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 r127281 = x;
        double r127282 = y;
        double r127283 = r127281 * r127282;
        double r127284 = z;
        double r127285 = t;
        double r127286 = r127284 * r127285;
        double r127287 = r127283 + r127286;
        return r127287;
}
↓
double f(double x, double y, double z, double t) {
        double r127288 = x;
        double r127289 = y;
        double r127290 = z;
        double r127291 = t;
        double r127292 = r127290 * r127291;
        double r127293 = fma(r127288, r127289, r127292);
        return r127293;
}

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 2020045 +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)))