Average Error: 0.0 → 0.0
Time: 5.1s
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 r232845 = x;
        double r232846 = 2.0;
        double r232847 = r232845 / r232846;
        double r232848 = y;
        double r232849 = r232848 * r232845;
        double r232850 = r232847 + r232849;
        double r232851 = z;
        double r232852 = r232850 + r232851;
        return r232852;
}
↓
double f(double x, double y, double z) {
        double r232853 = x;
        double r232854 = y;
        double r232855 = 2.0;
        double r232856 = r232853 / r232855;
        double r232857 = fma(r232853, r232854, r232856);
        double r232858 = z;
        double r232859 = r232857 + r232858;
        return r232859;
}

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 2019326 +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))