Average Error: 0.0 → 0.0
Time: 10.0s
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 r4378158 = x;
        double r4378159 = y;
        double r4378160 = r4378158 * r4378159;
        double r4378161 = z;
        double r4378162 = t;
        double r4378163 = r4378161 * r4378162;
        double r4378164 = r4378160 + r4378163;
        return r4378164;
}
↓
double f(double x, double y, double z, double t) {
        double r4378165 = x;
        double r4378166 = y;
        double r4378167 = z;
        double r4378168 = t;
        double r4378169 = r4378167 * r4378168;
        double r4378170 = fma(r4378165, r4378166, r4378169);
        return r4378170;
}

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 2019171 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))