Average Error: 0.0 → 0.0
Time: 5.8s
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 r176287 = x;
        double r176288 = 2.0;
        double r176289 = r176287 / r176288;
        double r176290 = y;
        double r176291 = r176290 * r176287;
        double r176292 = r176289 + r176291;
        double r176293 = z;
        double r176294 = r176292 + r176293;
        return r176294;
}
↓
double f(double x, double y, double z) {
        double r176295 = x;
        double r176296 = y;
        double r176297 = 2.0;
        double r176298 = r176295 / r176297;
        double r176299 = fma(r176295, r176296, r176298);
        double r176300 = z;
        double r176301 = r176299 + r176300;
        return r176301;
}

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 2019323 +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))