Calculating in an optimized way pow(x,y) for 0

For a project of mine, I am required to do a very fast computation of pow(x,y), hopefully, it is kinda restricted to a precise domain, but it need to be memory efficient enough too if it is not fast enough.

Like I said, it is in an short scope of x between 0 and 1 and y between 1 and 2. Therefore, it has to be precise enough on the whole scope to have even a slight diminution when called recursively (and not to stall on a number)

If you guys runned into such a thing or have suggestion...