Expounding implementation details of a paper and provide a full computational analysis

Recently I've implemented a pipeline given from a paper, there are three main steps two of these are offline and the third one is real time. The real time part was particularly difficult to implement, and mainly because of lack of details. More specifically the problem was the authors provided a function and they said "we minimize this function". The problem with that is that is wasn't explained how they actually solved the problem and I had in the first place work out all the mathematical details by myself. I've done a detailed analysis that wasn't provided by the original paper, like predicting solution in some cases, computational complexity. Given that this algorithm was real time then this analysis can be useful for whoever would like to implement it.

The question is, given a paper that tells you "we solved our problem using this and we have obtained these numbers" can be worth publishing all the analysis that can theoretically justify those numbers?

In my mind this could also be useful for validation purpose of whoever wants to implement it.

Also, it would be nice to have some example of this if it happens.

This is a problem with a lot of research these days: reproducibility. From my experience publishing an implementation approach to a paper, when no approach was given is a valid academic contribution, as there could be various approaches each with its own advantages and disadvantages. If you can expand your work to include multiple reasonable potential approaches and their outcomes, as well as potential pitfalls that could arise (you probably already went through both of these with your work), it would be a significant worthwhile contribution.

The next question is whether the journal you submit to sees it this way, and that can be a hit or miss. The only way to know is to try. Try to frame your work as "Approaches to X (where X is the sub-problem you tackled), instead of linking it too heavily with the original work (where X is e.g. the name of the original paper). If everything else fails, you can always try a conference or open publication although the "social credit" for these will be much less.

I also support the idea of publishing your code on github. The more we share the better off we all will be. This open sharing approach has aided in the significant machine learning publishing boom, and fast pace of improvements we are seeing.