Really slow extraction from raster even after using crop?

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I have a large raster file (245295396) cells and stacks of rasters having 4 layers each which lie in the extent of this large raster. To start with I am trying to get value from one stack (3 channels) and for the same zone from the large raster. Every things works fine, just the extraction from large raster takes 5 mins. So, if I repeat this process for 4000 more times it will take 13 days.

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