Average Error: 0.0 → 0.0
Time: 1.1s
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 r133210 = x;
        double r133211 = 2.0;
        double r133212 = r133210 / r133211;
        double r133213 = y;
        double r133214 = r133213 * r133210;
        double r133215 = r133212 + r133214;
        double r133216 = z;
        double r133217 = r133215 + r133216;
        return r133217;
}
↓
double f(double x, double y, double z) {
        double r133218 = x;
        double r133219 = y;
        double r133220 = 2.0;
        double r133221 = r133218 / r133220;
        double r133222 = fma(r133218, r133219, r133221);
        double r133223 = z;
        double r133224 = r133222 + r133223;
        return r133224;
}

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))