Average Error: 0.0 → 0.0
Time: 1.2s
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 r118560 = x;
        double r118561 = y;
        double r118562 = r118560 * r118561;
        double r118563 = z;
        double r118564 = t;
        double r118565 = r118563 * r118564;
        double r118566 = r118562 + r118565;
        return r118566;
}
↓
double f(double x, double y, double z, double t) {
        double r118567 = x;
        double r118568 = y;
        double r118569 = z;
        double r118570 = t;
        double r118571 = r118569 * r118570;
        double r118572 = fma(r118567, r118568, r118571);
        return r118572;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))