You've missed my point. Why do you not consider sqrt(3!)? It's not integral, but if you multiply by sqrt(6), the result IS integral. I don't think an optimal solution will have non-integral subexpressions, but you need an argument to justify that. Or you need to include them in your brute force search.
That's right, sorry I missed your point. I edited the post accordingly, thanks a lot for your input!
Note however that I did not pretend to have an exhaustive search, just a "brute" one to find a solution. I changed "enumerating all the candidate" to "enumerating the candidate" to remove some confusion.
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You've missed my point. Why do you not consider sqrt(3!)? It's not integral, but if you multiply by sqrt(6), the result IS integral. I don't think an optimal solution will have non-integral subexpressions, but you need an argument to justify that. Or you need to include them in your brute force search.
That's right, sorry I missed your point. I edited the post accordingly, thanks a lot for your input!
Note however that I did not pretend to have an exhaustive search, just a "brute" one to find a solution. I changed "enumerating all the candidate" to "enumerating the candidate" to remove some confusion.