Adjust degree bit automatically

[eigmax]

Now the degree bit for shrinking the Stark verifier circuit in prove_root is assigned manually, the range of the degree bits is too large and lead to large memory consuming.

[VanhGer]

First idea: Determine the relationship between the segment size and the original_degree_bit of each table.
Currently, the degree_bits_range for each table is:

const DEGREE_BITS_RANGE: [Range(usize); 6] = [10..21, 12..22, 12..21, 8..21, 6..21, 13..23];

Below are the tables of segment size and degree bit of 6 module tables

sha2-rust-program

Segment size	Arithmetic	Cpu	Poseidon	Poseidon Sponge	Logic	Memory
2^10 = 1024	16	11	11	11	6	17
2^11 = 2048	16	11	11	11	6	17
2^12 = 4096	16	11-12	11	11	7-10	17
2^13 = 8192	16	12-13	11-12	11-12	9-11	17-18
2^14 = 16384	16	14	12	12	11	18
2^15 = 32768	16	14	12	12	11	18
2^16 = 65536	16	14	12	12	11	18
2^17 = 131072	16	14	12	12	11	18
2^21 = 2097152	16	14	12	12	11	18

revme-program

Segment size	Arithmetic	Cpu	Poseidon	Poseidon Sponge	Logic	Memory
2^15 = 32768	16	15	12-14	12-14	6-14	18-19
2^16 = 65536	16	16	13-14	13-14	10-15	19-20
2^17 = 131072	16	16-17	13-14	13-14	11-15	19-21
2^18 = 262144	16	18	15	15	15	21
2^19 = 524288	18	19	15	15	16	22
2^20 = 1048576	18	19	15	15	16	22
2^21 = 2097152	18	19	15	15	16	22

It seems that with different segments of the same size, the number of each type of instruction varies. This makes it challenging to fix the degree bit for each table, particularly for the memory and logic tables. So this idea is difficult to implement.