Average Error: 0.0 → 0.0
Time: 2.2s
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 r2138543 = x;
        double r2138544 = y;
        double r2138545 = r2138543 * r2138544;
        double r2138546 = z;
        double r2138547 = t;
        double r2138548 = r2138546 * r2138547;
        double r2138549 = r2138545 + r2138548;
        return r2138549;
}
↓
double f(double x, double y, double z, double t) {
        double r2138550 = x;
        double r2138551 = y;
        double r2138552 = z;
        double r2138553 = t;
        double r2138554 = r2138552 * r2138553;
        double r2138555 = fma(r2138550, r2138551, r2138554);
        return r2138555;
}

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 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))