Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(z, t, y \cdot x\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(z, t, y \cdot x\right)
double f(double x, double y, double z, double t) {
        double r6052291 = x;
        double r6052292 = y;
        double r6052293 = r6052291 * r6052292;
        double r6052294 = z;
        double r6052295 = t;
        double r6052296 = r6052294 * r6052295;
        double r6052297 = r6052293 + r6052296;
        return r6052297;
}
↓
double f(double x, double y, double z, double t) {
        double r6052298 = z;
        double r6052299 = t;
        double r6052300 = y;
        double r6052301 = x;
        double r6052302 = r6052300 * r6052301;
        double r6052303 = fma(r6052298, r6052299, r6052302);
        return r6052303;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(z, t, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(z, t, y \cdot x\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))