Average Error: 0.0 → 0
Time: 2.3s
Precision: 64
\[\left(x + y\right) + x\]
↓
\[2 \cdot x + y\]
\left(x + y\right) + x
↓
2 \cdot x + y
double code(double x, double y) {
	return ((x + y) + x);
}
↓
double code(double x, double y) {
	return ((2.0 * 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

Original0.0
Target0
Herbie0
\[y + 2 \cdot x\]

Derivation

  1. Initial program 0.0

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

  3. Applied flip-+47.2

    \[\leadsto \color{blue}{\frac{\left(x + y\right) \cdot \left(x + y\right) - x \cdot x}{\left(x + y\right) - x}}\]

  4. Simplified47.2

    \[\leadsto \frac{\color{blue}{y \cdot \left(\left(x + y\right) + x\right)}}{\left(x + y\right) - x}\]

  5. Simplified23.3

    \[\leadsto \frac{y \cdot \left(\left(x + y\right) + x\right)}{\color{blue}{y}}\]
  6. Using strategy rm

  7. Applied associate-/l*7.6

    \[\leadsto \color{blue}{\frac{y}{\frac{y}{\left(x + y\right) + x}}}\]

  8. Taylor expanded around 0 0

    \[\leadsto \color{blue}{2 \cdot x + y}\]

  9. Final simplification0

    \[\leadsto 2 \cdot x + y\]

Reproduce

herbie shell --seed 2020075 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2 x))

  (+ (+ x y) x))