Density of semantics in syntax Let $L$ be a programming language, and $\cong$ a notion of equality of $L$-programs (in general $\cong$ will be undecidable).  Let $syntax(n)$ be the number  of $L$-programs of size $n$ (for some reasonable notion of program  size), and $semantics(n)$ denotes the number of $\cong$-equivalence  classes of $L$-programs of size $n$. Now define
$$  density(n) = semantics(n)\ /\ syntax(n)$$
So $density(n)$ tells us how many really distinct programs we can
write of size $n$. What is known about the limit:
$$   \lim_{n \rightarrow \infty} density(n)?$$
I conjecture that $\lim_{n \rightarrow \infty} density(n) = 0$ for
reasonable choices of $L$ and $\cong$, since the larger programs are
allowed to be, the more room for redundancies like $M+N \cong N+M$.
Question. What is related work this direction?
In terms of related work, Marek Zaionc and collaborators have been studying similar kinds of questions for some time.  The following paper includes many results:

René David, Katarzyna Grygiel, Jakub Kozic, Christophe Raffalli, Guillaume Theyssier, Marek Zaionc.  Asymptotically almost all λ-terms are strongly normalizing.  Logical Methods in Computer Science, Volume 9, Issue 1 (February 15, 2013). arXiv

The result stated in the title is not exactly the same as the one you are asking about, but related: they prove that the asymptotic density of strongly normalizing terms among all terms of $\lambda$-calculus is 1.  Surprisingly, they also prove that the asymptotic density of strongly normalizing SKI combinator terms among all SKI combinator terms is 0.
As suggested by Gabriel Scherer's response, the specific formulation of density you are asking about is related to the density of normal terms among all terms, or in other words the probability that a uniformly random term of a given size is already normalized.  For subsystems of $\lambda$-calculus the probability that a term is normal typically decreases exponentially with size, and I believe it should be a small step from there to proving that the asymptotic density you are interested in is 0.  Certainly this is true for linear $\lambda$-terms: since normalization cannot increase the size of a term, the number of equivalence classes of terms of size $n$ is at most $n$ times the number of normal terms of size $n$, hence the ratio of equivalence classes to terms is asymptotically 0.