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

Average Error: 10.3 → 0.2

Time: 2.2s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))

↓

(FPCore (x y) :precision binary64 (* (* 3.0 x) (* x y)))

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Target

Original	10.3
Target	0.2
Herbie	0.2

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

Alternatives

Alternative 1
Error	41.3
Cost	64

\[0\]

Alternative 2
Error	61.8
Cost	64

\[1\]

Derivation

1. Initial program 10.3

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

3. Applied associate-*l*_binary64_20138 0.2

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

4. Simplified 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2021044 
(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))