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

Average Error: 0.3 → 0.2

Time: 7.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r570192 = x;
        double r570193 = 3.0;
        double r570194 = r570192 * r570193;
        double r570195 = y;
        double r570196 = r570194 * r570195;
        double r570197 = r570196 * r570195;
        return r570197;
}

↓

double f(double x, double y) {
        double r570198 = y;
        double r570199 = x;
        double r570200 = r570199 * r570198;
        double r570201 = 3.0;
        double r570202 = r570200 * r570201;
        double r570203 = r570198 * r570202;
        return r570203;
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

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

2. Simplified 0.2

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

4. Applied pow1 0.2

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

5. Applied pow1 0.2

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

6. Applied pow-prod-down 0.2

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

7. Applied pow1 0.2

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

8. Applied pow1 0.2

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

9. Applied pow-prod-down 0.2

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

10. Applied pow-prod-down 0.2

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

11. Simplified 0.2

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

13. Applied *-un-lft-identity 0.2

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

14. Applied associate-*r* 0.2

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

15. Simplified 0.2

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

16. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))