Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(x, y, z \cdot t\right)
double f(double x, double y, double z, double t) {
        double r156285 = x;
        double r156286 = y;
        double r156287 = r156285 * r156286;
        double r156288 = z;
        double r156289 = t;
        double r156290 = r156288 * r156289;
        double r156291 = r156287 + r156290;
        return r156291;
}
↓
double f(double x, double y, double z, double t) {
        double r156292 = x;
        double r156293 = y;
        double r156294 = z;
        double r156295 = t;
        double r156296 = r156294 * r156295;
        double r156297 = fma(r156292, r156293, r156296);
        return r156297;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot t\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, z \cdot t\right)\]

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))