Average Error: 0.0 → 0.0
Time: 4.4s
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 r6624171 = x;
        double r6624172 = y;
        double r6624173 = r6624171 * r6624172;
        double r6624174 = z;
        double r6624175 = t;
        double r6624176 = r6624174 * r6624175;
        double r6624177 = r6624173 + r6624176;
        return r6624177;
}
↓
double f(double x, double y, double z, double t) {
        double r6624178 = x;
        double r6624179 = y;
        double r6624180 = z;
        double r6624181 = t;
        double r6624182 = r6624180 * r6624181;
        double r6624183 = fma(r6624178, r6624179, r6624182);
        return r6624183;
}

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)))