Average Error: 0.0 → 0.0
Time: 520.0ms
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 r215090 = x;
        double r215091 = 2.0;
        double r215092 = r215090 / r215091;
        double r215093 = y;
        double r215094 = r215093 * r215090;
        double r215095 = r215092 + r215094;
        double r215096 = z;
        double r215097 = r215095 + r215096;
        return r215097;
}
↓
double f(double x, double y, double z) {
        double r215098 = x;
        double r215099 = y;
        double r215100 = z;
        double r215101 = fma(r215098, r215099, r215100);
        double r215102 = 2.0;
        double r215103 = r215098 / r215102;
        double r215104 = r215101 + r215103;
        return r215104;
}

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 2020056 +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))