More LEM benchmarks and Coproc derivied implementations

[arthurpaulino]

[Post #738]

This PR implement the missing benchmarks for LEM. Here's the data I collected on my machine w.r.t. Alpha:

end2end proving

end2end_benchmark/end2end_go_base_nova/_10_0
                        time:   [1.1503 s 1.1551 s 1.1583 s]
                        change: [-19.754% -19.255% -18.666%] (p = 0.00 < 0.05)
                        Performance has improved.

synthesis

synthesis/Synthesis-rc/5
                        time:   [7.2469 ms 7.2700 ms 7.2888 ms]
                        change: [-64.198% -64.043% -63.892%] (p = 0.00 < 0.05)
                        Performance has improved.
synthesis/Synthesis-rc/10
                        time:   [14.649 ms 14.656 ms 14.664 ms]
                        change: [-63.761% -63.730% -63.699%] (p = 0.00 < 0.05)
                        Performance has improved.
synthesis/Synthesis-rc/100
                        time:   [151.00 ms 151.11 ms 151.21 ms]
                        change: [-63.398% -63.337% -63.283%] (p = 0.00 < 0.05)
                        Performance has improved.
synthesis/Synthesis-rc/200
                        time:   [298.47 ms 299.53 ms 300.16 ms]
                        change: [-63.713% -63.527% -63.346%] (p = 0.00 < 0.05)
                        Performance has improved.

@winston-h-zhang was correct: synthesis is ~2.75x faster in LEM

sha256 (IVC)

prove/2023-10-14:cff480d56f112511ebbfdba41799a31774492652:rc=10:sha256_ivc_1/1
                        time:   [7.7633 s 7.8085 s 7.8601 s]
                        change: [-31.809% -31.067% -30.408%] (p = 0.00 < 0.05)
                        Performance has improved.

I didn't have enough RAM for higher RCs

sha256 (NIVC)

prove/2023-10-14:cff480d56f112511ebbfdba41799a31774492652:rc=10:sha256_ivc_1/1
                        time:   [3.6714 s 3.6822 s 3.6908 s]
                        change: [-18,164% -18,566% -18,912%] (p = 0.00 < 0.05)
                        Performance has improved.

I didn't have enough RAM for higher RCs
Note: there's a typo in the group name, where it says "ivc"

fibonacci

Prove/2023-10-14:cff480d56f112511ebbfdba41799a31774492652:Fibonacci-rc=100/100
                        time:   [21.800 s 21.823 s 21.847 s]
                        change: [-19.070% -18.909% -18.743%] (p = 0.00 < 0.05)
                        Performance has improved.

I didn't have enough RAM for higher RCs

[huitseeker]

Thanks for the ports!