Average Error: 0.0 → 0.0
Time: 13.0s
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 r18124922 = x;
        double r18124923 = y;
        double r18124924 = r18124922 * r18124923;
        double r18124925 = z;
        double r18124926 = t;
        double r18124927 = r18124925 * r18124926;
        double r18124928 = r18124924 + r18124927;
        return r18124928;
}
↓
double f(double x, double y, double z, double t) {
        double r18124929 = x;
        double r18124930 = y;
        double r18124931 = z;
        double r18124932 = t;
        double r18124933 = r18124931 * r18124932;
        double r18124934 = fma(r18124929, r18124930, r18124933);
        return r18124934;
}

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 2019173 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))