@stevebronder has been making some efficiency improvements in the distributions by pulling out conditions. Here’s a recent PR. I made a note on that PR that all those tests are static traits test. So the compiler should inline them. I’m not entirely sure if the generated code will be much different.

The big thing that would be great to do in some of these, maybe starting with `normal_lpdf`

, would be to figure out (again with traits), when a bunch of additions can be replaced with a multiplication. For example, in evaluating

```
normal_lpdf(y | mu, sigma)
```

if `y`

is a vector of size `N`

and `sigma`

is a scalar, then we should be able to do this:

```
if (log_sigma.size() == 1)
lpdf -= N * log_sigma[0];
else
for (int n = 0; n < N; ++n)
lpdf -= log_sigma[n];
```

This is all primitive arithmetic, so it’s not going to be the kind of saving we’d get with autodiff (though it should be bigger for forward mode), I still think

replacing 100 additions with a single multiplication will be a win.

This might actually be a bit slower due to the multiply in the all-scalar case, so that again could be pulled out and evaluated separately.