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 r14465 = x;
        double r14466 = y;
        double r14467 = r14465 * r14466;
        double r14468 = z;
        double r14469 = t;
        double r14470 = r14468 * r14469;
        double r14471 = r14467 + r14470;
        return r14471;
}
↓
double f(double x, double y, double z, double t) {
        double r14472 = x;
        double r14473 = y;
        double r14474 = z;
        double r14475 = t;
        double r14476 = r14474 * r14475;
        double r14477 = fma(r14472, r14473, r14476);
        return r14477;
}

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)))