Sourdough rising but not doubling

Hi!

I have a sourdough starter which rises quite substantially (like one third of the container) but not doubles. Also it takes long to rise and long to go down. I had tried the float test and it worked. Any suggestions on how to make it more active? Like rising and doubling in a shorter span of time?

I had read that my culture of yeast could be a long acting one rather than short acting one. That is takes time to rise and takes time to go back down. Is this true? At the moment it rises at around 12 hours and goes back down at 24 hours after feeding sometimes more. 

thanks