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

Average Error: 10.6 → 0.2

Time: 7.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r491481 = x;
        double r491482 = 3.0;
        double r491483 = r491481 * r491482;
        double r491484 = r491483 * r491481;
        double r491485 = y;
        double r491486 = r491484 * r491485;
        return r491486;
}

↓

double f(double x, double y) {
        double r491487 = x;
        double r491488 = y;
        double r491489 = r491487 * r491488;
        double r491490 = 3.0;
        double r491491 = r491489 * r491490;
        double r491492 = r491491 * r491487;
        return r491492;
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.6
Target	0.3
Herbie	0.2

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

Derivation

1. Initial program 10.6

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

3. Applied associate-*l* 0.3

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

4. Simplified 0.3

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

6. Applied associate-*l* 0.2

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

7. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019196 
(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))