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

Average Error: 10.4 → 0.2

Time: 2.4s

Precision: binary64

Math

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

↓

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

C

double code(double x, double y) {
	return ((double) (((double) (((double) (x * 3.0)) * x)) * y));
}

↓

double code(double x, double y) {
	return ((double) (x * ((double) (3.0 * ((double) (x * y))))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.4
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 10.4

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

3. Applied associate-*l* 0.2

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

5. Applied associate-*l* 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020150 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

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

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