Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A

Average Error: 0.0 → 0

Time: 5.0s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[2 \cdot x + y\]

C

double code(double x, double y) {
	return ((double) (((double) (x + y)) + x));
}

↓

double code(double x, double y) {
	return ((double) (((double) (2.0 * x)) + y));
}

Error

Bits error versus x

Bits error versus y

Target

Original	0.0
Target	0
Herbie	0

\[y + 2 \cdot x\]

Derivation

1. Initial program 0.0

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

3. Applied add-cbrt-cube 42.4

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

4. Simplified 42.4

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

5. Taylor expanded around 0 0

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

6. Final simplification 0

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

Reproduce

herbie shell --seed 2020182 
(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))