Average Error: 0.0 → 0.0
Time: 1.6s
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 r142988 = x;
        double r142989 = y;
        double r142990 = r142988 * r142989;
        double r142991 = z;
        double r142992 = t;
        double r142993 = r142991 * r142992;
        double r142994 = r142990 + r142993;
        return r142994;
}
↓
double f(double x, double y, double z, double t) {
        double r142995 = x;
        double r142996 = y;
        double r142997 = z;
        double r142998 = t;
        double r142999 = r142997 * r142998;
        double r143000 = fma(r142995, r142996, r142999);
        return r143000;
}

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 2019194 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))