Average Error: 0.0 → 0.0
Time: 1.1s
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 r122200 = x;
        double r122201 = y;
        double r122202 = r122200 * r122201;
        double r122203 = z;
        double r122204 = t;
        double r122205 = r122203 * r122204;
        double r122206 = r122202 + r122205;
        return r122206;
}
↓
double f(double x, double y, double z, double t) {
        double r122207 = x;
        double r122208 = y;
        double r122209 = z;
        double r122210 = t;
        double r122211 = r122209 * r122210;
        double r122212 = fma(r122207, r122208, r122211);
        return r122212;
}

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 2019347 +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)))