There is no need to evaluate the gate again for these values. It can instead be computed as a dot product of the second half of the assignment vector $w(1, -)$ and the second half of the evaluation point eq vector.
If we clone the assignments or decide to use it destructively we can fold it as we do the eq vector and continue computing $g_j(1)$ this way for $j > 0$ as well.
It may be that for low degree gates the extra work of folding the assignment (causing a total of 2 multiplication passes to compute $g_j(1)$ may not be worthwhile for linear or quadratic gates) It would probably be best to count the number of multiplication operations in the gate to decide this.
There is no need to evaluate the gate again for these values. It can instead be computed as a dot product of the second half of the assignment vector$w(1, -)$ and the second half of the evaluation point eq vector.$g_j(1)$ this way for $j > 0$ as well.
If we clone the assignments or decide to use it destructively we can fold it as we do the eq vector and continue computing
It may be that for low degree gates the extra work of folding the assignment (causing a total of 2 multiplication passes to compute$g_j(1)$ may not be worthwhile for linear or quadratic gates) It would probably be best to count the number of multiplication operations in the gate to decide this.