It's not just expressions; it's any computation you normally would do with doubles. Take a look at the simple bundle adjustment example:

http://code.google.com/p/ceres-solver/source/browse/examples...

In particular, search for "SnavelyReprojectionError". In this case there are no loops or if statements, but they work fine too. The only issue with branches is that you can make the cost function discontiguous, which can cause issues.

The way this works is that you write your cost functions templated on T. For pure-cost evaluation, this is a double. For cost and jacobian, T is replaced with the "Jet" object, found in jet.h. However, you never see this; Ceres does the substitution for you.

There are some caveats; for example, sqrt(0) doesn't work on autodiff objects since the derivative is undefined. You have to use a taylor approximation or similar if the argument to sqrt is exactly zero.

If you want to see some more complicated code that runs with autodiff, check out the included rotation.h header. We use that internally for 3D reconstruction type cost functions:

http://code.google.com/p/ceres-solver/source/browse/include/...

We have conditionals overloaded which allow you to compare with other jets, and doubles, which boil down to a comparison with the "value" part of the jet.

So conditionals are not a problem. Loops I would stay away from, since they would destroy the inlining. But if you have an example of a dynamic loop, we would like to hear about it.