Consider the code corresponding to Figure 1 (I now realise I should have included the code snippet in the paper!): the term 'ab' occurs twice in the expression for 'result'. In typical expression evaluation, 'ab' is evaluated once then its result used in many places. However, in back-propagation evaluations (like those found in adjoint automatic differentiation), evaluation begins at 'result' and propagates to the terminals 'a' and 'b'. The problem is that the back-propagation will visit the sub-expression tree for 'ab' twice since it occurs twice upstream.
Regarding the second point: I came across Andrew Sutton's paper, P2237R0, after submitting my own. Whilst skimming it I saw something that may be doing what I am proposing, namely 'meta::location_of(e)', p15 ff. Are the reflection mechanisms you are referring to those mentioned by Andrew in his paper or are you referring to another language proposal? If it is another, I'd be grateful if I could get a link to the paper.
I agree that if there are not sufficiently broad use case examples for my proposal then it does not warrant further consideration; amassing a broad range of use cases is something I still need to work on. (Klaus Iglberger, I believe, has a use case for his math library 'Blaze' which I need to ask him for.) However, presently, I don't know how the same end could be achieved without a top level API function. Early on, I thought it could be by proposing a language extension whereby `address of' in a constexpr context would return a constexpr variable ID, much like what varid would do. However, even with this, a second language change would need to be made, one whereby a constexpr function could return a constexpr result despite taking non-constexpr arguments (i.e. resolving the compilation error presented in Listing 3).
In response to your final comment: unfortunately, only having equality wouldn't do; it would be minimally useful, facilitating expression transformations for only trivial expressions, such as 'c0*c1' or 'c0*c0', but nothing more complicated than that.
Regards,
Dominic