Average Error: 0.1 → 0.1
Time: 10.7s
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 r443006 = x;
        double r443007 = y;
        double r443008 = z;
        double r443009 = r443007 + r443008;
        double r443010 = r443006 * r443009;
        double r443011 = 5.0;
        double r443012 = r443008 * r443011;
        double r443013 = r443010 + r443012;
        return r443013;
}
↓
double f(double x, double y, double z) {
        double r443014 = x;
        double r443015 = y;
        double r443016 = z;
        double r443017 = r443015 + r443016;
        double r443018 = 5.0;
        double r443019 = r443016 * r443018;
        double r443020 = fma(r443014, r443017, r443019);
        return r443020;
}

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 2019208 +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)))