Average Error: 0.3 → 0.2
Time: 18.0s
Precision: binary64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(y \cdot 3\right) \cdot \left(x \cdot y\right)\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(y \cdot 3\right) \cdot \left(x \cdot y\right)
double code(double x, double y) {
	return ((double) (((double) (((double) (x * 3.0)) * y)) * y));
}
↓
double code(double x, double y) {
	return ((double) (((double) (y * 3.0)) * ((double) (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

Original0.3
Target0.2
Herbie0.2
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

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

  3. Applied associate-*l*0.2

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

  4. Simplified0.2

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

  5. Taylor expanded around 0 10.9

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))