Average Error: 0.0 → 0.0
Time: 1.4s
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 r108812 = x;
        double r108813 = y;
        double r108814 = r108812 * r108813;
        double r108815 = z;
        double r108816 = t;
        double r108817 = r108815 * r108816;
        double r108818 = r108814 + r108817;
        return r108818;
}
↓
double f(double x, double y, double z, double t) {
        double r108819 = x;
        double r108820 = y;
        double r108821 = z;
        double r108822 = t;
        double r108823 = r108821 * r108822;
        double r108824 = fma(r108819, r108820, r108823);
        return r108824;
}

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 2020036 +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)))