add bench results

workflow/BENCHMARKS.md

@@ -23,19 +23,44 @@ The following operations were benchmarked:
 - **Prove Circuit**: Time taken to generate a proof for the constructed circuit.
 - **Verify Circuit**: Time taken to verify the generated proof.
 
-#### Build Time
+## Bench Results
+The following is the result of running the codex storage proof circuit (sample_cells).
+The bench uses the Goldilocks field and Poseidon2 Hash. All results were run on Mac Mini with M2 Pro and 16GB RAM. 
 
+### Bench params
+The benchmark runs with the default params which are the following:
 
-#### Prove Time
+```bash
+export MAXDEPTH=32        # Maximum depth of the slot tree
+export MAXSLOTS=256       # Maximum number of slots
+export CELLSIZE=2048      # Cell size in bytes
+export BLOCKSIZE=65536    # Block size in bytes
+export NSAMPLES=5         # Number of samples to prove
 
+export ENTROPY=1234567    # External randomness
+export SEED=12345         # Seed for creating fake data
 
-#### Verify Time
+export NSLOTS=11          # Number of slots in the dataset
+export SLOTINDEX=3        # Which slot to prove (0..NSLOTS-1)
+export NCELLS=512         # Number of cells in this slot
+```
 
+### Build Time
+Build time for plonky2 circuits is 39.644 ms.
+Baseline Groth16 with same params: 61 seconds for the circuit specific setup.
 
-#### Proof Size
+### Prove Time
+Prove time for plonky2 circuits is 53.940 ms.
+Baseline Groth16 with same params: 4.56 seconds using snarkjs
 
+improvement: approx 80x
 
-#### Peak Memory Usage
+### Verify Time
+To be done once recursion is added to the codebase.
 
+### Proof Size
+Plonky Proof size: 116008 bytes
+This is without recursion or Groth16 wrapper.
 
-### Remarks
+### Peak Memory Usage
+To be done.