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The rate for vocal extraction is the same as vocal reduction, see this

Vocal extraction and re-mixing

Why is suppressing the backing music more difficult than suppressing vocals?

It is often thought (even by professionals) that if you can remove vocals by subtraction of left and right channels (phase cancellation), then you can also extract vocals using the same principle. Here it is argued in a very simple way that this reasoning is in fact wrong.

Suppose we represent the backing music by M, the vocal by V, and the left and right channels by L and R respectively.
If the vocal is centre-panned, then its left and right parts are the same (VL=VR=V)so that we can say L = ML + V, R = MR + V
Taking L-R or R-L we cancel the V (vocal) component, leaving the difference of MR and ML, because L-R = ML+V-(MR+V)=ML-MR. Assuming ML and MR are different, 'some' music is left (side-effects like reverb effects etc are disregarded here, for simplicity)

Now, it is often claimed that subtracting the vocal-less track from a (mono) mix with vocal, will similarly cancel the music and leave the vocal. This is not true.
Let's say the vocal-less track is L-R, like in the above. A mono (sum) mix is L+R. Subtracting these two will yield either 2L or 2R, so certainly not something that would consist of an enhanced vocal with suppressed music.
Any variation on this, involving factors 1/2 etc, will not make any difference: the end result is always just a linear mix of left and right channels, and there is no reason at all why the backing music should be suppressed.
The point is that a vocal can be removed because it is basically mono, and occupies a single point in space (disregarding reverb). This is not true for the backing music, which is spatially spread out, which is why suppressing the backing music is fundamentally more difficult. For the same reason, as reverb spreads the vocal in space, reverb limits successful removal of vocals, a well-known fact.

Another approach sometimes found is to derive a spectral mask from the vocal-less track, that is then used to reduce the backing music by spectral subtraction (like noise reduction), which is a quite different technique. Although not very good in practice, it may work occasionally, and yield a very moderate reduction of the backing music. However, it is an extremely cumbersome procedure, and the results are usually very disappointing.

One other approach, that does sometimes work, is to subtract an original instrumental, from the (exact same) track with vocal . You are then using the fact that the 'separation' has practically been done for you by the engineer who mixed the track with and without vocals. Obviously, you need to have both tracks available to do this!

If your efforts to extract a vocal, that you really want, fail, we can help.

Now, as CSP's vocal removal does not rely on the cancellation principle, and leaves the stereo image intact, CSP can perform vocal enhancement or extraction. Though it is still more difficult than vocal suppression, on most stereo material significant reduction of backing music can be obtained with little effect on the vocal itself.
In most cases, we can make 'a-capellas' that make re-mixing a lot easier!.