refactor: witness caching skips the 1st witness.

[huitseeker]

• Optimized the prove_recursively function in RecursiveSNARKTrait for performance enhancement
• Implemented on-demand computation for first circuit's witness in prove_step

[arthurpaulino]

It's missing the corresponding change in supernova.rs

[huitseeker]

It's missing the corresponding change in supernova.rs

It's intentional, this is for benchmarking.

[huitseeker]

!benchmark --features cuda

[github-actions]

!gpu-benchmark action failed ❌

https://github.com/lurk-lab/lurk-rs/actions/runs/8361561494

[samuelburnham]

!benchmark --features cuda

[github-actions]

Benchmark for 090931a

Click to view benchmark

Test	Base	PR	%
LEM Fibonacci Prove - rc = 100/fib/num-100	1493.9±8.03ms	1474.3±9.15ms	-1.31%
LEM Fibonacci Prove - rc = 100/fib/num-200	2.8±0.01s	2.8±0.01s	0.00%
LEM Fibonacci Prove - rc = 600/fib/num-100	1933.9±4.27ms	1842.8±18.73ms	-4.71%
LEM Fibonacci Prove - rc = 600/fib/num-200	3.1±0.01s	3.0±0.01s	-3.23%

[github-actions]

!gpu-benchmark action succeeded! 🚀

https://github.com/lurk-lab/lurk-rs/actions/runs/8361585884

[arthurpaulino]

🎉