Profile the sequential version

- [ ] cachegrind
- [ ] gprof
- [ ] discuss sequential performance

## Sequential Perf:

## Improvements:

## Hotspots:

## Cache:

Start by locating the sequential version and profiling entry point in the repository, then run the requested cachegrind and gprof checks. Record the sequential performance discussion, improvements, hotspots, and cache findings in the corresponding sections; the issue does not name specific files or tests.

Written by the indexing model from the issue text.