Average Error: 0.0 → 0.0
Time: 1.7s
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 r131499 = x;
        double r131500 = y;
        double r131501 = r131499 * r131500;
        double r131502 = z;
        double r131503 = t;
        double r131504 = r131502 * r131503;
        double r131505 = r131501 + r131504;
        return r131505;
}
↓
double f(double x, double y, double z, double t) {
        double r131506 = x;
        double r131507 = y;
        double r131508 = z;
        double r131509 = t;
        double r131510 = r131508 * r131509;
        double r131511 = fma(r131506, r131507, r131510);
        return r131511;
}

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 2020045 +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)))