Benchmarks

Criterion.rs benchmarks, algorithm comparisons, and scaling analysis.

The solver uses Criterion.rs v0.5 for statistically rigorous benchmarking with HTML reports.

Running Benchmarks

# Full benchmark suite
cargo bench

# Specific benchmark
cargo bench -- chain_solve

HTML reports are generated in target/criterion/<benchmark>/report/index.html.

Benchmark	Description	Parameters
`chain_solve`	Serial distance constraints	5 / 20 links
`grid_solve`	2D grid with horizontal + vertical	4×4 grid
`tangent_garden_solve`	Multiple tangent circles	6 circles
`mixed_solve`	Mix of all constraint types	30 constraints
`overconstrained_solve`	Redundant constraints	2× overdetermined

The headline comparison on the chain-20 benchmark:

Algorithm	Time	Relative	Iterations
DogLeg	2.41 ms	1.0×	12
BFGS	3.30 ms	1.4×	15
L-BFGS	3.15 ms	1.3×	16
Sparse CG	5.20 ms	2.2×	22
LM	54.8 ms	22.7×	48

DogLeg dominates on chain problems because the Gauss-Newton step is nearly exact, and the trust-region framework avoids LM's conservative damping.

Isolated measurement of individual operations:

Benchmark	What It Measures
`compute_residuals`	Residual vector evaluation
`compute_jacobian`	Analytical Jacobian computation
`finalise`	Solution extraction and verification

These help identify bottlenecks independently of the solver algorithm.

Chain problems at increasing sizes:

Problem	Parameters	DogLeg	LM
chain-50	100	6.2 ms	142 ms
chain-100	200	14.8 ms	410 ms
chain-200	400	38.5 ms	1200 ms

DogLeg scales roughly linearly with problem size for chain problems, while LM scales superlinearly due to the dense linear system solves.

Runs all algorithms on the same problem and compares results:

cargo bench -- cross_validation

Measures the overhead of running multiple algorithms in sequence. Typical overhead is 2–3× compared to a single algorithm.

Problem	Single Start	Multi-Start (20)	Best-of
chain-20	2.41 ms	28.5 ms	2.38 ms
tangent_garden	5.10 ms	62.3 ms	3.90 ms

Multi-start finds better solutions on problems with multiple local minima, at the cost of 10–15× runtime.

Problem	n	BFGS	L-BFGS (m=10)
chain-20	40	3.30 ms	3.15 ms
chain-100	200	18.2 ms	12.1 ms
chain-200	400	52.8 ms	24.3 ms

L-BFGS becomes significantly faster for n ≥ 100 due to O(mn) vs O(n²) per-iteration cost.

Problem	Stagnation ON	Stagnation OFF
chain-20	2.41 ms	2.41 ms
overconstrained	1.80 ms	4.20 ms

Stagnation detection has negligible overhead on well-conditioned problems but dramatically speeds up pathological cases by terminating early.

Enabling tracing and diagnostics adds ~5% overhead:

A baseline benchmark report is maintained at:

benchmarks/BASELINE.md

CI runs benchmarks and compares against the baseline. Regressions larger than 10% trigger a warning.