Performance

Method

bench/compare.sh runs the Go benchmarks of bench_test.go and the same problems through SciPy (bench/scipy_bench.py, under uv run --with scipy --with numpy) alternately, five rounds, and reports the median of each side. Each SciPy figure is the median of 7 repeats of a timed loop lasting about 0.2 s; each Go figure is go test -bench with -benchtime 1s.

SciPy’s time includes calling the Python integrand or right-hand side, which is the price of writing it in Python, not of SciPy’s algorithms. The script also estimates that part: it counts the calls SciPy makes on one run and multiplies by the cost of one call of the same Python function measured alone. The last column divides SciPy’s time without that part by Go’s: what remains is SciPy’s own machinery (QUADPACK in C for quad, NumPy-level Python for solve_ivp, ODEPACK in Fortran for odeint and method="LSODA").

Host: Apple M4 Max (16 cores), macOS, Go 1.27.2, Python 3.12.12, SciPy 1.18.1, NumPy 2.5.4. The machine is shared with other jobs: uptime gave load averages of 7.4 at the start and 8.2 at the end of the run below (16 cores), so absolute numbers carry some noise; the ratios are stable across rounds.

Results (2026-10-10)

Reading the numbers

• quad: SciPy’s QUADPACK is compiled C, and 55–62 % of its time is the Python integrand. The same subdivision (same evaluation count, see verification.md) costs 3× less here without the callbacks, 6–8× with them.
• solve_ivp: SciPy’s RK45, DOP853, Radau and BDF are written in Python on NumPy; per step they pay NumPy call overhead on 2-element arrays, which the callbacks do not explain (they are 2–14 % of the time). The step sequences are the same as here, so the 80–190× is per-step overhead, not a different amount of work.
• LSODA and odeint: SciPy runs ODEPACK’s Fortran; most of odeint’s time on Robertson is the Python right-hand side. ODEPACK’s own work is about 2× ours on that problem. The comparison is between two different algorithms (see design.md): on Van der Pol μ = 1000 this package’s switching method uses 2 337 evaluations to ODEPACK’s 1 803, on Robertson 2 175 to 1 683, and is still faster in wall time because each evaluation is a Go call.
• Allocation: a Quad call allocates its subinterval workspace (6 allocations for QAGS); an ODE step allocates only what it stores in the Solution (the state at each output time) plus, for Radau, the interpolant reused as the next step’s predictor.

To reproduce: ROUNDS=5 ./bench/compare.sh (needs uv on the PATH).