Average Error: 0.0 → 0.0
Time: 1.8s
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 r137557 = x;
        double r137558 = y;
        double r137559 = r137557 * r137558;
        double r137560 = z;
        double r137561 = t;
        double r137562 = r137560 * r137561;
        double r137563 = r137559 + r137562;
        return r137563;
}
↓
double f(double x, double y, double z, double t) {
        double r137564 = x;
        double r137565 = y;
        double r137566 = z;
        double r137567 = t;
        double r137568 = r137566 * r137567;
        double r137569 = fma(r137564, r137565, r137568);
        return r137569;
}

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 2020047 +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)))