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

Average Error: 10.1 → 0.2

Time: 2.7s

Precision: binary64

Math

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

↓

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

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) (((double) (x * 3.0)) * y))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	10.1
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 10.1

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

2. Simplified 0.3

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

4. Applied associate-*r* 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020196 
(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))