Average Error: 0.1 → 0.1
Time: 7.4s
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 r605107 = x;
        double r605108 = y;
        double r605109 = z;
        double r605110 = r605108 + r605109;
        double r605111 = r605107 * r605110;
        double r605112 = 5.0;
        double r605113 = r605109 * r605112;
        double r605114 = r605111 + r605113;
        return r605114;
}
↓
double f(double x, double y, double z) {
        double r605115 = x;
        double r605116 = y;
        double r605117 = z;
        double r605118 = r605116 + r605117;
        double r605119 = 5.0;
        double r605120 = r605117 * r605119;
        double r605121 = fma(r605115, r605118, r605120);
        return r605121;
}

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 2020047 +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)))