Average Error: 0.0 → 0.0
Time: 1.3s
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 r3500079 = x;
        double r3500080 = y;
        double r3500081 = r3500079 * r3500080;
        double r3500082 = z;
        double r3500083 = t;
        double r3500084 = r3500082 * r3500083;
        double r3500085 = r3500081 + r3500084;
        return r3500085;
}
↓
double f(double x, double y, double z, double t) {
        double r3500086 = x;
        double r3500087 = y;
        double r3500088 = z;
        double r3500089 = t;
        double r3500090 = r3500088 * r3500089;
        double r3500091 = fma(r3500086, r3500087, r3500090);
        return r3500091;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))