Average Error: 0.0 → 0
Time: 2.8s
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 r25756254 = x;
        double r25756255 = y;
        double r25756256 = r25756254 + r25756255;
        double r25756257 = r25756256 + r25756254;
        return r25756257;
}
↓
double f(double x, double y) {
        double r25756258 = 2.0;
        double r25756259 = x;
        double r25756260 = y;
        double r25756261 = fma(r25756258, r25756259, r25756260);
        return r25756261;
}

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 2019200 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))