Average Error: 0.0 → 0.0
Time: 10.1s
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 r301044 = x;
        double r301045 = 2.0;
        double r301046 = r301044 / r301045;
        double r301047 = y;
        double r301048 = r301047 * r301044;
        double r301049 = r301046 + r301048;
        double r301050 = z;
        double r301051 = r301049 + r301050;
        return r301051;
}
↓
double f(double x, double y, double z) {
        double r301052 = x;
        double r301053 = y;
        double r301054 = z;
        double r301055 = fma(r301052, r301053, r301054);
        double r301056 = 2.0;
        double r301057 = r301052 / r301056;
        double r301058 = r301055 + r301057;
        return r301058;
}

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 2020081 +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))