Average Error: 0.1 → 0.1
Time: 13.4s
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 r381572 = x;
        double r381573 = y;
        double r381574 = z;
        double r381575 = r381573 + r381574;
        double r381576 = r381572 * r381575;
        double r381577 = 5.0;
        double r381578 = r381574 * r381577;
        double r381579 = r381576 + r381578;
        return r381579;
}
↓
double f(double x, double y, double z) {
        double r381580 = x;
        double r381581 = y;
        double r381582 = z;
        double r381583 = r381581 + r381582;
        double r381584 = 5.0;
        double r381585 = r381582 * r381584;
        double r381586 = fma(r381580, r381583, r381585);
        return r381586;
}

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 2019326 +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)))