Average Error: 0.0 → 0
Time: 405.0ms
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 r541661 = x;
        double r541662 = y;
        double r541663 = r541661 + r541662;
        double r541664 = r541663 + r541661;
        return r541664;
}
↓
double f(double x, double y) {
        double r541665 = 2.0;
        double r541666 = x;
        double r541667 = y;
        double r541668 = fma(r541665, r541666, r541667);
        return r541668;
}

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 2020001 +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))