Average Error: 0.0 → 0
Time: 1.5s
Precision: binary64
\[\left(x + y\right) + x\]
↓
\[y + \left(x + x\right)\]
\left(x + y\right) + x
↓
y + \left(x + x\right)
double code(double x, double y) {
	return ((double) (((double) (x + y)) + x));
}
↓
double code(double x, double y) {
	return ((double) (y + ((double) (x + x))));
}

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-+47.5

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

  4. Simplified47.5

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

  5. Simplified24.1

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

  6. Taylor expanded around 0 0

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

  7. Simplified0

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

  8. Final simplification0

    \[\leadsto y + \left(x + x\right)\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))