Average Error: 0.0 → 0.0
Time: 8.7s
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 r5234363 = x;
        double r5234364 = y;
        double r5234365 = r5234363 * r5234364;
        double r5234366 = z;
        double r5234367 = t;
        double r5234368 = r5234366 * r5234367;
        double r5234369 = r5234365 + r5234368;
        return r5234369;
}
↓
double f(double x, double y, double z, double t) {
        double r5234370 = x;
        double r5234371 = y;
        double r5234372 = z;
        double r5234373 = t;
        double r5234374 = r5234372 * r5234373;
        double r5234375 = fma(r5234370, r5234371, r5234374);
        return r5234375;
}

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 2019170 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))