Average Error: 0.0 → 0.0
Time: 658.0ms
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 r244780 = x;
        double r244781 = 2.0;
        double r244782 = r244780 / r244781;
        double r244783 = y;
        double r244784 = r244783 * r244780;
        double r244785 = r244782 + r244784;
        double r244786 = z;
        double r244787 = r244785 + r244786;
        return r244787;
}
↓
double f(double x, double y, double z) {
        double r244788 = x;
        double r244789 = y;
        double r244790 = z;
        double r244791 = fma(r244788, r244789, r244790);
        double r244792 = 2.0;
        double r244793 = r244788 / r244792;
        double r244794 = r244791 + r244793;
        return r244794;
}

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 2020057 +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))