Average Error: 0.0 → 0.0
Time: 2.8s
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 r129094 = x;
        double r129095 = 2.0;
        double r129096 = r129094 / r129095;
        double r129097 = y;
        double r129098 = r129097 * r129094;
        double r129099 = r129096 + r129098;
        double r129100 = z;
        double r129101 = r129099 + r129100;
        return r129101;
}
↓
double f(double x, double y, double z) {
        double r129102 = x;
        double r129103 = y;
        double r129104 = 2.0;
        double r129105 = r129102 / r129104;
        double r129106 = fma(r129102, r129103, r129105);
        double r129107 = z;
        double r129108 = r129106 + r129107;
        return r129108;
}

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 2019208 +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))