Average Error: 0.0 → 0.0
Time: 937.0ms
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 r153091 = x;
        double r153092 = y;
        double r153093 = r153091 * r153092;
        double r153094 = z;
        double r153095 = t;
        double r153096 = r153094 * r153095;
        double r153097 = r153093 + r153096;
        return r153097;
}
↓
double f(double x, double y, double z, double t) {
        double r153098 = x;
        double r153099 = y;
        double r153100 = z;
        double r153101 = t;
        double r153102 = r153100 * r153101;
        double r153103 = fma(r153098, r153099, r153102);
        return r153103;
}

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 2020035 +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)))