Average Error: 0.0 → 0.0
Time: 3.6s
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 r83856 = x;
        double r83857 = y;
        double r83858 = r83856 * r83857;
        double r83859 = z;
        double r83860 = t;
        double r83861 = r83859 * r83860;
        double r83862 = r83858 + r83861;
        return r83862;
}
↓
double f(double x, double y, double z, double t) {
        double r83863 = x;
        double r83864 = y;
        double r83865 = z;
        double r83866 = t;
        double r83867 = r83865 * r83866;
        double r83868 = fma(r83863, r83864, r83867);
        return r83868;
}

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 2019323 +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)))