Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\left(\frac{x}{2} + y \cdot x\right) + z\]
↓
\[z + \mathsf{fma}\left(y, x, \frac{x}{2}\right)\]
\left(\frac{x}{2} + y \cdot x\right) + z
↓
z + \mathsf{fma}\left(y, x, \frac{x}{2}\right)
double f(double x, double y, double z) {
        double r10038253 = x;
        double r10038254 = 2.0;
        double r10038255 = r10038253 / r10038254;
        double r10038256 = y;
        double r10038257 = r10038256 * r10038253;
        double r10038258 = r10038255 + r10038257;
        double r10038259 = z;
        double r10038260 = r10038258 + r10038259;
        return r10038260;
}
↓
double f(double x, double y, double z) {
        double r10038261 = z;
        double r10038262 = y;
        double r10038263 = x;
        double r10038264 = 2.0;
        double r10038265 = r10038263 / r10038264;
        double r10038266 = fma(r10038262, r10038263, r10038265);
        double r10038267 = r10038261 + r10038266;
        return r10038267;
}

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

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

Reproduce

herbie shell --seed 2019171 +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))