It's been over two years since Rubi 4.16.1 was released. Although far from perfect, it is based on a fairly powerful, stable system of rules. The integration rules and associated test-suite on Rubi's website are the most up-to-date, publicly available versions.
I’m in the midst of totally redesigning the decision tree implicit in Rubi 4's pattern matching rules used to integrate rational and algebraic functions (they account for about half the system's current 7800 rules). This redesign will
- greatly increase the class of expressions Rubi can integrate,
- provide simpler, more straight-forward derivations when single-stepping, and
- facilitate the compilation of Rubi 4’s pattern matching rules into Rubi 5’s if-then-else decision tree.
I will not release the next, and hopefully last, version of Rubi 4 until a coherent set of rules are derived, debugged and thoroughly tested. I cannot predict when that new version will be released, given the creative nature of the work. It all depends on where the math leads me.
Once this is accomplished, I can begin work in earnest on Rubi 5. That involves compiling Rubi 4's pattern matching rules into a deeply nested if-then-else decision tree. Thus far I have been doing this manually. Considering the tree has around 7800 leaves, it is extremely tedious, error-prone and time-consuming work.
Clearly this compilation should be automated. Conceptually that should be relatively fairly straight-forward to do, given the hierarchical nature of the decision tree implicit in Rubi 4's pattern matching rules.
Such a compiler would greatly facilitate the release of Rubi 5 with its numerous advantages. It will be relatively easy to port Rubi 5 to virtually any CAS supporting an if-then-else control construct. Also preliminary testing indicates selecting rules using an if-then-else tree rather than pattern matching means Rubi 5 will run almost 2-orders of magnitude faster than Rubi 4.
For more on implementing and porting Rubi, see the Plan for Implementing Rubi 5.
Finally, I'm keeping my focus squarely on perfecting Rubi 4 to my satisfaction before turning my attention to Rubi 5. So I invite others having the interest and expertise required to oversee the implementation of Rubi 5.