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Benchmarks

Mean time per call for each engine (lower is better), generated from benchmarks/benchmarks.csv by scripts/bench_report.py. Each engine has two bars: Trajectory (fire a trajectory) and Zero (find the zero angle). The vertical scales are logarithmic.

Mean time

Mean time per call by engine

Speedup vs python.rk4

Speedup vs python.rk4

  • Version: 3.0.0b3.dev7+ga8145b128.d20260921 (branch new-entry-points, commit ef170c8)
  • Where an engine was run several times, the run with the most repeats is used.
  • Only engines present in the benchmark data are listed.

Results

Engine Trajectory, ms vs python.rk4 Zero, ms vs python.rk4 Repeats
python.euler 95.744 0.579x 422.462 0.571x 50
python.verlet 66.536 0.833x 293.166 0.823x 50
python.rk4 55.455 1x 241.340 1x 50
scipy.bdf 37.744 1.47x 311.273 0.775x 100
scipy.radau 37.555 1.48x 166.027 1.45x 500
scipy.rk23 17.228 3.22x 71.026 3.4x 500
scipy.lsoda 12.939 4.29x 83.901 2.88x 500
scipy.dop853 11.439 4.85x 135.603 1.78x 100
scipy.rk45 5.678 9.77x 44.611 5.41x 500
cython.euler 1.267 43.8x 4.455 54.2x 500
cython.rk4 0.429 129x 1.179 205x 1000
tiny_bclibc_ctypes:TinyBclibcDoubleIntegrationEngine 0.245 226x 0.233 1036x 500
cython.tsitouras 0.170 326x 0.094 2567x 2000
cython.dopri 0.170 326x 0.094 2567x 2000
cython.rkck 0.170 326x 0.094 2567x 2000

Note

Adaptive engines (cython.rkck, cython.dopri, cython.tsitouras) take far fewer steps than fixed-step RK4, which is why Zero shows such a large gap. Results depend on hardware and workload; treat them as relative figures. See Engines for the engine overview.