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

Average Error: 0.3 → 0.2

Time: 1.2s

Precision: 64

Math

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

↓

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

C

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

↓

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

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 *-commutative 0.3

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

4. Applied associate-*l* 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020078 
(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))