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Is there any chance that MD5's compression function can be represented in a completely different way so that it's much easier to compute/reverse it?

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    $\begingroup$ Is the question asking for something giving the exact same result as MD5's compression function? Also, define easier. We can replace MD5's compression function by something (different) with two out of three characteristics: secure, simple enough to easily remember, and fast. $\endgroup$ – fgrieu Aug 18 '16 at 16:25
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    $\begingroup$ @fgrieu I meant a function that executes much faster than MD5's compression function, and also gives the same result. $\endgroup$ – nrg Aug 18 '16 at 16:46
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Not that we know of.

Although we have no proof, there is still a strong belief that MD5 represents a one-way hash. It is broken, but that doesn't mean we can reverse it (or the compression function that it is based on).

Similarly, we don't know a faster way to compute it (in the algorithmic sense) but we cannot proof that there isn't a faster "representation".

One of the things to consider here is P versus NP. As long as this remains unsolved we don't know if P = NP could hold, which would have interesting consequences.

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