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

Average Error: 0.0 → 0

Time: 357.0ms

Precision: 64

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

Math

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

↓

\[\mathsf{fma}\left(2, x, y\right)\]

C

double f(double x, double y) {
        double r503095 = x;
        double r503096 = y;
        double r503097 = r503095 + r503096;
        double r503098 = r503097 + r503095;
        return r503098;
}

↓

double f(double x, double y) {
        double r503099 = 2.0;
        double r503100 = x;
        double r503101 = y;
        double r503102 = fma(r503099, r503100, r503101);
        return r503102;
}

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. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, y\right)}\]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(2, x, y\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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))