Average Error: 0.0 → 0
Time: 887.0ms
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 r21019936 = x;
        double r21019937 = y;
        double r21019938 = r21019936 + r21019937;
        double r21019939 = r21019938 + r21019936;
        return r21019939;
}
↓
double f(double x, double y) {
        double r21019940 = 2.0;
        double r21019941 = x;
        double r21019942 = y;
        double r21019943 = fma(r21019940, r21019941, r21019942);
        return r21019943;
}

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 2019163 +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 x))

  (+ (+ x y) x))