- Add docs/src/benchmarks.md mirroring CuQuantum.jl pattern: problem
  description, result tables, environment info, reproduction instructions
- Wire benchmarks page into docs/make.jl
- Extract shared problem constructors to benchmark/problem_utils.jl
  (make_bilinear_problem, make_scaled_problem) to eliminate duplication
- Remove hardcoded package_version, pass runner consistently
- Update README with docs link and regression detection example

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

- Remove fragile Base.loaded_modules_order lookup for MadNLPSolverExt;
  MadNLPOptions is exported directly from DirectTrajOpt
- Change MadNLP print_level from 1 (TRACE) to 6 (ERROR) to match
  Ipopt's silent output and avoid polluting benchmark stdout
- Derive state_dim/control_dim from problem_dims(prob) instead of
  hardcoding in micro-benchmark MicroBenchmarkResult
- Set BENCHMARK_RUNNER=github-actions in CI workflow so results
  are distinguishable from local runs
- Remove unused ForwardDiff and LinearAlgebra from benchmark/Project.toml

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

- Pin HarmoniqsBenchmarks source to fix/widen-dto-compat branch which
  has DirectTrajOpt compat "0.8, 0.9" (fixes Pkg.instantiate failure)
- Run JuliaFormatter on benchmark files

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

…merge

The compat-widening branch has merged to HBJ main, so point the benchmark
Project.toml at main. HBJ is not yet registered in General, so we still
need the explicit URL+rev source.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

`contains(ti.filename, "benchmark")` would silently exclude any future
testitem whose filename happens to contain "benchmark" (e.g.
`test/regressions/hessian_benchmark.jl`). Switch to a path-component
match via `splitpath` so only files actually under a `benchmark/`
directory are excluded.

Tracking `rev = "main"` makes benchmark CI results non-reproducible: a
force-push or follow-up commit on HBJ silently changes the benchmark
schema for every old commit's CI re-run. Pin to the v0.2.0 prep tip
(5401542c — convergence schema + extractors), bump as needed when we
adopt new HBJ helpers.

Drop in favor of `[compat]` once HBJ registers in General.

`make_scaled_problem` accepted `seed::Int = 42` but the scaling sweep
never passed one — so every cell used seed 42, which means the timing
table was effectively measuring nine variations of the same random
instance rather than a sweep across instances.

Generate a deterministic per-cell seed (`1000 + 100*N + dim`). Both
solvers still receive the same instance for that cell so the
Ipopt-vs-MadNLP comparison stays apples-to-apples; only across cells
does the underlying problem change.

This is still single-shot per cell — a follow-up could sweep K seeds
and report median if we want statistical robustness.

The bare `try … catch end` blocks for `pkg_version` and the inline
`try … catch; ; "unknown" end` for the git SHA both hid real failures
silently (and the latter had a syntactically dubious `;` continuation).
Capture the exception with `@warn` so CI surfaces a "Failed to look up
…" message if the lookup ever breaks, rather than letting downstream
results carry "unknown" with no explanation.

Also hoist the git rev-parse into a named local for readability.

First-call JIT compile (Ipopt/MadNLP extension load, KKT/AD codegen)
dominates wall-time on small problems and biases the Ipopt-vs-MadNLP
comparison by solver order — whichever solver runs first pays the MOI
extension JIT that the second avoids.

Add a tiny `max_iter = 2` warmup solve per solver before the timed
section in both the macro-benchmark and the memory-scaling sweep. Each
@testitem runs in its own Julia process, so the warmup needs to be
inside the testitem (compilation cache is per-process).

This makes the reported wall-times steady-state numbers rather than
"cold start + a few iterations of solve work".

The numbers in the benchmark page were single-run local samples that
got captured into the docs build verbatim. Without a workflow wiring
real CI artifacts into the docs, presenting them as bolded headline
claims ("MadNLP is 33% faster", "40–45% less memory") would let them
become the canonical DirectTrajOpt figures people quote — which is
misleading because they shift with hardware, BLAS, MUMPS, Julia
version, and even solver order before the warmup fix.

- Add an upfront note that the tables are example output showing the
  schema of each benchmark, not pinned reference measurements.
- Remove the "33% faster / 43% fewer / 40–45% less / 30–35% faster"
  bolded comparison sentences.
- Reframe the scaling table around what it's actually good for: each
  solver vs itself over time, not a single-shot solver comparison.

Real numbers should come from the CI workflow's JLD2 artifacts. Wiring
those into the docs build is a follow-up.

JuliaFormatter line-broke the `DirectTrajOpt.solve!(...; options=...)`
calls in the warmup blocks. Apply the formatter pass so the Formatter
CI check stays green.