Average Error: 0.0 → 0.0
Time: 4.4s
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 r91114 = x;
        double r91115 = y;
        double r91116 = r91114 * r91115;
        double r91117 = z;
        double r91118 = t;
        double r91119 = r91117 * r91118;
        double r91120 = r91116 + r91119;
        return r91120;
}
↓
double f(double x, double y, double z, double t) {
        double r91121 = x;
        double r91122 = y;
        double r91123 = z;
        double r91124 = t;
        double r91125 = r91123 * r91124;
        double r91126 = fma(r91121, r91122, r91125);
        return r91126;
}

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 2019325 +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)))