perf(prover): powers of alpha (#2000) #6789

Job	Run time
Test (x86-64)	28m 8s
Cargo Check	5m 27s
Examples	6m 4s
Formatting & Clippy	5m 37s
Check Verifier `no_std`	1m 17s
Check lock files	6m 1s
Test (ARM)	31m 33s
Test Verifier Crate	16m 11s
Spell Check	3m 15s
Build patches and zkvm in host	1m 22s
	1h 44m 55s

Provide feedback