Profile remaining slow binary benchmark cases

[GiggleLiu]

Context

PR #29 added the benchmark harnesses and multiple CPU contraction optimizations. The latest full benchmark refresh on that PR shows the network scenarios are faster than the one-thread Julia baseline, but several binary benchmark scenarios remain substantially slower.

Full benchmark refresh command set:

make bench-binary
make bench-network
JULIA_NUM_THREADS=1 OPENBLAS_NUM_THREADS=1 make bench-julia
python3 benchmarks/compare.py
make check

Current binary rows from the PR #29 full benchmark refresh:

| Benchmark  | Scenario                         |   Julia (ns) |    Rust (ns) | Julia/Rust | Drop vs Julia |
|------------|----------------------------------|--------------|--------------|------------|---------------|
| binary     | batched_matmul_8x8_batch_4       |         3000 |        26247 |    0.114 |  774.90% |
| binary     | high_d_12x12_contract_4_batch_4  |         8709 |        42167 |    0.207 |  384.18% |
| binary     | high_d_12x12_contract_6          |        22875 |        54340 |    0.421 |  137.55% |
| binary     | high_d_15x15_contract_5_batch_5  |        52958 |       119670 |    0.443 |  125.97% |
| binary     | high_d_15x15_contract_7          |       364417 |       375286 |    0.971 |    2.98% |
| binary     | high_d_18x18_contract_8          |     10882416 |     10720317 |    1.015 |    0.00% |
| binary     | high_d_20x20_contract_9          |     84399125 |     78107208 |    1.081 |    0.00% |
| binary     | matmul_10x10                     |         4333 |        35552 |    0.122 |  720.50% |

Problem

The largest remaining gaps are in small, batched, and materialization-heavy binary cases:

• batched_matmul_8x8_batch_4: Rust is +774.90% slower.
• matmul_10x10: Rust is +720.50% slower.
• high_d_12x12_contract_4_batch_4: Rust is +384.18% slower.

The larger pure-contraction cases are now competitive or faster, so the remaining cost is likely not the large GEMM kernel itself.

Suggested investigation

• Add or reuse a focused binary profiling harness similar to profile_network so setup cost and Criterion overhead do not obscure hotspots.
• Profile matmul_10x10 and batched_matmul_8x8_batch_4 first.
• Check whether remaining time is dominated by contraction setup, layout analysis, small-GEMM dispatch overhead, permutation/materialization, or tensor allocation.
• Decide whether small Standard contractions need a separate fast path from the large faer-backed path.

Acceptance criteria

• Record a focused profile for at least matmul_10x10 and batched_matmul_8x8_batch_4.
• Identify the dominant cost bucket for each.
• Either implement a targeted optimization with before/after benchmark numbers, or document why the current behavior is acceptable.