Average Error: 0.1 → 0.1
Time: 9.7s
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 r502935 = x;
        double r502936 = y;
        double r502937 = z;
        double r502938 = r502936 + r502937;
        double r502939 = r502935 * r502938;
        double r502940 = 5.0;
        double r502941 = r502937 * r502940;
        double r502942 = r502939 + r502941;
        return r502942;
}
↓
double f(double x, double y, double z) {
        double r502943 = x;
        double r502944 = y;
        double r502945 = z;
        double r502946 = r502944 + r502945;
        double r502947 = 5.0;
        double r502948 = r502945 * r502947;
        double r502949 = fma(r502943, r502946, r502948);
        return r502949;
}

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)))