Double hashing as a mining shortcut countermeasure

[Come-from-Beyond]

As it's known, any hash function output bit can be represented as a polynomial of input bits. If the degree of this polynomial is low then mining ASICs can get a speedup by analyzing first N bits of the hash before doing actual hashing. A double hashing increases degree of the polynomial reducing speedup or even making it negative. Does anyone know if doubling is enough to make it unprofitable to do N-bit analysis (for any N) in mining hardware, or maybe triple hashing should be done?