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 r187897 = x;
        double r187898 = y;
        double r187899 = r187897 * r187898;
        double r187900 = z;
        double r187901 = t;
        double r187902 = r187900 * r187901;
        double r187903 = r187899 + r187902;
        return r187903;
}
↓
double f(double x, double y, double z, double t) {
        double r187904 = x;
        double r187905 = y;
        double r187906 = z;
        double r187907 = t;
        double r187908 = r187906 * r187907;
        double r187909 = fma(r187904, r187905, r187908);
        return r187909;
}

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 2019350 +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)))