Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + \mathsf{fma}\left(x, y, \frac{x}{2}\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + \mathsf{fma}\left(x, y, \frac{x}{2}\right)
double f(double x, double y, double z) {
        double r10993152 = x;
        double r10993153 = 2.0;
        double r10993154 = r10993152 / r10993153;
        double r10993155 = y;
        double r10993156 = r10993155 * r10993152;
        double r10993157 = r10993154 + r10993156;
        double r10993158 = z;
        double r10993159 = r10993157 + r10993158;
        return r10993159;
}
↓
double f(double x, double y, double z) {
        double r10993160 = z;
        double r10993161 = x;
        double r10993162 = y;
        double r10993163 = 2.0;
        double r10993164 = r10993161 / r10993163;
        double r10993165 = fma(r10993161, r10993162, r10993164);
        double r10993166 = r10993160 + r10993165;
        return r10993166;
}

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

    \[\leadsto z + \mathsf{fma}\left(x, y, \frac{x}{2}\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))