Average Error: 0.0 → 0
Time: 441.0ms
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 r497214 = x;
        double r497215 = y;
        double r497216 = r497214 + r497215;
        double r497217 = r497216 + r497214;
        return r497217;
}
↓
double f(double x, double y) {
        double r497218 = 2.0;
        double r497219 = x;
        double r497220 = y;
        double r497221 = fma(r497218, r497219, r497220);
        return r497221;
}

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 2020033 +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))