Average Error: 10.4 → 0.2
Time: 2.2s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y\]
↓
\[3 \cdot \left(x \cdot \left(x \cdot y\right)\right)\]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
3 \cdot \left(x \cdot \left(x \cdot y\right)\right)
(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))
↓
(FPCore (x y) :precision binary64 (* 3.0 (* x (* x y))))
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

Original10.4
Target0.2
Herbie0.2
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right)\]

Derivation

  1. Initial program 10.4

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

  2. Taylor expanded around 0 10.4

    \[\leadsto \color{blue}{3 \cdot \left({x}^{2} \cdot y\right)}\]

  3. Simplified10.4

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

  5. Applied associate-*l*_binary640.2

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

  6. Final simplification0.2

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

Alternatives

Reproduce

herbie shell --seed 2021110 
(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))