This PR should improve efficiency of new_dynamic. Many of the basic math ops such as add, add_eq, sub, sub_eq, mul, mul_eq, div, div_eq, and azmul catch cases where one argument is a CppAD Constant and has value either 0 or 1, when this allows avoiding placing an operation on the AD tape. For example y = x + c where c is identically 0 does not require an addition op to be placed on the tape.

However, such checking was not in place for cases where neither argument is a CppAD Variable but rather at least one of them is a CppAD Dynamic. This meant that the operation tape used for updating dynamics (via new_dynamic) could include potentially many trivial operations such as adding 0 or multiplying by 1. In a simple example such as double-taping of second derivatives of a quadratic form such as in a multivariate normal density calculation (e.g. x' A x, where A is dynamic and derivatives are with respect to x) could generate a mostly wasteful new_dynamic tape.

This PR attempts to imitate the logic used for the Variable cases to handle similar cases for Dynamic. In my test problem, it fixes a memory explosion that was occurring. All the ops listed above were modified.

This PR is likely not ready to merge because I am not sure how to add to CppAD's test suite. @bradbell is that something you could do, or provide guidance on? I am not clear if there is comprehensive testing of Dynamic operations or other similar place that might be obvious to extend. My own motivating problem only touches a couple of these ops, so the others remain untested. I am making this PR now to see if this looks on the right track to you before spending more time on it.

I note that pow could also receive the same kind of extension as the other ops listed above. However, I noticed that for the Variable cases, it checks for if( IdenticalZero( y.value_ ) ) and if( IdenticalZero( x.value_ ) ), so it is not checking if y or x are constants the way the code for the other ops does. E.g. in the other ops, there would be something like if( (!dyn_y) && IdenticalZero( y.value_ ) ). Any chance this is a bug for pow?

Also @bradbell you told me to be sure I could run bin/check_all.sh. That has been pretty hard to get fully working. I believe all the code checks run, and make check (called from build) passes. But bin/check_all.sh gets stuck in a documentation step and it's been a bit of an obstacle.