Average Error: 0.1 → 0.1
Time: 12.4s
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 r314114 = x;
        double r314115 = y;
        double r314116 = z;
        double r314117 = r314115 + r314116;
        double r314118 = r314114 * r314117;
        double r314119 = 5.0;
        double r314120 = r314116 * r314119;
        double r314121 = r314118 + r314120;
        return r314121;
}
↓
double f(double x, double y, double z) {
        double r314122 = x;
        double r314123 = y;
        double r314124 = z;
        double r314125 = r314123 + r314124;
        double r314126 = 5.0;
        double r314127 = r314124 * r314126;
        double r314128 = fma(r314122, r314125, r314127);
        return r314128;
}

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 2019304 +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)))