Average Error: 0.0 → 0.0
Time: 2.7s
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 r138513 = x;
        double r138514 = y;
        double r138515 = r138513 * r138514;
        double r138516 = z;
        double r138517 = t;
        double r138518 = r138516 * r138517;
        double r138519 = r138515 + r138518;
        return r138519;
}
↓
double f(double x, double y, double z, double t) {
        double r138520 = x;
        double r138521 = y;
        double r138522 = z;
        double r138523 = t;
        double r138524 = r138522 * r138523;
        double r138525 = fma(r138520, r138521, r138524);
        return r138525;
}

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 2020047 +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)))