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

Average Error: 0.0 → 0

Time: 345.0ms

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 r73082 = x;
        double r73083 = y;
        double r73084 = r73082 + r73083;
        double r73085 = r73084 + r73082;
        return r73085;
}

↓

double f(double x, double y) {
        double r73086 = 2.0;
        double r73087 = x;
        double r73088 = y;
        double r73089 = fma(r73086, r73087, r73088);
        return r73089;
}

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 2020045 +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))