Average Error: 9.9 → 0.3
Time: 1.7s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot x\right) \cdot y \]
↓
\[x \cdot \left(\left(x \cdot 3\right) \cdot y\right) \]
\left(\left(x \cdot 3\right) \cdot x\right) \cdot y
↓
x \cdot \left(\left(x \cdot 3\right) \cdot y\right)

(FPCore (x y) :precision binary64 (* (* (* x 3.0) x) y))
↓
(FPCore (x y) :precision binary64 (* x (* (* x 3.0) y)))
double code(double x, double y) {
	return ((x * 3.0) * x) * y;
}
↓
double code(double x, double y) {
	return x * ((x * 3.0) * 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

Original9.9
Target0.2
Herbie0.3
\[\left(x \cdot 3\right) \cdot \left(x \cdot y\right) \]

Derivation

  1. Initial program 9.9

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

  2. Applied associate-*l*_binary640.2

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

  3. Applied associate-*l*_binary640.3

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

  4. Applied associate-*r*_binary640.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2022067 
(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))