Average Error: 0.0 → 0.0
Time: 1.0s
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 r122620 = x;
        double r122621 = y;
        double r122622 = r122620 * r122621;
        double r122623 = z;
        double r122624 = t;
        double r122625 = r122623 * r122624;
        double r122626 = r122622 + r122625;
        return r122626;
}
↓
double f(double x, double y, double z, double t) {
        double r122627 = x;
        double r122628 = y;
        double r122629 = z;
        double r122630 = t;
        double r122631 = r122629 * r122630;
        double r122632 = fma(r122627, r122628, r122631);
        return r122632;
}

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 2020046 +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)))