Benchmarks

Measured on an Apple M3 Pro (12 threads) with min_rigidity=1, max_rigidity=55, delta_rigidity=0.5, dt=1e-5, max_time=1.0.

GMRC throughput

Mode	Field	Solver	Samples	Successful traj/s	Total traj evaluated	Total traj/s	Time
evaluate_batch() (C++)	Table	RK45	100k	48k/s	~839k	~400k/s	2.1s
evaluate() (ThreadPool)	Table	RK45	10k	11k/s	~84k (est.)	~93k/s	0.9s
evaluate() (ProcessPool)	IGRF	RK4	1k	67/s	~8k (est.)	~540/s	14.9s

"Total traj evaluated" is the number of individual trajectory integrations (each MC direction requires scanning multiple rigidities to find the cutoff). The batch mode reports this exactly; Python modes are estimated from the ~8.4 trajectories/direction ratio observed in batch mode.

Solver performance

Single forbidden trajectory at Kamioka, zenith=45°, azimuth=90°, rigidity=7 GV, dt=1e-5, max_time=1 s. Table pre-loaded once; numbers measure integration only.

Solver	B-field	Steps	Eval/s	Ratio to RK4+IGRF
RK4	IGRF	9372	216	1.00×
Boris	IGRF	9159	228	1.06×
RK45	IGRF	56	5393	25×
RK4	Dipole	11823	906	4.2×
Boris	Dipole	11794	1047	4.8×
RK45	Dipole	39	98156	454×
RK4	Table	9300	1067	4.9×
Boris	Table	9091	1339	6.2×
RK45	Table	55	59446	275×

Running benchmarks

# Solver comparison (accuracy + timing)
python examples/eval_solver_comparison.py --n-perf 100

# Full GMRC benchmark
python examples/eval_gmcutoff.py --iter-num 100000 --bfield-type table --solver rk45