Average Error: 0.0 → 0.0
Time: 8.4s
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 r5554676 = x;
        double r5554677 = y;
        double r5554678 = r5554676 * r5554677;
        double r5554679 = z;
        double r5554680 = t;
        double r5554681 = r5554679 * r5554680;
        double r5554682 = r5554678 + r5554681;
        return r5554682;
}
↓
double f(double x, double y, double z, double t) {
        double r5554683 = x;
        double r5554684 = y;
        double r5554685 = z;
        double r5554686 = t;
        double r5554687 = r5554685 * r5554686;
        double r5554688 = fma(r5554683, r5554684, r5554687);
        return r5554688;
}

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 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))