Average Error: 0.0 → 0
Time: 554.0ms
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 r560311 = x;
        double r560312 = y;
        double r560313 = r560311 + r560312;
        double r560314 = r560313 + r560311;
        return r560314;
}
↓
double f(double x, double y) {
        double r560315 = 2.0;
        double r560316 = x;
        double r560317 = y;
        double r560318 = fma(r560315, r560316, r560317);
        return r560318;
}

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 2020035 +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))