Not much, if at all. The Library of Alexandria could very well had been the most prestigous library in Ancient Mediterranean, but it was far from the only one. Most larger cities had libraries, the one in Pergamum deserving a special mention.

With the term "set human race back", I would expect the implication being scientific progress. In that case, nothing of value was lost. Practical technologies will survive on their own if they remain useful to people. Even IF they constructed a steam engine in the Library as the myth goes, it clearly was not useful at the time. Nobody cared about it. If it had been important, we would have other contemporary sources or records speaking of it.

If you’re more concerned with intellectual progress then again the destruction of the library was largely inconsequential. The most important and influential works of Antiquity have all more or less survived the ages. True, very few of them are complete, but we at least had fragments or references to them in other literature. We have enough information on these works to have a gist about their main thesis.

The biggest loss from the destruction of the library wasn’t in terms of human progress, but simply in the preservation of the historical record. History itself is the real victim.

While philosophical treatises can be summarized or read in an incomplete form, actual books on history need every single page intact to be of full value. And as things stand today, we have very, very few complete historical narratives from Antiquity. Entire sections of key works are missing, some are just plain gone, and we know of them only through references in other works.