Average Error: 0.0 → 0.0
Time: 1.8s
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 r125711 = x;
        double r125712 = y;
        double r125713 = r125711 * r125712;
        double r125714 = z;
        double r125715 = t;
        double r125716 = r125714 * r125715;
        double r125717 = r125713 + r125716;
        return r125717;
}
↓
double f(double x, double y, double z, double t) {
        double r125718 = x;
        double r125719 = y;
        double r125720 = z;
        double r125721 = t;
        double r125722 = r125720 * r125721;
        double r125723 = fma(r125718, r125719, r125722);
        return r125723;
}

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 2020046 +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)))