Average Error: 0.0 → 0.0
Time: 519.0ms
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 r232164 = x;
        double r232165 = 2.0;
        double r232166 = r232164 / r232165;
        double r232167 = y;
        double r232168 = r232167 * r232164;
        double r232169 = r232166 + r232168;
        double r232170 = z;
        double r232171 = r232169 + r232170;
        return r232171;
}
↓
double f(double x, double y, double z) {
        double r232172 = x;
        double r232173 = y;
        double r232174 = z;
        double r232175 = fma(r232172, r232173, r232174);
        double r232176 = 2.0;
        double r232177 = r232172 / r232176;
        double r232178 = r232175 + r232177;
        return r232178;
}

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 2020064 +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))