Average Error: 0.0 → 0.0
Time: 5.5s
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 r91280 = x;
        double r91281 = y;
        double r91282 = r91280 * r91281;
        double r91283 = z;
        double r91284 = t;
        double r91285 = r91283 * r91284;
        double r91286 = r91282 + r91285;
        return r91286;
}
↓
double f(double x, double y, double z, double t) {
        double r91287 = x;
        double r91288 = y;
        double r91289 = z;
        double r91290 = t;
        double r91291 = r91289 * r91290;
        double r91292 = fma(r91287, r91288, r91291);
        return r91292;
}

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 2019235 +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)))