Average Error: 0.0 → 0.0
Time: 667.0ms
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 r234455 = x;
        double r234456 = 2.0;
        double r234457 = r234455 / r234456;
        double r234458 = y;
        double r234459 = r234458 * r234455;
        double r234460 = r234457 + r234459;
        double r234461 = z;
        double r234462 = r234460 + r234461;
        return r234462;
}
↓
double f(double x, double y, double z) {
        double r234463 = x;
        double r234464 = y;
        double r234465 = z;
        double r234466 = fma(r234463, r234464, r234465);
        double r234467 = 2.0;
        double r234468 = r234463 / r234467;
        double r234469 = r234466 + r234468;
        return r234469;
}

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 2020024 +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))