equation solving - SystemException["MemoryAllocationFailure"] Uncaught SystemException returned to top level from NSolve

Bug introduced in 10.0.0 and fixed in 11.0.0

When trying to solve 8 equations in 8 unknowns, I get SystemException["MemoryAllocationFailure"]. I am not sure if I am doing something wrong, or is this something that should not really happen. Here is the code:

f={w1 + w2 + w3 + w4 == 2, w1*x1 + w2*x2 + w3*x3 + w4*x4 == 0, 
 w1*x1^2 + w2*x2^2 + w3*x3^2 + w4*x4^2 == 2/3, 
 w1*x1^3 + w2*x2^3 + w3*x3^3 + w4*x4^3 == 0, 

 w1*x1^4 + w2*x2^4 + w3*x3^4 + w4*x4^4 == 2/5, 
 w1*x1^5 + w2*x2^5 + w3*x3^5 + w4*x4^5 == 0, 
 w1*x1^6 + w2*x2^6 + w3*x3^6 + w4*x4^6 == 2/7, 
 w1*x1^7 + w2*x2^7 + w3*x3^7 + w4*x4^7 == 0};

NSolve[f, {w1, w2, w3, w4, x1, x2, x3, x4}]

Mathematica graphics

This is using Mathematica 10.4, on Windows 7, 16 GB RAM, 64 bits.

This happens only with NSolve. Using Solve does not generate this error, which is even more strange.

question is: Should this error be generated? Is this a user error, or a problem in NSolve?

Comments

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