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

Average Error: 0.0 → 0

Time: 340.0ms

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 r629672 = x;
        double r629673 = y;
        double r629674 = r629672 + r629673;
        double r629675 = r629674 + r629672;
        return r629675;
}

↓

double f(double x, double y) {
        double r629676 = 2.0;
        double r629677 = x;
        double r629678 = y;
        double r629679 = fma(r629676, r629677, r629678);
        return r629679;
}

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 2020042 +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))