Average Error: 0.1 → 0.1
Time: 14.6s
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 r399869 = x;
        double r399870 = y;
        double r399871 = z;
        double r399872 = r399870 + r399871;
        double r399873 = r399869 * r399872;
        double r399874 = 5.0;
        double r399875 = r399871 * r399874;
        double r399876 = r399873 + r399875;
        return r399876;
}
↓
double f(double x, double y, double z) {
        double r399877 = x;
        double r399878 = y;
        double r399879 = z;
        double r399880 = r399878 + r399879;
        double r399881 = 5.0;
        double r399882 = r399879 * r399881;
        double r399883 = fma(r399877, r399880, r399882);
        return r399883;
}

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 2019323 +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)))