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

Average Error: 10.5 → 0.2

Time: 1.7s

Precision: 64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Target

Original	10.5
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 10.5

   \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
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. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* (* x 3) (* x y))

  (* (* (* x 3) x) y))