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

Average Error: 0.0 → 0

Time: 354.0ms

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 r613237 = x;
        double r613238 = y;
        double r613239 = r613237 + r613238;
        double r613240 = r613239 + r613237;
        return r613240;
}

↓

double f(double x, double y) {
        double r613241 = 2.0;
        double r613242 = x;
        double r613243 = y;
        double r613244 = fma(r613241, r613242, r613243);
        return r613244;
}

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 2020047 +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))