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

Average Error: 0.0 → 0

Time: 400.0ms

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 r435729 = x;
        double r435730 = y;
        double r435731 = r435729 + r435730;
        double r435732 = r435731 + r435729;
        return r435732;
}

↓

double f(double x, double y) {
        double r435733 = 2.0;
        double r435734 = x;
        double r435735 = y;
        double r435736 = fma(r435733, r435734, r435735);
        return r435736;
}

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 2019351 +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))