Average Error: 0.0 → 0.0
Time: 1.2s
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 r630 = x;
        double r631 = y;
        double r632 = r630 * r631;
        double r633 = z;
        double r634 = t;
        double r635 = r633 * r634;
        double r636 = r632 + r635;
        return r636;
}
↓
double f(double x, double y, double z, double t) {
        double r637 = x;
        double r638 = y;
        double r639 = z;
        double r640 = t;
        double r641 = r639 * r640;
        double r642 = fma(r637, r638, r641);
        return r642;
}

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 2020025 +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)))