Average Error: 0.1 → 0.1
Time: 6.1s
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 r550028 = x;
        double r550029 = y;
        double r550030 = z;
        double r550031 = r550029 + r550030;
        double r550032 = r550028 * r550031;
        double r550033 = 5.0;
        double r550034 = r550030 * r550033;
        double r550035 = r550032 + r550034;
        return r550035;
}
↓
double f(double x, double y, double z) {
        double r550036 = x;
        double r550037 = y;
        double r550038 = z;
        double r550039 = r550037 + r550038;
        double r550040 = 5.0;
        double r550041 = r550038 * r550040;
        double r550042 = fma(r550036, r550039, r550041);
        return r550042;
}

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 2020045 +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)))