Average Error: 0.0 → 0.0
Time: 960.0ms
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}
double f(double x, double y, double z) {
        double r236164 = x;
        double r236165 = 2.0;
        double r236166 = r236164 / r236165;
        double r236167 = y;
        double r236168 = r236167 * r236164;
        double r236169 = r236166 + r236168;
        double r236170 = z;
        double r236171 = r236169 + r236170;
        return r236171;
}
↓
double f(double x, double y, double z) {
        double r236172 = x;
        double r236173 = y;
        double r236174 = z;
        double r236175 = fma(r236172, r236173, r236174);
        double r236176 = 2.0;
        double r236177 = r236172 / r236176;
        double r236178 = r236175 + r236177;
        return r236178;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2} + y \cdot x\right) + z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, z\right) + \frac{x}{2}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  :precision binary64
  (+ (+ (/ x 2) (* y x)) z))