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

Average Error: 0.0 → 0

Time: 3.4s

Precision: 64

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

Math

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

↓

\[2 \cdot x + y\]

C

double f(double x, double y) {
        double r567388 = x;
        double r567389 = y;
        double r567390 = r567388 + r567389;
        double r567391 = r567390 + r567388;
        return r567391;
}

↓

double f(double x, double y) {
        double r567392 = 2.0;
        double r567393 = x;
        double r567394 = r567392 * r567393;
        double r567395 = y;
        double r567396 = r567394 + r567395;
        return r567396;
}

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 42.2

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

4. Simplified 42.2

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

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 2019350 
(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))