Average Error: 0.0 → 0.0
Time: 1.1s
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 r164833 = x;
        double r164834 = 2.0;
        double r164835 = r164833 / r164834;
        double r164836 = y;
        double r164837 = r164836 * r164833;
        double r164838 = r164835 + r164837;
        double r164839 = z;
        double r164840 = r164838 + r164839;
        return r164840;
}
↓
double f(double x, double y, double z) {
        double r164841 = x;
        double r164842 = y;
        double r164843 = 2.0;
        double r164844 = r164841 / r164843;
        double r164845 = fma(r164841, r164842, r164844);
        double r164846 = z;
        double r164847 = r164845 + r164846;
        return r164847;
}

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 2019212 +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))