Average Error: 0.0 → 0
Time: 1.0s
Precision: 64
\[\left(x + y\right) + x\]
↓
\[\mathsf{fma}\left(2, x, y\right)\]
\left(x + y\right) + x
↓
\mathsf{fma}\left(2, x, y\right)
double f(double x, double y) {
        double r358712 = x;
        double r358713 = y;
        double r358714 = r358712 + r358713;
        double r358715 = r358714 + r358712;
        return r358715;
}
↓
double f(double x, double y) {
        double r358716 = 2.0;
        double r358717 = x;
        double r358718 = y;
        double r358719 = fma(r358716, r358717, r358718);
        return r358719;
}

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Target0
Herbie0
\[y + 2 \cdot x\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019303 +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))