Average Error: 0.0 → 0.0
Time: 5.7s
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 r156804 = x;
        double r156805 = 2.0;
        double r156806 = r156804 / r156805;
        double r156807 = y;
        double r156808 = r156807 * r156804;
        double r156809 = r156806 + r156808;
        double r156810 = z;
        double r156811 = r156809 + r156810;
        return r156811;
}
↓
double f(double x, double y, double z) {
        double r156812 = x;
        double r156813 = y;
        double r156814 = 2.0;
        double r156815 = r156812 / r156814;
        double r156816 = fma(r156812, r156813, r156815);
        double r156817 = z;
        double r156818 = r156816 + r156817;
        return r156818;
}

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 2019303 +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))