Average Error: 0.0 → 0.0
Time: 4.3s
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 r93437 = x;
        double r93438 = y;
        double r93439 = r93437 * r93438;
        double r93440 = z;
        double r93441 = t;
        double r93442 = r93440 * r93441;
        double r93443 = r93439 + r93442;
        return r93443;
}
↓
double f(double x, double y, double z, double t) {
        double r93444 = x;
        double r93445 = y;
        double r93446 = z;
        double r93447 = t;
        double r93448 = r93446 * r93447;
        double r93449 = fma(r93444, r93445, r93448);
        return r93449;
}

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 2019323 +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)))