Average Error: 0.1 → 0.1
Time: 1.2s
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 r499856 = x;
        double r499857 = y;
        double r499858 = z;
        double r499859 = r499857 + r499858;
        double r499860 = r499856 * r499859;
        double r499861 = 5.0;
        double r499862 = r499858 * r499861;
        double r499863 = r499860 + r499862;
        return r499863;
}
↓
double f(double x, double y, double z) {
        double r499864 = x;
        double r499865 = y;
        double r499866 = z;
        double r499867 = r499865 + r499866;
        double r499868 = 5.0;
        double r499869 = r499866 * r499868;
        double r499870 = fma(r499864, r499867, r499869);
        return r499870;
}

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 2020033 +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)))