Average Error: 0.0 → 0.0
Time: 524.0ms
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 r176240 = x;
        double r176241 = 2.0;
        double r176242 = r176240 / r176241;
        double r176243 = y;
        double r176244 = r176243 * r176240;
        double r176245 = r176242 + r176244;
        double r176246 = z;
        double r176247 = r176245 + r176246;
        return r176247;
}
↓
double f(double x, double y, double z) {
        double r176248 = x;
        double r176249 = y;
        double r176250 = z;
        double r176251 = fma(r176248, r176249, r176250);
        double r176252 = 2.0;
        double r176253 = r176248 / r176252;
        double r176254 = r176251 + r176253;
        return r176254;
}

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 2020027 +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))