Average Error: 0.0 → 0.0
Time: 13.2s
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 r99574 = x;
        double r99575 = y;
        double r99576 = r99574 * r99575;
        double r99577 = z;
        double r99578 = t;
        double r99579 = r99577 * r99578;
        double r99580 = r99576 + r99579;
        return r99580;
}
↓
double f(double x, double y, double z, double t) {
        double r99581 = x;
        double r99582 = y;
        double r99583 = z;
        double r99584 = t;
        double r99585 = r99583 * r99584;
        double r99586 = fma(r99581, r99582, r99585);
        return r99586;
}

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 2019212 +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)))