Average Error: 0.1 → 0.1
Time: 15.9s
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 r33394263 = x;
        double r33394264 = y;
        double r33394265 = z;
        double r33394266 = r33394264 + r33394265;
        double r33394267 = r33394263 * r33394266;
        double r33394268 = 5.0;
        double r33394269 = r33394265 * r33394268;
        double r33394270 = r33394267 + r33394269;
        return r33394270;
}
↓
double f(double x, double y, double z) {
        double r33394271 = x;
        double r33394272 = y;
        double r33394273 = z;
        double r33394274 = r33394272 + r33394273;
        double r33394275 = 5.0;
        double r33394276 = r33394273 * r33394275;
        double r33394277 = fma(r33394271, r33394274, r33394276);
        return r33394277;
}

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 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))