Benchmark

September 23, 2026

• Data and prediction points are randomly distributed over a unit sphere.
• Data values are generated by unconditional Gaussian RF simulation with gstat.
• Simple global kriging with the exponential model C(h) = exp(-3 r/a), a = 0.06.
• For jizai, fitting tolerance of 1e-3 and evaluation accuracy of 1e-5 are used.
• Wall-clock time of a single run, without I/O.

# of points		Kriging prediction time (s)				Max |Δpred|
Data	Pred	R/gstat	jizai
			Fit	Eval	Total
1k	1k	0.349	0.015	0.000	0.015	5.33e-15
	10k	3.229	0.013	0.005	0.018	9.99e-15
	100k	31.778	0.013	0.049	0.062	1.11e-14
	1M	335.703	0.012	0.429	0.441	1.18e-14
10k	1k	45.108	0.355	0.005	0.360	4.96e-08
	10k	428.813	0.352	0.055	0.407	3.15e-07
	100k	–	0.356	0.094	0.450	–
	1M	–	0.374	0.463	0.837	–
100k	1k	–	3.284	0.045	3.329	–
	10k	–	3.018	0.333	3.351	–
	100k	–	3.026	0.405	3.431	–
	1M	–	3.075	1.291	4.366	–
1M	1k	–	53.151	0.496	53.647	–
	10k	–	55.587	3.905	59.492	–
	100k	–	53.901	4.090	57.991	–
	1M	–	53.115	7.288	60.403	–

Environment:

  CPU: 16-core Apple M4 Max
  RAM: 128 GB
   OS: macOS 27 Golden Gate
jizai: fb58fb9e81ac674f6d8fa2c6ec72a1ce9f9c6898
Clang: 23.1.1
    R: 4.6.1
gstat: 2.1.6