Average Error: 0.0 → 0.0
Time: 1.8s
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 r99325 = x;
        double r99326 = y;
        double r99327 = r99325 * r99326;
        double r99328 = z;
        double r99329 = t;
        double r99330 = r99328 * r99329;
        double r99331 = r99327 + r99330;
        return r99331;
}
↓
double f(double x, double y, double z, double t) {
        double r99332 = x;
        double r99333 = y;
        double r99334 = z;
        double r99335 = t;
        double r99336 = r99334 * r99335;
        double r99337 = fma(r99332, r99333, r99336);
        return r99337;
}

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 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))