Average Error: 0.0 → 0.0
Time: 6.3s
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 r94295 = x;
        double r94296 = y;
        double r94297 = r94295 * r94296;
        double r94298 = z;
        double r94299 = t;
        double r94300 = r94298 * r94299;
        double r94301 = r94297 + r94300;
        return r94301;
}
↓
double f(double x, double y, double z, double t) {
        double r94302 = x;
        double r94303 = y;
        double r94304 = z;
        double r94305 = t;
        double r94306 = r94304 * r94305;
        double r94307 = fma(r94302, r94303, r94306);
        return r94307;
}

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)))