Biggroup from_witness (used in recurisve verifiers) costs 97 gates before finalization in ultra

[Rumata888]

The cost of biggroup is extremely high with our attempt to cover all cases

[suyash67]

When using from_witness to create a biggroup element, the breakdown of gate count (even before finalization) is:

Operation	Gates	Notes
Fq::from_witness(x)	8	6 NNF + 2 arith
Fq::from_witness(y)	8	same
_x.assert_zero_if(is_infinity)	5	1 mul gate per limb (×5)
_y.assert_zero_if(is_infinity)	5	same
adjusted_b = conditional_assign(is_infinity, 0, b)	5	1 madd gate per limb (×5)
_x.sqr()	26	q, r creation and NNF multiplication
mult_madd({x²,y},{x,−y},{b}) on-curve check	23	same
Total	~80

This cost is unlikely to change and we do not intend to further optimise any non-native arithmetic or ultra arithmetisation.