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

Average Error: 0.3 → 0.2

Time: 6.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r584084 = x;
        double r584085 = 3.0;
        double r584086 = r584084 * r584085;
        double r584087 = y;
        double r584088 = r584086 * r584087;
        double r584089 = r584088 * r584087;
        return r584089;
}

↓

double f(double x, double y) {
        double r584090 = y;
        double r584091 = 3.0;
        double r584092 = r584090 * r584091;
        double r584093 = x;
        double r584094 = r584093 * r584090;
        double r584095 = r584092 * r584094;
        return r584095;
}

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. Using strategy rm

3. Applied associate-*l* 0.2

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

4. Simplified 0.2

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

6. Applied pow1 0.2

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

7. Applied pow1 0.2

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

8. Applied pow1 0.2

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

9. Applied pow-prod-down 0.2

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

10. Applied pow1 0.2

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

11. Applied pow-prod-down 0.2

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

12. Applied pow-prod-down 0.2

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

13. Simplified 0.2

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

15. Applied associate-*r* 0.2

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

16. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019235 
(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))