Average Error: 0.0 → 0.0
Time: 4.7s
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 r4119990 = x;
        double r4119991 = y;
        double r4119992 = r4119990 * r4119991;
        double r4119993 = z;
        double r4119994 = t;
        double r4119995 = r4119993 * r4119994;
        double r4119996 = r4119992 + r4119995;
        return r4119996;
}
↓
double f(double x, double y, double z, double t) {
        double r4119997 = x;
        double r4119998 = y;
        double r4119999 = z;
        double r4120000 = t;
        double r4120001 = r4119999 * r4120000;
        double r4120002 = fma(r4119997, r4119998, r4120001);
        return r4120002;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))