Average Error: 0.0 → 0.0
Time: 6.4s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[\mathsf{fma}\left(y, x, \frac{x}{2}\right) + z\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
\mathsf{fma}\left(y, x, \frac{x}{2}\right) + z
double f(double x, double y, double z) {
        double r26073543 = x;
        double r26073544 = 2.0;
        double r26073545 = r26073543 / r26073544;
        double r26073546 = y;
        double r26073547 = r26073546 * r26073543;
        double r26073548 = r26073545 + r26073547;
        double r26073549 = z;
        double r26073550 = r26073548 + r26073549;
        return r26073550;
}
↓
double f(double x, double y, double z) {
        double r26073551 = y;
        double r26073552 = x;
        double r26073553 = 2.0;
        double r26073554 = r26073552 / r26073553;
        double r26073555 = fma(r26073551, r26073552, r26073554);
        double r26073556 = z;
        double r26073557 = r26073555 + r26073556;
        return r26073557;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \frac{x}{2}\right) + z}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x, \frac{x}{2}\right) + z\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"
  (+ (+ (/ x 2.0) (* y x)) z))