Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(\frac{x}{2.0} + y \cdot x\right) + z\]
↓
\[z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)\]
\left(\frac{x}{2.0} + y \cdot x\right) + z
↓
z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)
double f(double x, double y, double z) {
        double r10769423 = x;
        double r10769424 = 2.0;
        double r10769425 = r10769423 / r10769424;
        double r10769426 = y;
        double r10769427 = r10769426 * r10769423;
        double r10769428 = r10769425 + r10769427;
        double r10769429 = z;
        double r10769430 = r10769428 + r10769429;
        return r10769430;
}
↓
double f(double x, double y, double z) {
        double r10769431 = z;
        double r10769432 = y;
        double r10769433 = x;
        double r10769434 = 2.0;
        double r10769435 = r10769433 / r10769434;
        double r10769436 = fma(r10769432, r10769433, r10769435);
        double r10769437 = r10769431 + r10769436;
        return r10769437;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2.0} + y \cdot x\right) + z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \frac{x}{2.0}\right) + z}\]

  3. Final simplification0.0

    \[\leadsto z + \mathsf{fma}\left(y, x, \frac{x}{2.0}\right)\]

Reproduce

herbie shell --seed 2019162 +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))