  In this paper we study the problem of testing of constrained samplers over
high-dimensional distributions with $(\varepsilon,\eta,\delta)$ guarantees.
Samplers are increasingly used in a wide range of safety-critical ML
applications, and hence the testing problem has gained importance. For
$n$-dimensional distributions, the existing state-of-the-art algorithm,
$\mathsf{Barbarik2}$, has a worst case query complexity of exponential in $n$
and hence is not ideal for use in practice. Our primary contribution is an
exponentially faster algorithm that has a query complexity linear in $n$ and
hence can easily scale to larger instances. We demonstrate our claim by
implementing our algorithm and then comparing it against $\mathsf{Barbarik2}$.
Our experiments on the samplers $\mathsf{wUnigen3}$ and $\mathsf{wSTS}$, find
that $\mathsf{Barbarik3}$ requires $10\times$ fewer samples for
$\mathsf{wUnigen3}$ and $450\times$ fewer samples for $\mathsf{wSTS}$ as
compared to $\mathsf{Barbarik2}$.
