Average Error: 0.0 → 0.0
Time: 1.2s
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 r142414 = x;
        double r142415 = 2.0;
        double r142416 = r142414 / r142415;
        double r142417 = y;
        double r142418 = r142417 * r142414;
        double r142419 = r142416 + r142418;
        double r142420 = z;
        double r142421 = r142419 + r142420;
        return r142421;
}
↓
double f(double x, double y, double z) {
        double r142422 = x;
        double r142423 = y;
        double r142424 = 2.0;
        double r142425 = r142422 / r142424;
        double r142426 = fma(r142422, r142423, r142425);
        double r142427 = z;
        double r142428 = r142426 + r142427;
        return r142428;
}

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 2019325 +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))