Average Error: 0.0 → 0.0
Time: 672.0ms
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 r128504 = x;
        double r128505 = y;
        double r128506 = r128504 * r128505;
        double r128507 = z;
        double r128508 = t;
        double r128509 = r128507 * r128508;
        double r128510 = r128506 + r128509;
        return r128510;
}
↓
double f(double x, double y, double z, double t) {
        double r128511 = x;
        double r128512 = y;
        double r128513 = z;
        double r128514 = t;
        double r128515 = r128513 * r128514;
        double r128516 = fma(r128511, r128512, r128515);
        return r128516;
}

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 2020021 +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)))