Average Error: 0.0 → 0.0
Time: 3.6s
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 r70771 = x;
        double r70772 = y;
        double r70773 = r70771 * r70772;
        double r70774 = z;
        double r70775 = t;
        double r70776 = r70774 * r70775;
        double r70777 = r70773 + r70776;
        return r70777;
}
↓
double f(double x, double y, double z, double t) {
        double r70778 = x;
        double r70779 = y;
        double r70780 = z;
        double r70781 = t;
        double r70782 = r70780 * r70781;
        double r70783 = fma(r70778, r70779, r70782);
        return r70783;
}

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 2019306 +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)))