Average Error: 0.0 → 0.0
Time: 4.3s
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 r6031565 = x;
        double r6031566 = y;
        double r6031567 = r6031565 * r6031566;
        double r6031568 = z;
        double r6031569 = t;
        double r6031570 = r6031568 * r6031569;
        double r6031571 = r6031567 + r6031570;
        return r6031571;
}
↓
double f(double x, double y, double z, double t) {
        double r6031572 = x;
        double r6031573 = y;
        double r6031574 = z;
        double r6031575 = t;
        double r6031576 = r6031574 * r6031575;
        double r6031577 = fma(r6031572, r6031573, r6031576);
        return r6031577;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))