Average Error: 0.1 → 0.1
Time: 12.4s
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 r354869 = x;
        double r354870 = y;
        double r354871 = z;
        double r354872 = r354870 + r354871;
        double r354873 = r354869 * r354872;
        double r354874 = 5.0;
        double r354875 = r354871 * r354874;
        double r354876 = r354873 + r354875;
        return r354876;
}
↓
double f(double x, double y, double z) {
        double r354877 = x;
        double r354878 = y;
        double r354879 = z;
        double r354880 = r354878 + r354879;
        double r354881 = 5.0;
        double r354882 = r354879 * r354881;
        double r354883 = fma(r354877, r354880, r354882);
        return r354883;
}

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 2019322 +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)))