Average Error: 0.0 → 0.0
Time: 1.7s
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 r4141760 = x;
        double r4141761 = y;
        double r4141762 = r4141760 * r4141761;
        double r4141763 = z;
        double r4141764 = t;
        double r4141765 = r4141763 * r4141764;
        double r4141766 = r4141762 + r4141765;
        return r4141766;
}
↓
double f(double x, double y, double z, double t) {
        double r4141767 = x;
        double r4141768 = y;
        double r4141769 = z;
        double r4141770 = t;
        double r4141771 = r4141769 * r4141770;
        double r4141772 = fma(r4141767, r4141768, r4141771);
        return r4141772;
}

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 2019169 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))