Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, y, \frac{x}{2}\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(x, y, \frac{x}{2}\right) + z
double f(double x, double y, double z) {
        double r163714 = x;
        double r163715 = 2.0;
        double r163716 = r163714 / r163715;
        double r163717 = y;
        double r163718 = r163717 * r163714;
        double r163719 = r163716 + r163718;
        double r163720 = z;
        double r163721 = r163719 + r163720;
        return r163721;
}
↓
double f(double x, double y, double z) {
        double r163722 = x;
        double r163723 = y;
        double r163724 = 2.0;
        double r163725 = r163722 / r163724;
        double r163726 = fma(r163722, r163723, r163725);
        double r163727 = z;
        double r163728 = r163726 + r163727;
        return r163728;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +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))