Average Error: 0.0 → 0.0
Time: 5.2s
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 r12276217 = x;
        double r12276218 = 2.0;
        double r12276219 = r12276217 / r12276218;
        double r12276220 = y;
        double r12276221 = r12276220 * r12276217;
        double r12276222 = r12276219 + r12276221;
        double r12276223 = z;
        double r12276224 = r12276222 + r12276223;
        return r12276224;
}
↓
double f(double x, double y, double z) {
        double r12276225 = z;
        double r12276226 = y;
        double r12276227 = x;
        double r12276228 = 2.0;
        double r12276229 = r12276227 / r12276228;
        double r12276230 = fma(r12276226, r12276227, r12276229);
        double r12276231 = r12276225 + r12276230;
        return r12276231;
}

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 2019170 +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))