Average Error: 0.0 → 0.0
Time: 582.0ms
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 r181632 = x;
        double r181633 = 2.0;
        double r181634 = r181632 / r181633;
        double r181635 = y;
        double r181636 = r181635 * r181632;
        double r181637 = r181634 + r181636;
        double r181638 = z;
        double r181639 = r181637 + r181638;
        return r181639;
}
↓
double f(double x, double y, double z) {
        double r181640 = x;
        double r181641 = y;
        double r181642 = z;
        double r181643 = fma(r181640, r181641, r181642);
        double r181644 = 2.0;
        double r181645 = r181640 / r181644;
        double r181646 = r181643 + r181645;
        return r181646;
}

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 2020002 +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))