Average Error: 10.6 → 0.3
Time: 1.0s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
3 \cdot \left(x \cdot \left(x \cdot y\right)\right)
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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target0.2
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.6

    \[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
  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 *-commutative0.2

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

  6. Applied associate-*l*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020078 
(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))