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 r5765544 = x;
        double r5765545 = y;
        double r5765546 = r5765544 * r5765545;
        double r5765547 = z;
        double r5765548 = t;
        double r5765549 = r5765547 * r5765548;
        double r5765550 = r5765546 + r5765549;
        return r5765550;
}
↓
double f(double x, double y, double z, double t) {
        double r5765551 = x;
        double r5765552 = y;
        double r5765553 = z;
        double r5765554 = t;
        double r5765555 = r5765553 * r5765554;
        double r5765556 = fma(r5765551, r5765552, r5765555);
        return r5765556;
}

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 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))