Average Error: 0.0 → 0.0
Time: 839.0ms
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 r107315 = x;
        double r107316 = y;
        double r107317 = r107315 * r107316;
        double r107318 = z;
        double r107319 = t;
        double r107320 = r107318 * r107319;
        double r107321 = r107317 + r107320;
        return r107321;
}
↓
double f(double x, double y, double z, double t) {
        double r107322 = x;
        double r107323 = y;
        double r107324 = z;
        double r107325 = t;
        double r107326 = r107324 * r107325;
        double r107327 = fma(r107322, r107323, r107326);
        return r107327;
}

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 2020089 +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)))