Average Error: 0.0 → 0.0
Time: 1.0s
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 r140588 = x;
        double r140589 = y;
        double r140590 = r140588 * r140589;
        double r140591 = z;
        double r140592 = t;
        double r140593 = r140591 * r140592;
        double r140594 = r140590 + r140593;
        return r140594;
}
↓
double f(double x, double y, double z, double t) {
        double r140595 = x;
        double r140596 = y;
        double r140597 = z;
        double r140598 = t;
        double r140599 = r140597 * r140598;
        double r140600 = fma(r140595, r140596, r140599);
        return r140600;
}

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 2020039 +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)))