Average Error: 0.0 → 0.0
Time: 8.1s
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 r90046 = x;
        double r90047 = y;
        double r90048 = r90046 * r90047;
        double r90049 = z;
        double r90050 = t;
        double r90051 = r90049 * r90050;
        double r90052 = r90048 + r90051;
        return r90052;
}
↓
double f(double x, double y, double z, double t) {
        double r90053 = x;
        double r90054 = y;
        double r90055 = z;
        double r90056 = t;
        double r90057 = r90055 * r90056;
        double r90058 = fma(r90053, r90054, r90057);
        return r90058;
}

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 2019209 +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)))