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

Average Error: 0.3 → 0.2

Time: 15.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y) {
        double r996571 = x;
        double r996572 = 3.0;
        double r996573 = r996571 * r996572;
        double r996574 = y;
        double r996575 = r996573 * r996574;
        double r996576 = r996575 * r996574;
        return r996576;
}

↓

double f(double x, double y) {
        double r996577 = x;
        double r996578 = y;
        double r996579 = r996577 * r996578;
        double r996580 = 3.0;
        double r996581 = r996579 * r996580;
        double r996582 = r996581 * r996578;
        return r996582;
}

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 pow1 0.3

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

4. Applied pow1 0.3

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

5. Applied pow1 0.3

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

6. Applied pow-prod-down 0.3

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

7. Applied pow-prod-down 0.3

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

8. Simplified 0.2

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

9. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020042 
(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))