Benchmarks

• Run: python scripts/bench_compare.py --degrees 3,5,8,12 --methods hybrid,aberth,dk --trials 10 --out docs/assets/bench.csv --agg_out docs/assets/bench_agg.csv
• Plot: python scripts/plot_bench.py --in docs/assets/bench_agg.csv --out docs/assets

Newton vs hybrid (tuned)

Summary (medians over 5 trials):

degree	method	time_median(s)	res_median
3	hybrid	0.0027	2.48e-16
3	newton	0.0000	3.33e-16
5	hybrid	0.0060	2.22e-15
5	newton	0.0000	1.89e-15
8	hybrid	0.0142	1.22e-14
8	newton	0.0001	8.30e-15
12	hybrid	0.0314	6.17e-13
12	newton	0.0003	6.17e-13
16	hybrid	0.0796	5.60e-11
16	newton	0.0017	2.70e-11
20	hybrid	0.1191	1.91e-10
20	newton	0.0027	3.19e-10

CSV: docs/assets/newton_vs_hybrid_tuned.csv

Edge cases: iteration profile

We measure time, residual, and (for Newton) total iteration count on a few tougher instances (clusters, ill‑scaled, |t|≈1). Hybrid and Aberth reach the target with minimal polish; Newton iteration counts can spike.

case	hybrid time(s)	aberth time(s)	newton time(s)	newton iters	residual (≈)
double_root	0.0041	0.0005	0.0001	87	1e-16–1e-23
cluster_eps_1e-12	0.0038	0.0005	0.0001	96	1e-38–1e-25
cluster_eps_1e-10	0.0038	0.0005	0.0001	96	1e-39–1e-25
cluster_eps_1e-08	0.0035	0.0005	0.0001	95	1e-16–1e-48
cluster_eps_1e-06	0.0034	0.0005	0.0001	81	1e-41–1e-60
cluster_eps_1e-4	0.0030	0.0006	0.0001	63	1e-16–1e-60
ill_scaled	0.0036	0.0007	0.0001	68	1e-14
rotated_cluster	0.0071	0.0012	0.0002	320	1e-16
near_t_one	0.0032	0.0009	0.0001	72	1e-16

CSV: docs/assets/edge_cases.csv