Average Error: 0.1 → 0.1
Time: 12.7s
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 r396639 = x;
        double r396640 = y;
        double r396641 = z;
        double r396642 = r396640 + r396641;
        double r396643 = r396639 * r396642;
        double r396644 = 5.0;
        double r396645 = r396641 * r396644;
        double r396646 = r396643 + r396645;
        return r396646;
}
↓
double f(double x, double y, double z) {
        double r396647 = x;
        double r396648 = y;
        double r396649 = z;
        double r396650 = r396648 + r396649;
        double r396651 = 5.0;
        double r396652 = r396649 * r396651;
        double r396653 = fma(r396647, r396650, r396652);
        return r396653;
}

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 2019323 +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)))