Whether the hex representation is shorter than the decimal changes several times as numbers get bigger http://stackoverflow.com/questions/9458614/at-what-point-do-hexadecimal-representations-of-numbers-take-up-less-chars-than …
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This seems to be a pretty challenging problem even if you assume no usage or declaration of functions in the available space
Finding the shortest expression which evaluates to a given float is basically a problem of Kolmogorov complexity (I could be wrong)
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In the worst case, we systematically test every expression with fewer characters than the decimal representation (24 characters at worst)
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But I think we can do quite a lot better than that!
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at least it's computable if you disallow control flow (because there's a trivial upper bound on length, so a finite number of candidates)
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More importantly, disallowing control flow guarantees that the evaluation of any expression will terminate, as will the brute force search
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