Average Error: 0.0 → 0.0
Time: 689.0ms
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 r123693 = x;
        double r123694 = y;
        double r123695 = r123693 * r123694;
        double r123696 = z;
        double r123697 = t;
        double r123698 = r123696 * r123697;
        double r123699 = r123695 + r123698;
        return r123699;
}
↓
double f(double x, double y, double z, double t) {
        double r123700 = x;
        double r123701 = y;
        double r123702 = z;
        double r123703 = t;
        double r123704 = r123702 * r123703;
        double r123705 = fma(r123700, r123701, r123704);
        return r123705;
}

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 2019351 +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)))