Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(x, y, z\right) + \frac{x}{2}\]
\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 r1254 = x;
        double r1255 = 2.0;
        double r1256 = r1254 / r1255;
        double r1257 = y;
        double r1258 = r1257 * r1254;
        double r1259 = r1256 + r1258;
        double r1260 = z;
        double r1261 = r1259 + r1260;
        return r1261;
}
↓
double f(double x, double y, double z) {
        double r1262 = x;
        double r1263 = y;
        double r1264 = z;
        double r1265 = fma(r1262, r1263, r1264);
        double r1266 = 2.0;
        double r1267 = r1262 / r1266;
        double r1268 = r1265 + r1267;
        return r1268;
}

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 2020025 +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))