Average Error: 0.0 → 0.0
Time: 7.7s
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 r74405 = x;
        double r74406 = y;
        double r74407 = r74405 * r74406;
        double r74408 = z;
        double r74409 = t;
        double r74410 = r74408 * r74409;
        double r74411 = r74407 + r74410;
        return r74411;
}
↓
double f(double x, double y, double z, double t) {
        double r74412 = x;
        double r74413 = y;
        double r74414 = z;
        double r74415 = t;
        double r74416 = r74414 * r74415;
        double r74417 = fma(r74412, r74413, r74416);
        return r74417;
}

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 2019303 +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)))