Average Error: 0.0 → 0.0
Time: 1.8s
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 r227352 = x;
        double r227353 = 2.0;
        double r227354 = r227352 / r227353;
        double r227355 = y;
        double r227356 = r227355 * r227352;
        double r227357 = r227354 + r227356;
        double r227358 = z;
        double r227359 = r227357 + r227358;
        return r227359;
}
↓
double f(double x, double y, double z) {
        double r227360 = x;
        double r227361 = y;
        double r227362 = z;
        double r227363 = fma(r227360, r227361, r227362);
        double r227364 = 2.0;
        double r227365 = r227360 / r227364;
        double r227366 = r227363 + r227365;
        return r227366;
}

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 2020089 +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))