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 r94568 = x;
        double r94569 = y;
        double r94570 = r94568 * r94569;
        double r94571 = z;
        double r94572 = t;
        double r94573 = r94571 * r94572;
        double r94574 = r94570 + r94573;
        return r94574;
}
↓
double f(double x, double y, double z, double t) {
        double r94575 = x;
        double r94576 = y;
        double r94577 = z;
        double r94578 = t;
        double r94579 = r94577 * r94578;
        double r94580 = fma(r94575, r94576, r94579);
        return r94580;
}

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 2020056 +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)))