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 r19277 = x;
        double r19278 = y;
        double r19279 = r19277 * r19278;
        double r19280 = z;
        double r19281 = t;
        double r19282 = r19280 * r19281;
        double r19283 = r19279 + r19282;
        return r19283;
}
↓
double f(double x, double y, double z, double t) {
        double r19284 = x;
        double r19285 = y;
        double r19286 = z;
        double r19287 = t;
        double r19288 = r19286 * r19287;
        double r19289 = fma(r19284, r19285, r19288);
        return r19289;
}

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)))