Average Error: 0.1 → 0.1
Time: 11.9s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5\]
↓
\[\mathsf{fma}\left(x, y + z, z \cdot 5\right)\]
x \cdot \left(y + z\right) + z \cdot 5
↓
\mathsf{fma}\left(x, y + z, z \cdot 5\right)
double f(double x, double y, double z) {
        double r319065 = x;
        double r319066 = y;
        double r319067 = z;
        double r319068 = r319066 + r319067;
        double r319069 = r319065 * r319068;
        double r319070 = 5.0;
        double r319071 = r319067 * r319070;
        double r319072 = r319069 + r319071;
        return r319072;
}
↓
double f(double x, double y, double z) {
        double r319073 = x;
        double r319074 = y;
        double r319075 = z;
        double r319076 = r319074 + r319075;
        double r319077 = 5.0;
        double r319078 = r319075 * r319077;
        double r319079 = fma(r319073, r319076, r319078);
        return r319079;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(x + 5\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y + z, z \cdot 5\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, y + z, z \cdot 5\right)\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5) z) (* x y))

  (+ (* x (+ y z)) (* z 5)))