Performance over time

How ConvolvedDistributions's benchmark suites have moved across recent revisions: an overall summary across the package first, then one section per suite.

Summary

Each benchmark suite's headline timing across recent revisions.

Suite	Median ratio	Trend	Status
Baseline	0.96	↘	ok
Convolved	1.11	↗	⚠ reg
Difference	1.25	↗	⚠ reg
Product	1.0	→	ok
Quantile	1.0	→	ok
Timeseries	1.44	↗	⚠ reg
AD gradients	n/a	→	n/a
time_to_load	1.0	→	ok

Ratio: latest vs oldest shown revision (1.00 = no change, higher = slower/larger). ⚠ reg = at/above the regression threshold.

Tables below show the most recent 4 revisions, columns labelled by commit date.

Baseline

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Gamma/cdf	2.89 ± 0.24 μs	2.89 ± 0.24 μs	2.91 ± 0.27 μs	2.78 ± 0.24 μs
Gamma/logpdf	2.27 ± 0.27 μs	2.17 ± 0.29 μs	2.28 ± 0.29 μs	2.16 ± 0.27 μs
Normal/cdf	1.4 ± 0.24 μs	1.36 ± 0.25 μs	1.4 ± 0.24 μs	1.35 ± 0.24 μs
Normal/logpdf	0.62 ± 0.29 μs	0.629 ± 0.29 μs	0.607 ± 0.29 μs	0.866 ± 0.02 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Gamma/cdf	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
Gamma/logpdf	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
Normal/cdf	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
Normal/logpdf	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB

Convolved

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf batched	2.3 ± 0.28 μs	2.29 ± 0.28 μs	2.28 ± 0.3 μs	2.29 ± 0.28 μs
analytic/cdf scalar	19.2 ± 0.033 ns	19.2 ± 0.032 ns	19.2 ± 0.053 ns	19.2 ± 0.032 ns
analytic/construction	3.25 ± 0.006 ns	2.62 ± 0.017 ns	3.25 ± 0.005 ns	3.58 ± 0.006 ns
analytic/logpdf batched	0.583 ± 0.089 μs	0.594 ± 0.16 μs	0.583 ± 0.069 μs	0.876 ± 0.024 μs
analytic/logpdf broadcast	2.06 ± 0.27 μs	2.06 ± 0.29 μs	2.06 ± 0.26 μs	2.09 ± 0.27 μs
analytic/logpdf scalar	18.6 ± 0.057 ns	18.5 ± 0.053 ns	18.6 ± 0.045 ns	18.6 ± 0.087 ns
analytic/mean	2.92 ± 0.008 ns	2.31 ± 0.059 ns	3.35 ± 0.11 ns	3.57 ± 0.005 ns
analytic/pdf batched	0.612 ± 0.3 μs	0.637 ± 0.29 μs	0.606 ± 0.29 μs	0.889 ± 0.023 μs
analytic/pdf scalar	18.9 ± 0.032 ns	18.9 ± 0.031 ns	18.9 ± 0.028 ns	18.9 ± 0.05 ns
analytic/rand	1.12 ± 0.22 μs	1.11 ± 0.17 μs	1.11 ± 0.24 μs	1.12 ± 0.037 μs
numeric/cdf batched	0.654 ± 0.0057 ms	0.657 ± 0.0051 ms	0.673 ± 0.0051 ms	0.653 ± 0.0058 ms
numeric/cdf scalar	14.5 ± 0.074 μs	14.2 ± 0.07 μs	14.2 ± 0.057 μs	14.2 ± 0.23 μs
numeric/construction	3.35 ± 0.11 ns	2.96 ± 0.099 ns	3.58 ± 0.006 ns	3.58 ± 0.006 ns
numeric/logpdf batched	0.518 ± 0.013 ms	0.516 ± 0.0072 ms	0.516 ± 0.0065 ms	0.517 ± 0.0077 ms
numeric/logpdf broadcast	0.903 ± 0.013 ms	0.896 ± 0.012 ms	0.897 ± 0.011 ms	0.9 ± 0.023 ms
numeric/logpdf scalar	8.56 ± 0.067 μs	8.31 ± 0.15 μs	8.31 ± 0.075 μs	8.3 ± 0.076 μs
numeric/mean	5.84 ± 0.19 ns	4.88 ± 0.009 ns	6.17 ± 0.011 ns	6.17 ± 0.011 ns
numeric/pdf batched	0.516 ± 0.011 ms	0.516 ± 0.0065 ms	0.516 ± 0.0072 ms	0.515 ± 0.0066 ms
numeric/pdf scalar	8.56 ± 0.099 μs	8.3 ± 0.065 μs	8.32 ± 0.081 μs	8.3 ± 0.075 μs
numeric/rand	2.5 ± 0.31 μs	2.5 ± 0.3 μs	2.49 ± 0.31 μs	2.44 ± 0.31 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf batched	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/cdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/logpdf batched	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/logpdf broadcast	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/logpdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/pdf batched	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/pdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
numeric/cdf batched	24 allocs: 8.32 kB	24 allocs: 8.32 kB	24 allocs: 8.32 kB	24 allocs: 8.32 kB
numeric/cdf scalar	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB
numeric/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/logpdf batched	25 allocs: 8.41 kB	25 allocs: 8.41 kB	25 allocs: 8.41 kB	25 allocs: 8.41 kB
numeric/logpdf broadcast	0.338 k allocs: 29.8 kB	0.338 k allocs: 29.8 kB	0.338 k allocs: 29.8 kB	0.338 k allocs: 29.8 kB
numeric/logpdf scalar	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB
numeric/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/pdf batched	23 allocs: 7.5 kB	23 allocs: 7.5 kB	23 allocs: 7.5 kB	23 allocs: 7.5 kB
numeric/pdf scalar	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB	3 allocs: 0.172 kB
numeric/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB

Difference

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf broadcast	3.12 ± 0.31 μs	3.11 ± 0.31 μs	3.09 ± 0.27 μs	3.26 ± 0.3 μs
analytic/cdf scalar	10.9 ± 0.025 ns	10.5 ± 0.035 ns	10.6 ± 0.018 ns	10.5 ± 0.023 ns
analytic/construction	2.61 ± 0.005 ns	2.94 ± 0.097 ns	2.61 ± 0.005 ns	3.28 ± 0.11 ns
analytic/logpdf broadcast	1.31 ± 0.26 μs	1.29 ± 0.25 μs	1.29 ± 0.25 μs	1.38 ± 0.25 μs
analytic/logpdf scalar	12.8 ± 0.025 ns	12.9 ± 0.41 ns	12.9 ± 0.033 ns	12.9 ± 0.034 ns
analytic/mean	2.29 ± 0.005 ns	2.3 ± 0.075 ns	2.93 ± 0.005 ns	2.92 ± 0.012 ns
analytic/rand	1.07 ± 0.28 μs	0.945 ± 0.28 μs	0.936 ± 0.28 μs	1.13 ± 0.044 μs
numeric/cdf broadcast	1.27 ± 0.02 ms	1.27 ± 0.017 ms	1.27 ± 0.018 ms	1.28 ± 0.034 ms
numeric/cdf scalar	18.2 ± 0.15 μs	18.2 ± 0.09 μs	18 ± 0.17 μs	18 ± 0.6 μs
numeric/construction	2.61 ± 0.012 ns	2.61 ± 0.006 ns	2.95 ± 0.032 ns	3.25 ± 0.026 ns
numeric/logpdf broadcast	1.12 ± 0.02 ms	1.11 ± 0.019 ms	1.11 ± 0.02 ms	1.11 ± 0.028 ms
numeric/logpdf scalar	11.3 ± 0.083 μs	11.2 ± 0.37 μs	11.1 ± 0.12 μs	11.2 ± 0.36 μs
numeric/mean	4.88 ± 0.008 ns	5.2 ± 0.34 ns	4.88 ± 0.01 ns	5.84 ± 0.01 ns
numeric/rand	2.53 ± 0.3 μs	2.48 ± 0.36 μs	2.52 ± 0.28 μs	2.5 ± 0.31 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf broadcast	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/cdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/logpdf broadcast	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/logpdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
numeric/cdf broadcast	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB
numeric/cdf scalar	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB
numeric/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/logpdf broadcast	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB
numeric/logpdf scalar	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB
numeric/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB

Product

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf broadcast	4.27 ± 0.19 μs	4.35 ± 0.2 μs	4.3 ± 0.21 μs	4.28 ± 0.18 μs
analytic/cdf scalar	20.4 ± 0.047 ns	20.5 ± 0.061 ns	20.4 ± 0.057 ns	20.5 ± 0.66 ns
analytic/construction	2.61 ± 0.008 ns	2.61 ± 0.007 ns	2.62 ± 0.32 ns	3.25 ± 0.027 ns
analytic/logpdf broadcast	1.68 ± 0.24 μs	1.67 ± 0.24 μs	1.67 ± 0.21 μs	1.69 ± 0.25 μs
analytic/logpdf scalar	15.8 ± 0.025 ns	15.8 ± 0.53 ns	15.8 ± 0.026 ns	15.8 ± 0.023 ns
analytic/mean	9.07 ± 0.65 ns	7.88 ± 0.029 ns	8.11 ± 0.014 ns	8.75 ± 0.016 ns
analytic/rand	3.83 ± 0.31 μs	3.87 ± 0.32 μs	3.82 ± 0.31 μs	3.82 ± 0.31 μs
numeric/cdf broadcast	1.42 ± 0.021 ms	1.41 ± 0.019 ms	1.41 ± 0.021 ms	1.42 ± 0.038 ms
numeric/cdf scalar	17.1 ± 0.12 μs	17 ± 0.091 μs	17 ± 0.095 μs	17.1 ± 0.57 μs
numeric/construction	2.94 ± 0.009 ns	2.61 ± 0.006 ns	2.61 ± 0.086 ns	3.59 ± 0.12 ns
numeric/logpdf broadcast	1.57 ± 0.019 ms	1.19 ± 0.018 ms	1.19 ± 0.015 ms	1.2 ± 0.026 ms
numeric/logpdf scalar	12 ± 0.086 μs	11.8 ± 0.11 μs	11.8 ± 0.082 μs	11.8 ± 0.11 μs
numeric/mean	4.77 ± 0.16 ns	4.77 ± 0.15 ns	4.89 ± 0.32 ns	6.04 ± 0.32 ns
numeric/rand	2.55 ± 0.33 μs	2.54 ± 0.29 μs	2.53 ± 0.28 μs	2.49 ± 0.31 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
analytic/cdf broadcast	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/cdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/logpdf broadcast	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
analytic/logpdf scalar	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
analytic/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB
numeric/cdf broadcast	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB
numeric/cdf scalar	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB
numeric/construction	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/logpdf broadcast	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB	0.402 k allocs: 0.0467 MB
numeric/logpdf scalar	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB	4 allocs: 0.469 kB
numeric/mean	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B	0 allocs: 0 B
numeric/rand	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB	2 allocs: 0.906 kB

Quantile

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Convolved analytic/grid	0.514 ± 0.023 ms	0.509 ± 0.025 ms	0.508 ± 0.02 ms	0.583 ± 0.039 ms
Convolved analytic/median	23.7 ± 3.8 μs	23.6 ± 3.7 μs	23.6 ± 3.7 μs	23.5 ± 0.74 μs
Convolved numeric/median	0.275 ± 0.0076 ms	0.271 ± 0.0073 ms	0.271 ± 0.0071 ms	0.269 ± 0.0068 ms
Difference numeric/median	0.313 ± 0.008 ms	0.313 ± 0.0078 ms	0.357 ± 0.0071 ms	0.359 ± 0.011 ms
Product numeric/median	0.368 ± 0.01 ms	0.368 ± 0.0084 ms	0.369 ± 0.0084 ms	0.368 ± 0.0077 ms

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Convolved analytic/grid	6.03 k allocs: 0.353 MB	6.03 k allocs: 0.353 MB	6.03 k allocs: 0.353 MB	6.03 k allocs: 0.353 MB
Convolved analytic/median	0.281 k allocs: 17.1 kB	0.281 k allocs: 17.1 kB	0.281 k allocs: 17.1 kB	0.281 k allocs: 17.1 kB
Convolved numeric/median	0.355 k allocs: 21.1 kB	0.355 k allocs: 21.1 kB	0.355 k allocs: 21.1 kB	0.355 k allocs: 21.1 kB
Difference numeric/median	0.318 k allocs: 23.2 kB	0.318 k allocs: 23.2 kB	0.318 k allocs: 23.2 kB	0.318 k allocs: 23.2 kB
Product numeric/median	0.397 k allocs: 28.4 kB	0.397 k allocs: 28.4 kB	0.397 k allocs: 28.4 kB	0.397 k allocs: 28.4 kB

Timeseries

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Convolved delay	0.2 ± 0.09 μs	0.205 ± 0.088 μs	0.2 ± 0.089 μs	0.288 ± 0.0095 μs
Gamma delay	0.198 ± 0.087 μs	0.198 ± 0.087 μs	0.201 ± 0.087 μs	0.288 ± 0.0093 μs
Poisson delay	1.14 ± 0.045 μs	1.15 ± 0.058 μs	1.14 ± 0.052 μs	1.16 ± 0.055 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Convolved delay	2 allocs: 0.297 kB	2 allocs: 0.297 kB	2 allocs: 0.297 kB	2 allocs: 0.297 kB
Gamma delay	2 allocs: 0.297 kB	2 allocs: 0.297 kB	2 allocs: 0.297 kB	2 allocs: 0.297 kB
Poisson delay	4 allocs: 0.594 kB	4 allocs: 0.594 kB	4 allocs: 0.594 kB	4 allocs: 0.594 kB

AD gradients

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Product Gamma*LogNormal mean+var moments/Enzyme forward				6.2 ± 0.15 μs
Difference Normal-Normal analytical/ForwardDiff				0.521 ± 0.06 μs
Convolved Gamma+LogNormal numerical/ReverseDiff (tape)				2.18 ± 0.16 ms
Convolved Normal+Normal analytical/ReverseDiff (tape)				15.2 ± 0.74 μs
Difference LogNormal-Gamma numerical wrt Y/Enzyme reverse				0.19 ± 0.007 ms
Timeseries convolve time-varying Poisson delays/Enzyme reverse				8.92 ± 0.42 μs
pgf Poisson closed form wrt rate/Enzyme reverse				0.0406 ± 0.018 μs
Convolved Gamma+LogNormal numerical/Enzyme reverse				0.101 ± 0.0042 ms
Timeseries convolve discrete Poisson delay/ForwardDiff				0.801 ± 0.11 μs
Convolved Normal+Normal analytical/Mooncake forward				5.07 ± 0.43 μs
Product Gamma*LogNormal mean+var moments/Mooncake forward				4.86 ± 0.41 μs
Convolved Gamma+LogNormal numerical/ForwardDiff				0.0558 ± 0.00017 ms
Convolved Normal+Normal analytical/Mooncake reverse				22.8 ± 2.8 μs
Convolved LogNormal+Gamma numerical/ReverseDiff (tape)				2.13 ± 0.17 ms
Difference Gamma-Normal mean+var moments/Enzyme reverse				0.0393 ± 0.011 μs
Convolved Gamma+LogNormal batched logpdf wrt points/ForwardDiff				0.0516 ± 0.0013 ms
Difference Gamma-LogNormal numerical wrt X/Mooncake reverse				0.725 ± 0.029 ms
Difference Gamma-LogNormal numerical wrt X/Mooncake forward				0.42 ± 0.0067 ms
Convolved Normal+Normal analytical/ForwardDiff				0.535 ± 0.059 μs
Timeseries convolve time-varying PMF matrix/Enzyme reverse				9.5 ± 0.51 μs
Timeseries convolve time-varying PMF matrix/Mooncake forward				6.87 ± 0.7 μs
Convolved LogNormal+Gamma numerical/Mooncake reverse				0.509 ± 0.034 ms
Difference LogNormal-Gamma numerical wrt Y/ReverseDiff (tape)				3.72 ± 0.29 ms
Product Gamma*LogNormal mean+var moments/Mooncake reverse				5.76 ± 0.76 μs
Timeseries convolve time-varying Poisson delays/ForwardDiff				2.3 ± 0.29 μs
Timeseries convolve time-varying PMF matrix/ForwardDiff				0.914 ± 0.12 μs
Convolved Gamma+Normal mean+var moments/ReverseDiff (tape)				2.41 ± 0.14 μs
Difference Normal-Normal analytical/Enzyme forward				7.04 ± 0.074 μs
Convolved Gamma+Normal mean+var moments/Enzyme reverse				0.0392 ± 0.011 μs
Difference LogNormal-Gamma numerical wrt Y/Mooncake forward				0.537 ± 0.0058 ms
Convolved Normal+Normal analytical/Enzyme reverse				3.13 ± 0.096 μs
Product Gamma*LogNormal mean+var moments/ReverseDiff (tape)				10 ± 0.49 μs
Convolved Gamma+LogNormal numerical/Mooncake reverse				0.481 ± 0.033 ms
Convolved Gamma+LogNormal batched logpdf wrt params/Enzyme reverse				0.445 ± 0.023 ms
Difference Normal-Normal analytical/ReverseDiff (tape)				16.3 ± 0.83 μs
Difference Normal-Normal analytical/Mooncake forward				4.91 ± 0.42 μs
Product LogNormal*Gamma numerical wrt Y/Mooncake forward				0.557 ± 0.0062 ms
Difference Gamma-LogNormal numerical wrt X/ForwardDiff				0.0974 ± 0.00067 ms
pgf Poisson closed form wrt rate/ForwardDiff				0.357 ± 0.056 μs
Timeseries convolve discrete Poisson delay/Enzyme reverse				1 ± 0.13 μs
Difference Gamma-Normal mean+var moments/Enzyme forward				6.19 ± 0.12 μs
Difference LogNormal-Gamma numerical wrt Y/Enzyme forward				0.121 ± 0.001 ms
Product Gamma*LogNormal numerical wrt X/Enzyme reverse				0.172 ± 0.0066 ms
Convolved Gamma+LogNormal batched logpdf wrt points/Enzyme forward				0.0672 ± 0.0029 ms
Difference Gamma-LogNormal numerical wrt X/Enzyme forward				0.0948 ± 0.00087 ms
Timeseries convolve time-varying Poisson delays/ReverseDiff (tape)				0.0613 ± 0.0083 ms
Difference Normal-Normal analytical/Mooncake reverse				22.9 ± 2.9 μs
Convolved Gamma+LogNormal batched logpdf wrt points/Mooncake reverse				0.522 ± 0.032 ms
Product LogNormal*LogNormal analytical/Mooncake forward				5.05 ± 0.41 μs
Product LogNormal*Gamma numerical wrt Y/Enzyme forward				0.124 ± 0.0017 ms
Convolved LogNormal+Gamma numerical/Enzyme reverse				0.117 ± 0.0044 ms
Difference Gamma-Normal mean+var moments/Mooncake forward				4.52 ± 0.42 μs
Difference Gamma-Normal mean+var moments/Mooncake reverse				4.07 ± 0.26 μs
pgf Poisson closed form wrt rate/Mooncake forward				4.13 ± 0.46 μs
Timeseries convolve discrete Poisson delay/Enzyme forward				6.22 ± 0.2 μs
Difference Gamma-LogNormal numerical wrt X/Enzyme reverse				0.166 ± 0.0064 ms
pgf Poisson closed form wrt rate/Enzyme forward				5.85 ± 0.16 μs
Convolved Gamma+LogNormal batched logpdf wrt params/ReverseDiff (tape)				1.98 ± 0.18 ms
Product Gamma*LogNormal numerical wrt X/Mooncake reverse				0.762 ± 0.034 ms
Product Gamma*LogNormal numerical wrt X/Enzyme forward				0.0993 ± 0.001 ms
Product LogNormal*Gamma numerical wrt Y/Enzyme reverse				0.203 ± 0.007 ms
Difference LogNormal-Gamma numerical wrt Y/Mooncake reverse				0.781 ± 0.038 ms
Convolved Gamma+LogNormal batched logpdf wrt points/Mooncake forward				0.437 ± 0.0075 ms
Convolved Gamma+LogNormal numerical/Enzyme forward				0.0585 ± 0.00038 ms
Product LogNormal*Gamma numerical wrt Y/ReverseDiff (tape)				4.17 ± 0.3 ms
Product LogNormal*Gamma numerical wrt Y/ForwardDiff				0.117 ± 0.00065 ms
Timeseries convolve discrete Poisson delay/Mooncake forward				5.43 ± 0.51 μs
pgf Poisson closed form wrt rate/Mooncake reverse				3.64 ± 0.13 μs
Product LogNormal*LogNormal analytical/Mooncake reverse				14.6 ± 0.94 μs
Product Gamma*LogNormal mean+var moments/ForwardDiff				0.529 ± 0.038 μs
Timeseries convolve time-varying PMF matrix/Enzyme forward				6.36 ± 0.16 μs
Product LogNormal*LogNormal analytical/Enzyme reverse				3.1 ± 0.099 μs
Convolved Gamma+LogNormal batched logpdf wrt params/Mooncake forward				0.207 ± 0.0044 ms
pgf Poisson closed form wrt rate/ReverseDiff (tape)				0.509 ± 0.19 μs
Difference Gamma-Normal mean+var moments/ReverseDiff (tape)				2.41 ± 0.13 μs
Convolved LogNormal+Gamma numerical/ForwardDiff				0.0702 ± 0.00029 ms
Product LogNormal*LogNormal analytical/ReverseDiff (tape)				19.5 ± 1 μs
Timeseries convolve time-varying Poisson delays/Mooncake reverse				0.0739 ± 0.0076 ms
Convolved Normal+Normal analytical/Enzyme forward				7.08 ± 0.062 μs
Convolved Gamma+Normal mean+var moments/ForwardDiff				0.478 ± 0.035 μs
Convolved Gamma+LogNormal batched logpdf wrt points/ReverseDiff (tape)				2.23 ± 0.18 ms
Product Gamma*LogNormal numerical wrt X/ReverseDiff (tape)				4.17 ± 0.28 ms
Timeseries convolve time-varying Poisson delays/Enzyme forward				8.33 ± 0.39 μs
Difference LogNormal-Gamma numerical wrt Y/ForwardDiff				0.116 ± 0.00052 ms
Timeseries convolve time-varying PMF matrix/Mooncake reverse				0.0328 ± 0.0063 ms
Convolved LogNormal+Gamma numerical/Enzyme forward				0.0771 ± 0.00073 ms
Timeseries convolve discrete Poisson delay/ReverseDiff (tape)				27.3 ± 0.93 μs
Product LogNormal*LogNormal analytical/ForwardDiff				0.495 ± 0.057 μs
Convolved Gamma+Normal mean+var moments/Mooncake reverse				4.03 ± 0.27 μs
Product LogNormal*Gamma numerical wrt Y/Mooncake reverse				0.814 ± 0.035 ms
Timeseries convolve discrete Poisson delay/Mooncake reverse				15 ± 0.86 μs
Product Gamma*LogNormal numerical wrt X/Mooncake forward				0.439 ± 0.0066 ms
Timeseries convolve time-varying PMF matrix/ReverseDiff (tape)				15.8 ± 0.7 μs
Product Gamma*LogNormal mean+var moments/Enzyme reverse				0.0546 ± 0.011 μs
Convolved Gamma+LogNormal batched logpdf wrt points/Enzyme reverse				0.45 ± 0.024 ms
Convolved Gamma+LogNormal batched logpdf wrt params/Enzyme forward				0.0519 ± 0.0019 ms
Product Gamma*LogNormal numerical wrt X/ForwardDiff				0.0979 ± 0.00046 ms
Convolved Gamma+LogNormal batched logpdf wrt params/ForwardDiff				0.0405 ± 0.00073 ms
Convolved Gamma+LogNormal batched logpdf wrt params/Mooncake reverse				0.522 ± 0.033 ms
Difference Gamma-LogNormal numerical wrt X/ReverseDiff (tape)				3.75 ± 0.33 ms
Difference Gamma-Normal mean+var moments/ForwardDiff				0.483 ± 0.035 μs
Convolved Gamma+Normal mean+var moments/Mooncake forward				4.54 ± 0.45 μs
Difference Normal-Normal analytical/Enzyme reverse				3.04 ± 0.096 μs
Convolved Gamma+LogNormal numerical/Mooncake forward				0.236 ± 0.0056 ms
Product LogNormal*LogNormal analytical/Enzyme forward				7.09 ± 0.086 μs
Convolved LogNormal+Gamma numerical/Mooncake forward				0.314 ± 0.0062 ms
Convolved Gamma+Normal mean+var moments/Enzyme forward				6.21 ± 0.21 μs
Timeseries convolve time-varying Poisson delays/Mooncake forward				16 ± 0.75 μs

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
Product Gamma*LogNormal mean+var moments/Enzyme forward				0.032 k allocs: 1.3 kB
Difference Normal-Normal analytical/ForwardDiff				7 allocs: 0.266 kB
Convolved Gamma+LogNormal numerical/ReverseDiff (tape)				31.1 k allocs: 1.29 MB
Convolved Normal+Normal analytical/ReverseDiff (tape)				0.238 k allocs: 9.92 kB
Difference LogNormal-Gamma numerical wrt Y/Enzyme reverse				0.159 k allocs: 23.2 kB
Timeseries convolve time-varying Poisson delays/Enzyme reverse				0.104 k allocs: 5.53 kB
pgf Poisson closed form wrt rate/Enzyme reverse				2 allocs: 0.0625 kB
Convolved Gamma+LogNormal numerical/Enzyme reverse				0.147 k allocs: 18.8 kB
Timeseries convolve discrete Poisson delay/ForwardDiff				11 allocs: 0.547 kB
Convolved Normal+Normal analytical/Mooncake forward				0.058 k allocs: 2.91 kB
Product Gamma*LogNormal mean+var moments/Mooncake forward				0.07 k allocs: 3.33 kB
Convolved Gamma+LogNormal numerical/ForwardDiff				21 allocs: 1.03 kB
Convolved Normal+Normal analytical/Mooncake reverse				0.289 k allocs: 0.0329 MB
Convolved LogNormal+Gamma numerical/ReverseDiff (tape)				30.2 k allocs: 1.26 MB
Difference Gamma-Normal mean+var moments/Enzyme reverse				2 allocs: 0.0938 kB
Convolved Gamma+LogNormal batched logpdf wrt points/ForwardDiff				0.081 k allocs: 7.2 kB
Difference Gamma-LogNormal numerical wrt X/Mooncake reverse				2.46 k allocs: 1.03 MB
Difference Gamma-LogNormal numerical wrt X/Mooncake forward				0.178 k allocs: 17 kB
Convolved Normal+Normal analytical/ForwardDiff				7 allocs: 0.266 kB
Timeseries convolve time-varying PMF matrix/Enzyme reverse				0.13 k allocs: 6.89 kB
Timeseries convolve time-varying PMF matrix/Mooncake forward				0.088 k allocs: 5.52 kB
Convolved LogNormal+Gamma numerical/Mooncake reverse				2.37 k allocs: 0.633 MB
Difference LogNormal-Gamma numerical wrt Y/ReverseDiff (tape)				0.0532 M allocs: 2.07 MB
Product Gamma*LogNormal mean+var moments/Mooncake reverse				0.093 k allocs: 5.09 kB
Timeseries convolve time-varying Poisson delays/ForwardDiff				0.037 k allocs: 2.44 kB
Timeseries convolve time-varying PMF matrix/ForwardDiff				16 allocs: 1.14 kB
Convolved Gamma+Normal mean+var moments/ReverseDiff (tape)				0.041 k allocs: 1.7 kB
Difference Normal-Normal analytical/Enzyme forward				0.036 k allocs: 1.11 kB
Convolved Gamma+Normal mean+var moments/Enzyme reverse				2 allocs: 0.0938 kB
Difference LogNormal-Gamma numerical wrt Y/Mooncake forward				0.178 k allocs: 17 kB
Convolved Normal+Normal analytical/Enzyme reverse				24 allocs: 1.03 kB
Product Gamma*LogNormal mean+var moments/ReverseDiff (tape)				0.127 k allocs: 5.25 kB
Convolved Gamma+LogNormal numerical/Mooncake reverse				2.35 k allocs: 0.639 MB
Convolved Gamma+LogNormal batched logpdf wrt params/Enzyme reverse				1.35 k allocs: 0.168 MB
Difference Normal-Normal analytical/ReverseDiff (tape)				0.268 k allocs: 10.9 kB
Difference Normal-Normal analytical/Mooncake forward				0.058 k allocs: 2.91 kB
Product LogNormal*Gamma numerical wrt Y/Mooncake forward				0.178 k allocs: 17 kB
Difference Gamma-LogNormal numerical wrt X/ForwardDiff				27 allocs: 2.61 kB
pgf Poisson closed form wrt rate/ForwardDiff				7 allocs: 0.203 kB
Timeseries convolve discrete Poisson delay/Enzyme reverse				10 allocs: 0.5 kB
Difference Gamma-Normal mean+var moments/Enzyme forward				0.032 k allocs: 1.3 kB
Difference LogNormal-Gamma numerical wrt Y/Enzyme forward				0.096 k allocs: 8.14 kB
Product Gamma*LogNormal numerical wrt X/Enzyme reverse				0.159 k allocs: 23.1 kB
Convolved Gamma+LogNormal batched logpdf wrt points/Enzyme forward				0.151 k allocs: 22.6 kB
Difference Gamma-LogNormal numerical wrt X/Enzyme forward				0.096 k allocs: 8.14 kB
Timeseries convolve time-varying Poisson delays/ReverseDiff (tape)				1.02 k allocs: 0.0418 MB
Difference Normal-Normal analytical/Mooncake reverse				0.289 k allocs: 0.0331 MB
Convolved Gamma+LogNormal batched logpdf wrt points/Mooncake reverse				2.07 k allocs: 0.665 MB
Product LogNormal*LogNormal analytical/Mooncake forward				0.058 k allocs: 2.91 kB
Product LogNormal*Gamma numerical wrt Y/Enzyme forward				0.096 k allocs: 8.14 kB
Convolved LogNormal+Gamma numerical/Enzyme reverse				0.147 k allocs: 18.8 kB
Difference Gamma-Normal mean+var moments/Mooncake forward				0.07 k allocs: 3.33 kB
Difference Gamma-Normal mean+var moments/Mooncake reverse				0.078 k allocs: 3.71 kB
pgf Poisson closed form wrt rate/Mooncake forward				0.052 k allocs: 2.69 kB
Timeseries convolve discrete Poisson delay/Enzyme forward				0.033 k allocs: 1.2 kB
Difference Gamma-LogNormal numerical wrt X/Enzyme reverse				0.159 k allocs: 23.1 kB
pgf Poisson closed form wrt rate/Enzyme forward				25 allocs: 0.766 kB
Convolved Gamma+LogNormal batched logpdf wrt params/ReverseDiff (tape)				28.5 k allocs: 1.2 MB
Product Gamma*LogNormal numerical wrt X/Mooncake reverse				2.57 k allocs: 1.15 MB
Product Gamma*LogNormal numerical wrt X/Enzyme forward				0.096 k allocs: 8.14 kB
Product LogNormal*Gamma numerical wrt Y/Enzyme reverse				0.159 k allocs: 23.2 kB
Difference LogNormal-Gamma numerical wrt Y/Mooncake reverse				2.46 k allocs: 1.03 MB
Convolved Gamma+LogNormal batched logpdf wrt points/Mooncake forward				0.519 k allocs: 0.0521 MB
Convolved Gamma+LogNormal numerical/Enzyme forward				0.078 k allocs: 3.41 kB
Product LogNormal*Gamma numerical wrt Y/ReverseDiff (tape)				0.058 M allocs: 2.44 MB
Product LogNormal*Gamma numerical wrt Y/ForwardDiff				27 allocs: 2.61 kB
Timeseries convolve discrete Poisson delay/Mooncake forward				0.068 k allocs: 3.58 kB
pgf Poisson closed form wrt rate/Mooncake reverse				0.057 k allocs: 2.52 kB
Product LogNormal*LogNormal analytical/Mooncake reverse				0.27 k allocs: 12.5 kB
Product Gamma*LogNormal mean+var moments/ForwardDiff				7 allocs: 0.484 kB
Timeseries convolve time-varying PMF matrix/Enzyme forward				0.043 k allocs: 2.17 kB
Product LogNormal*LogNormal analytical/Enzyme reverse				24 allocs: 1.02 kB
Convolved Gamma+LogNormal batched logpdf wrt params/Mooncake forward				0.264 k allocs: 27.2 kB
pgf Poisson closed form wrt rate/ReverseDiff (tape)				18 allocs: 0.609 kB
Difference Gamma-Normal mean+var moments/ReverseDiff (tape)				0.041 k allocs: 1.7 kB
Convolved LogNormal+Gamma numerical/ForwardDiff				21 allocs: 1.03 kB
Product LogNormal*LogNormal analytical/ReverseDiff (tape)				0.298 k allocs: 12 kB
Timeseries convolve time-varying Poisson delays/Mooncake reverse				0.865 k allocs: 0.0638 MB
Convolved Normal+Normal analytical/Enzyme forward				0.036 k allocs: 1.11 kB
Convolved Gamma+Normal mean+var moments/ForwardDiff				7 allocs: 0.484 kB
Convolved Gamma+LogNormal batched logpdf wrt points/ReverseDiff (tape)				0.0327 M allocs: 1.23 MB
Product Gamma*LogNormal numerical wrt X/ReverseDiff (tape)				0.058 M allocs: 2.44 MB
Timeseries convolve time-varying Poisson delays/Enzyme forward				0.102 k allocs: 4.61 kB
Difference LogNormal-Gamma numerical wrt Y/ForwardDiff				27 allocs: 2.61 kB
Timeseries convolve time-varying PMF matrix/Mooncake reverse				0.345 k allocs: 28.9 kB
Convolved LogNormal+Gamma numerical/Enzyme forward				0.078 k allocs: 3.41 kB
Timeseries convolve discrete Poisson delay/ReverseDiff (tape)				0.462 k allocs: 18.2 kB
Product LogNormal*LogNormal analytical/ForwardDiff				7 allocs: 0.266 kB
Convolved Gamma+Normal mean+var moments/Mooncake reverse				0.078 k allocs: 3.71 kB
Product LogNormal*Gamma numerical wrt Y/Mooncake reverse				2.57 k allocs: 1.15 MB
Timeseries convolve discrete Poisson delay/Mooncake reverse				0.198 k allocs: 16.1 kB
Product Gamma*LogNormal numerical wrt X/Mooncake forward				0.178 k allocs: 17 kB
Timeseries convolve time-varying PMF matrix/ReverseDiff (tape)				0.273 k allocs: 12.2 kB
Product Gamma*LogNormal mean+var moments/Enzyme reverse				2 allocs: 0.0938 kB
Convolved Gamma+LogNormal batched logpdf wrt points/Enzyme reverse				1.36 k allocs: 0.169 MB
Convolved Gamma+LogNormal batched logpdf wrt params/Enzyme forward				0.088 k allocs: 11.6 kB
Product Gamma*LogNormal numerical wrt X/ForwardDiff				27 allocs: 2.61 kB
Convolved Gamma+LogNormal batched logpdf wrt params/ForwardDiff				0.04 k allocs: 4.7 kB
Convolved Gamma+LogNormal batched logpdf wrt params/Mooncake reverse				2.08 k allocs: 0.666 MB
Difference Gamma-LogNormal numerical wrt X/ReverseDiff (tape)				0.0532 M allocs: 2.07 MB
Difference Gamma-Normal mean+var moments/ForwardDiff				7 allocs: 0.484 kB
Convolved Gamma+Normal mean+var moments/Mooncake forward				0.07 k allocs: 3.33 kB
Difference Normal-Normal analytical/Enzyme reverse				24 allocs: 1.02 kB
Convolved Gamma+LogNormal numerical/Mooncake forward				0.142 k allocs: 7.5 kB
Product LogNormal*LogNormal analytical/Enzyme forward				0.036 k allocs: 1.11 kB
Convolved LogNormal+Gamma numerical/Mooncake forward				0.142 k allocs: 7.5 kB
Convolved Gamma+Normal mean+var moments/Enzyme forward				0.032 k allocs: 1.3 kB
Timeseries convolve time-varying Poisson delays/Mooncake forward				0.238 k allocs: 11.6 kB

time_to_load

Time

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
time_to_load	0.889 ± 0.0073 s	0.889 ± 0.0066 s	0.879 ± 0.0041 s	0.885 ± 0.0072 s

Memory

Benchmark	v0.3.1	v0.3.0	v0.2.0	1f4127a895a19f...
time_to_load	0.149 k allocs: 11.2 kB	0.149 k allocs: 11.2 kB	0.149 k allocs: 11.2 kB	0.149 k allocs: 11.2 kB

Per-benchmark timelines

<details> <summary>Show 4 plots</summary>

</details>

About these benchmarks

Benchmarks for the convolution distributions, reading the analytic and numeric quadrature backends against the bare component distributions.

Quick start

Install the benchpkg CLI once:

bash

task benchmark-install
# Or: julia -e 'using Pkg; Pkg.add("AirspeedVelocity")'

then run the suite:

bash

# Benchmark current state
task benchmark

# Compare main branch vs current state
task benchmark-compare

# Filter to specific benchmarks
task benchmark -- --filter=Convolved
task benchmark-compare -- --filter=Quantile

Benchmark structure

Baseline/
  Gamma/               (logpdf, cdf)
  Normal/              (logpdf, cdf)

Convolved/
  analytic/            (construction, logpdf/pdf/cdf scalar,
                        logpdf broadcast, logpdf/pdf/cdf batched,
                        rand, mean)
  numeric/             (same operations)

Difference/
  analytic/            (construction, logpdf/cdf scalar,
                        logpdf/cdf broadcast, rand, mean)
  numeric/             (same operations)

Product/
  analytic/            (construction, logpdf/cdf scalar,
                        logpdf/cdf broadcast, rand, mean)
  numeric/             (same operations)

Ratio/
  analytic/            (construction, logpdf/cdf scalar,
                        logpdf/cdf broadcast, rand, mean)
  numeric/             (construction, logpdf/cdf scalar,
                        logpdf/cdf broadcast, rand -- no mean row:
                        the numeric pair has no closed-form moment)

Timeseries/
  Gamma delay          (convolve_series(pmf, series), pmf precomputed)
  Convolved delay
  Poisson delay        (discrete: convolve_series(delay, series))

Quantile/
  Convolved analytic/  (median, grid)
  Convolved numeric/   (median)
  Difference numeric/  (median)
  Product numeric/     (median)

AD gradients/
  <every test/ADFixtures scenario>/
    ForwardDiff, ReverseDiff (tape), Enzyme forward, Enzyme reverse,
    Mooncake forward, Mooncake reverse

Analytic vs numeric

convolved, difference, product, and ratio use a closed form where one exists (Normal + Normal, equal-scale Gamma, equal-rate Exponential; Normal - Normal; LogNormal * LogNormal; zero-mean Normal / Normal, Gamma / Gamma, Chisq / Chisq) and AD-safe Gauss-Legendre quadrature otherwise. The analytic rows should sit near the Baseline floor; the gap between the numeric rows and their analytic counterparts is the cost of the quadrature backend. The batched rows share the composite quadrature grid across evaluation points; their gap to the logpdf broadcast row over the same points is the headline batching win. Pass method = NumericSolver() to force the numeric path.

CI integration

Pull requests benchmark head and base in separate jobs via the benchmark workflow and post a single comparison comment. Pushes to main and tagged releases append to the performance history below.

Performance over time ​

Summary ​

Baseline ​

Time ​

Memory ​

Convolved ​

Time ​

Memory ​

Difference ​

Time ​

Memory ​

Product ​

Time ​

Memory ​

Quantile ​

Time ​

Memory ​

Timeseries ​

Time ​

Memory ​

AD gradients ​

Time ​

Memory ​

time_to_load ​

Time ​

Memory ​

Per-benchmark timelines ​

About these benchmarks ​

Quick start ​

Benchmark structure ​

Analytic vs numeric ​

CI integration ​

Performance over time

Summary

Baseline

Time

Memory

Convolved

Time

Memory

Difference

Time

Memory

Product

Time

Memory

Quantile

Time

Memory

Timeseries

Time

Memory

AD gradients

Time

Memory

time_to_load

Time

Memory

Per-benchmark timelines

About these benchmarks

Quick start

Benchmark structure

Analytic vs numeric

CI integration