Average Error: 0.0 → 0.0
Time: 3.2s
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 r240245 = x;
        double r240246 = 2.0;
        double r240247 = r240245 / r240246;
        double r240248 = y;
        double r240249 = r240248 * r240245;
        double r240250 = r240247 + r240249;
        double r240251 = z;
        double r240252 = r240250 + r240251;
        return r240252;
}
↓
double f(double x, double y, double z) {
        double r240253 = x;
        double r240254 = y;
        double r240255 = z;
        double r240256 = fma(r240253, r240254, r240255);
        double r240257 = 2.0;
        double r240258 = r240253 / r240257;
        double r240259 = r240256 + r240258;
        return r240259;
}

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 2020060 +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))