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

Average Error: 0.3 → 0.2

Time: 19.1s

Precision: 64

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 r493670 = x;
        double r493671 = 3.0;
        double r493672 = r493670 * r493671;
        double r493673 = y;
        double r493674 = r493672 * r493673;
        double r493675 = r493674 * r493673;
        return r493675;
}

↓

double f(double x, double y) {
        double r493676 = 3.0;
        double r493677 = y;
        double r493678 = r493676 * r493677;
        double r493679 = x;
        double r493680 = r493677 * r493679;
        double r493681 = r493678 * r493680;
        return r493681;
}

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

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

7. Applied pow1 0.2

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

8. Applied pow-prod-down 0.2

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

9. Applied pow1 0.2

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

10. Applied pow-prod-down 0.2

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

11. Simplified 0.3

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

13. Applied unpow-prod-down 0.3

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

14. Applied associate-*l* 0.2

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

15. Simplified 0.2

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

16. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019322 
(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))