Average Error: 0.0 → 0.0
Time: 1.2s
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 r91396 = x;
        double r91397 = y;
        double r91398 = r91396 * r91397;
        double r91399 = z;
        double r91400 = t;
        double r91401 = r91399 * r91400;
        double r91402 = r91398 + r91401;
        return r91402;
}
↓
double f(double x, double y, double z, double t) {
        double r91403 = x;
        double r91404 = y;
        double r91405 = z;
        double r91406 = t;
        double r91407 = r91405 * r91406;
        double r91408 = fma(r91403, r91404, r91407);
        return r91408;
}

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 2019305 +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)))