Benchmarks

These measurements compare the R binding and Rust GPU backend; they are shared reference results, not separately measured timings for each binding. Timings depend on hardware, drivers, thread availability, and workload; crossover points are observations from this run, not universal thresholds.

R and CPU Comparison

Runtime and speedup comparison of stats::lowess with serial and parallel rfastlowess across benchmark categories

The plot and table use mean CPU timings. Parentheses show speedup relative to stats::lowess; values above 1 indicate faster execution than R.

Scenario	`stats::lowess`	rfastlowess (serial)	rfastlowess (parallel)
clustered	2.34 ms	2.15 ms (1.1×)	1.07 ms (2.2×)
constant_y	1.62 ms	2.12 ms (0.8×)	0.76 ms (2.1×)
extreme_outliers	6.34 ms	6.35 ms (1.0×)	2.91 ms (2.2×)
financial_1000	0.26 ms	0.22 ms (1.2×)	0.22 ms (1.2×)
financial_500	0.22 ms	0.14 ms (1.6×)	0.15 ms (1.5×)
financial_5000	1.12 ms	0.92 ms (1.2×)	0.79 ms (1.4×)
fraction_0.05	0.97 ms	0.76 ms (1.3×)	0.93 ms (1.1×)
fraction_0.1	1.67 ms	1.39 ms (1.2×)	1.05 ms (1.6×)
fraction_0.2	2.58 ms	2.28 ms (1.1×)	1.20 ms (2.1×)
fraction_0.3	3.65 ms	3.20 ms (1.1×)	1.28 ms (2.9×)
fraction_0.5	4.97 ms	4.98 ms (1.0×)	1.87 ms (2.7×)
fraction_0.67	6.07 ms	6.73 ms (0.9×)	1.84 ms (3.3×)
genomic_1000	0.23 ms	0.28 ms (0.8×)	0.34 ms (0.7×)
genomic_100000	32.71 ms	25.84 ms (1.3×)	8.76 ms (3.7×)
genomic_5000	1.42 ms	1.57 ms (0.9×)	1.10 ms (1.3×)
high_noise	8.01 ms	7.46 ms (1.1×)	2.33 ms (3.4×)
iterations_0	0.48 ms	0.50 ms (1.0×)	0.36 ms (1.3×)
iterations_1	1.31 ms	1.47 ms (0.9×)	0.60 ms (2.2×)
iterations_10	7.29 ms	5.96 ms (1.2×)	2.63 ms (2.8×)
iterations_2	1.95 ms	2.09 ms (0.9×)	1.07 ms (1.8×)
iterations_3	2.57 ms	2.19 ms (1.2×)	1.10 ms (2.3×)
iterations_5	3.37 ms	3.33 ms (1.0×)	1.62 ms (2.1×)
large_delta_0	10 067.77 ms	5 279.61 ms (1.9×)	1 434.48 ms (7.0×)
large_delta_0.1	11.90 ms	12.68 ms (0.9×)	5.05 ms (2.4×)
large_high_fraction	9 434.85 ms	4 940.71 ms (1.9×)	1 216.33 ms (7.8×)
large_high_iter	31 189.44 ms	14 409.17 ms (2.2×)	4 475.26 ms (7.0×)
scale_1000	0.38 ms	0.36 ms (1.1×)	0.35 ms (1.1×)
scale_10000	2.69 ms	2.59 ms (1.0×)	1.51 ms (1.8×)
scale_5000	1.82 ms	1.43 ms (1.3×)	0.99 ms (1.8×)
scientific_1000	0.42 ms	0.60 ms (0.7×)	0.50 ms (0.8×)
scientific_500	0.29 ms	0.25 ms (1.2×)	0.30 ms (1.0×)
scientific_5000	1.92 ms	1.88 ms (1.0×)	1.35 ms (1.4×)

At small sizes, fixed per-call overhead can dominate, and parallel execution is not always faster. The large wide-window workload reaches 7.8× parallel speedup; the high-iteration workload reaches 2.2× serial speedup. Allowing default delta reduces the reference workload from approximately 10.07 s to 11.90 ms.

CPU-Parallel versus GPU

The first measured input size where GPU median time is below CPU-parallel median time:

Fraction	0 robustness iterations	3 robustness iterations
0.1	50 000	50 000
0.3	50 000	50 000
0.5	25 000	25 000

Selected median timings, with GPU speedup defined as CPU-parallel time divided by GPU time:

n	Fraction	Iterations	CPU-parallel	GPU	GPU speedup
10 000	0.5	3	4.66 ms	6.31 ms	0.74×
50 000	0.5	0	7.69 ms	2.64 ms	2.92×
100 000	0.5	3	52.40 ms	24.62 ms	2.13×
250 000	0.3	3	96.33 ms	49.14 ms	1.96×
1 000 000	0.5	3	1 118.35 ms	236.47 ms	4.73×

The GPU is slower for the selected 10 000-point case, but approximately 4.7× faster for the million-point case. Wider windows increase per-query work and can make GPU execution worthwhile at smaller input sizes.

The crossover is the first sampled GPU win, not a guarantee that every larger input favors the GPU. At fraction 0.1, CPU wins again at 100K for both iteration counts.

Full crossover sweep with text charts

fraction=0.1  iterations=0  - first GPU win: 50K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.06 ms     1.08 ms     0.06×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     0.27 ms     0.97 ms     0.27×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      5K     0.21 ms     0.87 ms     0.24×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
     10K     0.31 ms     1.73 ms     0.18×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
     25K     0.78 ms     2.03 ms     0.38×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒
     50K     2.78 ms     2.20 ms     1.26×  GPU █  ◀ crossover
    100K     5.52 ms     6.71 ms     0.82×  CPU ▒▒▒▒
    250K    23.10 ms    15.10 ms     1.53×  GPU ███
    500K    42.44 ms    35.62 ms     1.19×  GPU █
      1M    89.78 ms    62.94 ms     1.43×  GPU ██

fraction=0.3  iterations=0  - first GPU win: 50K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.11 ms     0.74 ms     0.15×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     0.30 ms     0.78 ms     0.38×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒
      5K     0.36 ms     0.83 ms     0.43×  CPU ▒▒▒▒▒▒▒▒▒▒▒
     10K     0.68 ms     1.48 ms     0.46×  CPU ▒▒▒▒▒▒▒▒▒▒▒
     25K     1.60 ms     1.83 ms     0.88×  CPU ▒▒
     50K     5.14 ms     2.40 ms     2.14×  GPU ██████  ◀ crossover
    100K     9.33 ms     5.69 ms     1.64×  GPU ███
    250K    30.04 ms    16.16 ms     1.86×  GPU ████
    500K    58.62 ms    34.27 ms     1.71×  GPU ████
      1M   126.25 ms    69.38 ms     1.82×  GPU ████

fraction=0.5  iterations=0  - first GPU win: 25K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.23 ms     0.92 ms     0.25×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     0.30 ms     0.86 ms     0.35×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒
      5K     0.51 ms     1.56 ms     0.32×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒
     10K     1.10 ms     1.46 ms     0.75×  CPU ▒▒▒▒▒
     25K     2.36 ms     1.85 ms     1.27×  GPU █  ◀ crossover
     50K     7.69 ms     2.64 ms     2.92×  GPU ██████████
    100K    15.81 ms     5.31 ms     2.98×  GPU ██████████
    250K    37.61 ms    17.10 ms     2.20×  GPU ██████
    500K    80.02 ms    35.82 ms     2.23×  GPU ██████
      1M   231.02 ms    70.12 ms     3.29×  GPU ███████████

fraction=0.1  iterations=3  - first GPU win: 50K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.26 ms     5.04 ms     0.05×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     1.09 ms     4.71 ms     0.23×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      5K     1.26 ms     4.80 ms     0.26×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
     10K     1.33 ms     5.72 ms     0.23×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
     25K     3.31 ms     6.55 ms     0.51×  CPU ▒▒▒▒▒▒▒▒▒▒
     50K     8.19 ms     8.04 ms     1.02×  GPU  ◀ crossover
    100K    14.35 ms    16.86 ms     0.85×  CPU ▒▒▒
    250K    58.75 ms    43.92 ms     1.34×  GPU ██
    500K   113.73 ms    86.19 ms     1.32×  GPU ██
      1M   304.22 ms   212.73 ms     1.43×  GPU ██

fraction=0.3  iterations=3  - first GPU win: 50K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.51 ms     4.96 ms     0.10×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     1.33 ms     4.70 ms     0.28×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      5K     1.80 ms     5.71 ms     0.31×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒
     10K     2.77 ms     6.09 ms     0.45×  CPU ▒▒▒▒▒▒▒▒▒▒▒
     25K     5.73 ms     7.33 ms     0.78×  CPU ▒▒▒▒
     50K    15.03 ms     9.70 ms     1.55×  GPU ███  ◀ crossover
    100K    27.16 ms    23.23 ms     1.17×  GPU █
    250K    96.33 ms    49.14 ms     1.96×  GPU █████
    500K   201.04 ms   113.25 ms     1.77×  GPU ████
      1M   673.32 ms   192.87 ms     3.49×  GPU ████████████

fraction=0.5  iterations=3  - first GPU win: 25K
       n   CPU (med)   GPU (med)   speedup  chart
--------  ----------  ----------  --------  ------------------------
      1K     0.80 ms     4.57 ms     0.17×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      2K     1.34 ms     5.03 ms     0.27×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒▒
      5K     2.43 ms     5.95 ms     0.41×  CPU ▒▒▒▒▒▒▒▒▒▒▒▒▒
     10K     4.66 ms     6.31 ms     0.74×  CPU ▒▒▒▒▒
     25K     9.19 ms     7.37 ms     1.25×  GPU █  ◀ crossover
     50K    23.77 ms    12.99 ms     1.83×  GPU ████
    100K    52.40 ms    24.62 ms     2.13×  GPU ██████
    250K   123.11 ms    55.82 ms     2.21×  GPU ██████
    500K   394.26 ms   139.10 ms     2.83×  GPU █████████
      1M  1118.35 ms   236.47 ms     4.73×  GPU ███████████████████

End-to-End GPU Fit

Recorded wall-clock timings for the complete Rust GPU workload:

n	Mean	Median	Minimum	Maximum
1 000	6.091 ms	6.512 ms	4.710 ms	7.170 ms
5 000	5.162 ms	5.136 ms	4.344 ms	5.957 ms
10 000	6.548 ms	6.606 ms	4.904 ms	8.548 ms
50 000	7.565 ms	7.376 ms	7.172 ms	8.352 ms
100 000	14.170 ms	14.396 ms	12.213 ms	16.029 ms
500 000	63.544 ms	63.831 ms	61.600 ms	64.527 ms
1 000 000	141.224 ms	141.413 ms	137.718 ms	143.109 ms

Small workloads have a substantial fixed setup cost. Beyond those sizes, runtime grows with the amount of fitting work.

Host/Device Transfer Overhead

Mean transfer latencies and effective bandwidth from the isolated transfer benchmark. Round-trip bandwidth uses the combined uploaded/downloaded bytes divided by mean round-trip time:

Transfer measurements used an Intel Arc 140V integrated GPU (16 GB) with the Vulkan backend.

n	Upload	Download	Round trip	Effective bandwidth
1 000	0.361 ms	0.399 ms	0.760 ms	0.026 GB/s
5 000	0.404 ms	0.403 ms	0.807 ms	0.124 GB/s
10 000	0.440 ms	0.506 ms	0.946 ms	0.212 GB/s
50 000	0.426 ms	0.326 ms	0.751 ms	1.331 GB/s
100 000	0.730 ms	0.853 ms	1.583 ms	1.263 GB/s
500 000	1.922 ms	2.212 ms	4.134 ms	2.419 GB/s
1 000 000	3.662 ms	4.295 ms	7.957 ms	2.514 GB/s

Fixed transfer latency dominates the smaller buffers; effective bandwidth reaches approximately 2.5 GB/s for the largest recorded transfer. These measurements isolate transfer operations, so they should not be subtracted directly from timings collected by a different fit benchmark.

The transfer-fraction report uses rfastlowess_parallel.json, which is a CPU reference, not an end-to-end GPU measurement. Its 216.4% fraction and negative kernel time are therefore not valid GPU timing results and are omitted here.