = r866302 * r866303;
        double r866305 = r866304 * r866303;
        return r866305;
}

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 *-un-lft-identity 0.2

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

8. Applied associate-*l* 0.2

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

9. Simplified 0.3

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

11. Applied associate-*r* 0.3

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

12. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020047 
(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))