Numbers

With Sum Bus Only:

Airgroup: Zisk Air: Main
Summary: nBits: 21 | blowUpFactor: 1 | maxConstraintDegree: 3 | 
Stage1: 31 | Stage2: 21 | StageQ: 6 | ImPols: 1 => 3 = 0 + 3 | Total: 58 | nConstraints: 31 | nEvals: 53

With Both Sum and Product Buses (applied to all main and mem_align permutations):

Airgroup: Zisk Air: Main
Summary: nBits: 21 | blowUpFactor: 1 | maxConstraintDegree: 3 | 
Stage1: 31 | Stage2: 18 | StageQ: 6 | ImPols: 0 => 0 = 0 + 0 | Total: 55 | nConstraints: 31 | nEvals: 52

Observations

1. Optimization Achieved: Using the product bus in combination with the sum bus reduces the total number of intermediate polynomials (ImPols) from 3 to 0, leading to a reduction in total constraints (Total: 58 -> 55) and evaluations (nEvals: 53 -> 52).
2. Trade-Off: Adding a product bus introduces one additional constraint per air, since airs using only the sum bus must explicitly prove their contribution to the product bus is zero.
3. Surprises: No optimizations were achieved for mem_align. If applied to other airs using permutations, it worsens the number of columns.