Average Error: 0.0 → 0.0
Time: 629.0ms
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 r222721 = x;
        double r222722 = 2.0;
        double r222723 = r222721 / r222722;
        double r222724 = y;
        double r222725 = r222724 * r222721;
        double r222726 = r222723 + r222725;
        double r222727 = z;
        double r222728 = r222726 + r222727;
        return r222728;
}
↓
double f(double x, double y, double z) {
        double r222729 = x;
        double r222730 = y;
        double r222731 = z;
        double r222732 = fma(r222729, r222730, r222731);
        double r222733 = 2.0;
        double r222734 = r222729 / r222733;
        double r222735 = r222732 + r222734;
        return r222735;
}

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 2020046 +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))