Average Error: 0.0 → 0.0
Time: 1.6s
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 r9595240 = x;
        double r9595241 = y;
        double r9595242 = r9595240 * r9595241;
        double r9595243 = z;
        double r9595244 = t;
        double r9595245 = r9595243 * r9595244;
        double r9595246 = r9595242 + r9595245;
        return r9595246;
}
↓
double f(double x, double y, double z, double t) {
        double r9595247 = x;
        double r9595248 = y;
        double r9595249 = z;
        double r9595250 = t;
        double r9595251 = r9595249 * r9595250;
        double r9595252 = fma(r9595247, r9595248, r9595251);
        return r9595252;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))