Average Error: 0.1 → 0.0
Time: 11.9s
Precision: 64
\[x \cdot \left(y + z\right) + z \cdot 5.0\]
↓
\[\mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)\]
x \cdot \left(y + z\right) + z \cdot 5.0
↓
\mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)
double f(double x, double y, double z) {
        double r25929880 = x;
        double r25929881 = y;
        double r25929882 = z;
        double r25929883 = r25929881 + r25929882;
        double r25929884 = r25929880 * r25929883;
        double r25929885 = 5.0;
        double r25929886 = r25929882 * r25929885;
        double r25929887 = r25929884 + r25929886;
        return r25929887;
}
↓
double f(double x, double y, double z) {
        double r25929888 = z;
        double r25929889 = 5.0;
        double r25929890 = x;
        double r25929891 = r25929889 + r25929890;
        double r25929892 = y;
        double r25929893 = r25929892 * r25929890;
        double r25929894 = fma(r25929888, r25929891, r25929893);
        return r25929894;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.0
\[\left(x + 5.0\right) \cdot z + x \cdot y\]

Derivation

  1. Initial program 0.1

    \[x \cdot \left(y + z\right) + z \cdot 5.0\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, 5.0 + x, x \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, 5.0 + x, y \cdot x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))