Benchmarks

Compare FFTLog, the bundled Table, and VBMicrolensing for magnification accuracy and evaluation speed. The inference comparison fits a stellar-lens event with annual parallax using NUTS and emcee. Measurements use CPU and float64; measurement details record the fixed settings, reference calculations, and timing protocol. Each method runs alone on the same machine. These are whole-machine timings; CPU usage and parallel execution settings accompany the reports.

Model(source="linear") uses Table; Model(source="linear", solver="fft") selects FFTLog. Neither requires numerical tuning. For astrometric accuracy and joint evaluation, see finite-source effects.

Accuracy

Compare maximum relative magnification error against independent source integration, for eight radii from 1e-6 to 10. Each radius has 105 sampled separations over 0 <= u/rho <= 50, including alignment and dense sampling near contact. Uniform sources and linear limb darkening (a1=.5) are shown separately. These are sampled maxima, not uniform error bounds.

One fixed configuration per method. Non-finite external-library values are excluded from maxima and counted in the report. See reference-package settings for valid domains and missing points.

Table’s largest sampled relative magnification error is 1.23e-7 across these radii and profiles.

Download the accuracy report and per-point errors. The FFTLog convergence study examines numerical resolution separately.

Magnification runtime

Evaluate the same event at 10–1000 epochs per batch, with rho=.01, u0=.005, t_e=20 days, and linear coefficient a1=.5. Observation times span two days around peak, covering 0.5 <= u/rho <= 5.03.

Median batch time over 100 synchronized calls after three warmups. Trajectories and API conversions are included; input preparation, model setup, and compilation are excluded. Methods retain their native approximations; achieved accuracy differs as shown above.

At 1000 epochs with linear limb darkening, Table is 3.87× faster than FFTLog and 6.12× faster than VBM. For uniform sources, VBM is fastest.

To time a light curve, construct the model before the timer, warm up each input shape, and call jax.block_until_ready on every measured result. The benchmark script uses the same event and timing protocol for all methods. Download timings and raw repeats.

The FFTLog resolution study records the cost of changing the transform grid.

Inference

Compare complete inference runs for the same annual-parallax event:

Finite-source calculation	Sampler	CPU execution
singlens Table	NumPyro NUTS (adaptive HMC)	16 parallel chains
VBMicrolensing	emcee ensemble sampler	16 worker processes

singlens uses Model(source="linear", solver="table"), interpolating its packaged finite-source bases. VBM uses its ESPL tables and limb-darkening integration. JAX autodiff supplies the NUTS posterior gradients. Both fit nine parameters, including source and blend fluxes; fluxes are sampled jointly. The observations, priors, exposure averaging, and ESS target are shared. This compares the solver and sampler together; measurement details specify each implementation.

Data and posterior

A synthetic stellar-lens event has \(t_E=67\) days, \(\rho=0.00458\), \(u_0/\rho=0.46\), and \((\pi_{E,N},\pi_{E,E})=(0.096,-0.072)\). A \(0.49\,M_\odot\) lens at 5.48 kpc and a source at 8 kpc give \(\theta_E=0.48\) mas; the source radius is \(2.2\,\mu\)as. The setup is inspired by OGLE-2007-BLG-050. The observations are synthetic.

An idealized ground network supplies 1,199 observations over 210 days: daily wings, hourly shoulders, and five-minute peak coverage. The 13-hour source transit contains 157 observations. The source has apparent \(I=18.5\) and supplies 80% of baseline light. Fixed 1–60 second exposures and known Gaussian errors include photon, sky, and read noise plus an independent 0.3% fractional floor. Weather and site visibility are not simulated.

Independent source integration supplies the exposure-averaged injection. This realization uses noise seed 43; all observations enter both fits.

Infer \(t_0,u_0,t_E,\rho,\pi_{E,N},\pi_{E,E}\), the linear limb-darkening coefficient \(a_1\), and fluxes \(f_s,f_b\). Both runs use the same priors and Table-based MAP/Hessian initialization. The model and priors include the NumPyro definition and the joint Gaussian flux prior.

Posteriors for noise seed 43, conditional on \(u_0>0\). Plot thinning affects only the display; ESS uses all saved chain steps. Download the full-size PDF.

The broad parallax posterior and competing signed solutions limit the lens-mass constraint. The comparison measures sampling within the positive branch; it does not measure movement between disconnected modes. Independent integration at sampled truth and MAP epochs checks both finite-source solvers. The largest flux errors are 2.8e-6 σ for Table and 0.40 σ for VBM, where \(\sigma\) is each observation’s uncertainty. Across the three noise draws, posterior means differ by up to 0.33 pooled posterior standard deviations. The comparison retains each method’s native numerical settings.

Sampling efficiency

Report the smallest effective sample size (ESS) per elapsed second among the nine sampled parameters. Both samplers target estimated ESS ≥ 5,000, with additional convergence checks. Total time includes model preparation, shared initialization, compilation, warmup, and production. Data generation, diagnostics, numerical validation, posterior selection, and plotting are excluded.

Noise seed 43: cumulative minimum ESS (left) and efficiency by parameter (right). Time includes setup, compilation, warmup, and sampling.

Across three noise realizations on an 18-core Apple M5 Pro, Table + NUTS achieves 6.2–8.8× higher minimum ESS/s than VBM + emcee (median 7.8×). Using measured CPU time summed over all threads and worker processes, minimum ESS per CPU-hour is 4.6–7.0× higher (median 6.0×). Total times are 28–47 seconds and 147–283 seconds, respectively. All runs pass the stated convergence checks. Execution layouts were selected using a separate noise draw; the reports retain measured CPU usage for both methods.

Download the three-seed summary, representative report, and input data. Measurement details provide the stopping rules, reproduction commands, and unthinned posterior chains.