Benchmarks

ModifiedDistributions benchmarks each modifier's hot paths so wrapper overhead is visible and regressions are caught on every pull request.

The suite (benchmark/benchmarks.jl) evaluates construction, logpdf, pdf, cdf/ccdf, quantile and rand for every modifier around the same base LogNormal, with the bare base as the shared baseline floor:

• Baseline: the bare base LogNormal.

• Affine: the change-of-variables paths through Y = scale * X + shift.

• Weighted: the logpdf weight paths, scalar and the vectorised Product{Weighted} form.

• Transformed: thin and cumulative, whose forward ops are transparent to every distribution method, so these rows should sit on the baseline.

• Modified: the hazard modification on both analytic links; the identity-link quantile and rand exercise the monotone-bisection cdf inversion, the one non-closed-form path.

• AD gradients: DifferentiationInterface.gradient of every test/ADFixtures scenario across the ForwardDiff, ReverseDiff, Mooncake and Enzyme backends, sharing the fixtures that drive the AD test suite.

Run the suite locally with task benchmark, or compare against main with task benchmark-compare (see benchmark/README.md). On pull requests the benchmark workflow benchmarks head and base in separate jobs and posts a single comparison comment. Pushes to main and tags append to the performance history shown below.

Performance history

The summary tracks each benchmark suite's headline timing across recent revisions.

Benchmark summary (overall)

Not enough comparable revisions to compute ratios yet — the summary populates once a second revision is benchmarked.

<details> <summary>Per-suite detail</summary>

Ratio summary

Most recent 1 revision, columns labelled by commit date.

AD gradients

Time

Benchmark	b105916a72bb9c...
Affine LogNormal scale+shift logpdf/Enzyme forward	8.52 ± 0.11 μs
Affine LogNormal scale+shift logpdf/Enzyme reverse	3.06 ± 0.1 μs
Affine LogNormal scale+shift logpdf/ForwardDiff	0.752 ± 0.094 μs
Affine LogNormal scale+shift logpdf/Mooncake forward	6.84 ± 0.37 μs
Affine LogNormal scale+shift logpdf/Mooncake reverse	18.5 ± 0.91 μs
Affine LogNormal scale+shift logpdf/ReverseDiff (tape)	16.6 ± 0.49 μs
Modified LogNormal identity-link logpdf/Enzyme forward	8.79 ± 0.11 μs
Modified LogNormal identity-link logpdf/Enzyme reverse	5.98 ± 1.1 μs
Modified LogNormal identity-link logpdf/ForwardDiff	0.984 ± 0.023 μs
Modified LogNormal identity-link logpdf/Mooncake forward	8.39 ± 0.19 μs
Modified LogNormal identity-link logpdf/Mooncake reverse	0.0452 ± 0.0057 ms
Modified LogNormal identity-link logpdf/ReverseDiff (tape)	0.0323 ± 0.00063 ms
Modified LogNormal log-link logpdf/Enzyme forward	8.54 ± 0.11 μs
Modified LogNormal log-link logpdf/Enzyme reverse	3.57 ± 0.076 μs
Modified LogNormal log-link logpdf/ForwardDiff	0.907 ± 0.1 μs
Modified LogNormal log-link logpdf/Mooncake forward	7.59 ± 0.19 μs
Modified LogNormal log-link logpdf/Mooncake reverse	0.0416 ± 0.0046 ms
Modified LogNormal log-link logpdf/ReverseDiff (tape)	26.6 ± 0.57 μs
Product{Weighted} LogNormal vector logpdf/Enzyme forward	8.37 ± 0.23 μs
Product{Weighted} LogNormal vector logpdf/Enzyme reverse	1.03 ± 0.28 μs
Product{Weighted} LogNormal vector logpdf/ForwardDiff	0.883 ± 0.062 μs
Product{Weighted} LogNormal vector logpdf/Mooncake forward	7.08 ± 1.1 μs
Product{Weighted} LogNormal vector logpdf/Mooncake reverse	28.1 ± 2.6 μs
Product{Weighted} LogNormal vector logpdf/ReverseDiff (tape)	16.7 ± 0.48 μs
Thinned convolved series sum/Enzyme forward	10.7 ± 0.15 μs
Thinned convolved series sum/Enzyme reverse	14.1 ± 0.21 μs
Thinned convolved series sum/ForwardDiff	3.26 ± 0.046 μs
Thinned convolved series sum/Mooncake forward	12.6 ± 0.49 μs
Thinned convolved series sum/Mooncake reverse	29.9 ± 5.1 μs
Thinned convolved series sum/ReverseDiff (tape)	0.0364 ± 0.00062 ms
Transformed cumulative LogNormal logpdf/Enzyme forward	8.07 ± 0.097 μs
Transformed cumulative LogNormal logpdf/Enzyme reverse	1.98 ± 0.068 μs
Transformed cumulative LogNormal logpdf/ForwardDiff	0.522 ± 0.077 μs
Transformed cumulative LogNormal logpdf/Mooncake forward	5.57 ± 0.47 μs
Transformed cumulative LogNormal logpdf/Mooncake reverse	24.4 ± 6.8 μs
Transformed cumulative LogNormal logpdf/ReverseDiff (tape)	15 ± 0.49 μs
Transformed thin LogNormal logpdf/Enzyme forward	8.11 ± 0.087 μs
Transformed thin LogNormal logpdf/Enzyme reverse	1.99 ± 0.048 μs
Transformed thin LogNormal logpdf/ForwardDiff	0.519 ± 0.078 μs
Transformed thin LogNormal logpdf/Mooncake forward	5.58 ± 0.36 μs
Transformed thin LogNormal logpdf/Mooncake reverse	24.8 ± 7.1 μs
Transformed thin LogNormal logpdf/ReverseDiff (tape)	14.8 ± 0.45 μs
Weighted Affine LogNormal nested logpdf/Enzyme forward	8.3 ± 0.12 μs
Weighted Affine LogNormal nested logpdf/Enzyme reverse	0.96 ± 0.076 μs
Weighted Affine LogNormal nested logpdf/ForwardDiff	0.771 ± 0.09 μs
Weighted Affine LogNormal nested logpdf/Mooncake forward	7.27 ± 0.17 μs
Weighted Affine LogNormal nested logpdf/Mooncake reverse	19.7 ± 1.9 μs
Weighted Affine LogNormal nested logpdf/ReverseDiff (tape)	18.3 ± 0.48 μs
Weighted LogNormal observation-time weight logpdf/Enzyme forward	8.02 ± 0.075 μs
Weighted LogNormal observation-time weight logpdf/Enzyme reverse	1.28 ± 0.32 μs
Weighted LogNormal observation-time weight logpdf/ForwardDiff	0.555 ± 0.074 μs
Weighted LogNormal observation-time weight logpdf/Mooncake forward	6.08 ± 1 μs
Weighted LogNormal observation-time weight logpdf/Mooncake reverse	29.9 ± 3.2 μs
Weighted LogNormal observation-time weight logpdf/ReverseDiff (tape)	17.3 ± 0.52 μs
Weighted LogNormal scalar logpdf/Enzyme forward	8.05 ± 0.075 μs
Weighted LogNormal scalar logpdf/Enzyme reverse	1.28 ± 0.34 μs
Weighted LogNormal scalar logpdf/ForwardDiff	0.547 ± 0.074 μs
Weighted LogNormal scalar logpdf/Mooncake forward	6.04 ± 0.89 μs
Weighted LogNormal scalar logpdf/Mooncake reverse	0.037 ± 0.0034 ms
Weighted LogNormal scalar logpdf/ReverseDiff (tape)	17.3 ± 0.47 μs
Weighted Sequential observed-total logpdf/Enzyme forward	0.115 ± 0.003 ms
Weighted Sequential observed-total logpdf/Enzyme reverse	0.358 ± 0.029 ms
Weighted Sequential observed-total logpdf/ForwardDiff	0.0839 ± 0.001 ms
Weighted Sequential observed-total logpdf/Mooncake forward	0.414 ± 0.024 ms
Weighted Sequential observed-total logpdf/Mooncake reverse	1.34 ± 0.1 ms
Weighted Sequential observed-total logpdf/ReverseDiff (tape)	2.4 ± 0.32 ms

Memory

Benchmark	b105916a72bb9c...
Affine LogNormal scale+shift logpdf/Enzyme forward	0.044 k allocs: 1.52 kB
Affine LogNormal scale+shift logpdf/Enzyme reverse	24 allocs: 0.969 kB
Affine LogNormal scale+shift logpdf/ForwardDiff	7 allocs: 0.484 kB
Affine LogNormal scale+shift logpdf/Mooncake forward	0.07 k allocs: 3.33 kB
Affine LogNormal scale+shift logpdf/Mooncake reverse	0.292 k allocs: 13.5 kB
Affine LogNormal scale+shift logpdf/ReverseDiff (tape)	0.248 k allocs: 10.6 kB
Modified LogNormal identity-link logpdf/Enzyme forward	0.04 k allocs: 1.25 kB
Modified LogNormal identity-link logpdf/Enzyme reverse	28 allocs: 3.41 kB
Modified LogNormal identity-link logpdf/ForwardDiff	7 allocs: 0.359 kB
Modified LogNormal identity-link logpdf/Mooncake forward	0.064 k allocs: 3.06 kB
Modified LogNormal identity-link logpdf/Mooncake reverse	0.485 k allocs: 0.0416 MB
Modified LogNormal identity-link logpdf/ReverseDiff (tape)	0.465 k allocs: 17.8 kB
Modified LogNormal log-link logpdf/Enzyme forward	0.04 k allocs: 1.25 kB
Modified LogNormal log-link logpdf/Enzyme reverse	24 allocs: 0.969 kB
Modified LogNormal log-link logpdf/ForwardDiff	7 allocs: 0.359 kB
Modified LogNormal log-link logpdf/Mooncake forward	0.064 k allocs: 3.06 kB
Modified LogNormal log-link logpdf/Mooncake reverse	0.439 k allocs: 0.039 MB
Modified LogNormal log-link logpdf/ReverseDiff (tape)	0.377 k allocs: 14.9 kB
Product{Weighted} LogNormal vector logpdf/Enzyme forward	0.053 k allocs: 2.31 kB
Product{Weighted} LogNormal vector logpdf/Enzyme reverse	16 allocs: 0.922 kB
Product{Weighted} LogNormal vector logpdf/ForwardDiff	15 allocs: 1.06 kB
Product{Weighted} LogNormal vector logpdf/Mooncake forward	0.116 k allocs: 6.31 kB
Product{Weighted} LogNormal vector logpdf/Mooncake reverse	0.372 k allocs: 23.5 kB
Product{Weighted} LogNormal vector logpdf/ReverseDiff (tape)	0.239 k allocs: 10 kB
Thinned convolved series sum/Enzyme forward	0.043 k allocs: 1.86 kB
Thinned convolved series sum/Enzyme reverse	0.036 k allocs: 1.86 kB
Thinned convolved series sum/ForwardDiff	13 allocs: 0.922 kB
Thinned convolved series sum/Mooncake forward	0.094 k allocs: 4.89 kB
Thinned convolved series sum/Mooncake reverse	0.263 k allocs: 21.5 kB
Thinned convolved series sum/ReverseDiff (tape)	0.486 k allocs: 19.4 kB
Transformed cumulative LogNormal logpdf/Enzyme forward	0.036 k allocs: 1.11 kB
Transformed cumulative LogNormal logpdf/Enzyme reverse	14 allocs: 0.609 kB
Transformed cumulative LogNormal logpdf/ForwardDiff	7 allocs: 0.266 kB
Transformed cumulative LogNormal logpdf/Mooncake forward	0.058 k allocs: 2.91 kB
Transformed cumulative LogNormal logpdf/Mooncake reverse	0.274 k allocs: 25.6 kB
Transformed cumulative LogNormal logpdf/ReverseDiff (tape)	0.213 k allocs: 9.06 kB
Transformed thin LogNormal logpdf/Enzyme forward	0.036 k allocs: 1.11 kB
Transformed thin LogNormal logpdf/Enzyme reverse	14 allocs: 0.609 kB
Transformed thin LogNormal logpdf/ForwardDiff	7 allocs: 0.266 kB
Transformed thin LogNormal logpdf/Mooncake forward	0.058 k allocs: 2.91 kB
Transformed thin LogNormal logpdf/Mooncake reverse	0.274 k allocs: 25.6 kB
Transformed thin LogNormal logpdf/ReverseDiff (tape)	0.213 k allocs: 9.06 kB
Weighted Affine LogNormal nested logpdf/Enzyme forward	0.036 k allocs: 1.38 kB
Weighted Affine LogNormal nested logpdf/Enzyme reverse	6 allocs: 0.484 kB
Weighted Affine LogNormal nested logpdf/ForwardDiff	7 allocs: 0.516 kB
Weighted Affine LogNormal nested logpdf/Mooncake forward	0.08 k allocs: 4.02 kB
Weighted Affine LogNormal nested logpdf/Mooncake reverse	0.329 k allocs: 15.6 kB
Weighted Affine LogNormal nested logpdf/ReverseDiff (tape)	0.269 k allocs: 11.3 kB
Weighted LogNormal observation-time weight logpdf/Enzyme forward	0.032 k allocs: 1.05 kB
Weighted LogNormal observation-time weight logpdf/Enzyme reverse	10 allocs: 1.14 kB
Weighted LogNormal observation-time weight logpdf/ForwardDiff	7 allocs: 0.297 kB
Weighted LogNormal observation-time weight logpdf/Mooncake forward	0.068 k allocs: 3.59 kB
Weighted LogNormal observation-time weight logpdf/Mooncake reverse	0.32 k allocs: 0.0353 MB
Weighted LogNormal observation-time weight logpdf/ReverseDiff (tape)	0.239 k allocs: 9.97 kB
Weighted LogNormal scalar logpdf/Enzyme forward	0.032 k allocs: 1.05 kB
Weighted LogNormal scalar logpdf/Enzyme reverse	10 allocs: 1.14 kB
Weighted LogNormal scalar logpdf/ForwardDiff	7 allocs: 0.297 kB
Weighted LogNormal scalar logpdf/Mooncake forward	0.068 k allocs: 3.59 kB
Weighted LogNormal scalar logpdf/Mooncake reverse	0.348 k allocs: 0.0453 MB
Weighted LogNormal scalar logpdf/ReverseDiff (tape)	0.239 k allocs: 9.97 kB
Weighted Sequential observed-total logpdf/Enzyme forward	0.668 k allocs: 26 kB
Weighted Sequential observed-total logpdf/Enzyme reverse	2.03 k allocs: 0.0977 MB
Weighted Sequential observed-total logpdf/ForwardDiff	0.198 k allocs: 10.1 kB
Weighted Sequential observed-total logpdf/Mooncake forward	1.65 k allocs: 0.0702 MB
Weighted Sequential observed-total logpdf/Mooncake reverse	8.5 k allocs: 0.854 MB
Weighted Sequential observed-total logpdf/ReverseDiff (tape)	31.3 k allocs: 1.29 MB

Affine

Time

Benchmark	b105916a72bb9c...
LogNormal/ccdf	3.3 ± 0.39 μs
LogNormal/cdf	3.4 ± 0.35 μs
LogNormal/construction	3.1 ± 0.01 ns
LogNormal/logpdf	2.63 ± 0.35 μs
LogNormal/pdf	3.82 ± 0.37 μs
LogNormal/quantile	0.49 ± 0.019 μs
LogNormal/rand	1.28 ± 0.078 μs

Memory

Benchmark	b105916a72bb9c...
LogNormal/ccdf	2 allocs: 0.906 kB
LogNormal/cdf	2 allocs: 0.906 kB
LogNormal/construction	0 allocs: 0 B
LogNormal/logpdf	2 allocs: 0.906 kB
LogNormal/pdf	2 allocs: 0.906 kB
LogNormal/quantile	2 allocs: 0.219 kB
LogNormal/rand	2 allocs: 0.906 kB

Baseline

Time

Benchmark	b105916a72bb9c...
LogNormal/ccdf	2.69 ± 0.32 μs
LogNormal/cdf	2.67 ± 0.33 μs
LogNormal/construction	1.55 ± 0.009 ns
LogNormal/logpdf	1.67 ± 0.32 μs
LogNormal/pdf	2.96 ± 0.33 μs
LogNormal/quantile	0.465 ± 0.018 μs
LogNormal/rand	1.04 ± 0.034 μs

Memory

Benchmark	b105916a72bb9c...
LogNormal/ccdf	2 allocs: 0.906 kB
LogNormal/cdf	2 allocs: 0.906 kB
LogNormal/construction	0 allocs: 0 B
LogNormal/logpdf	2 allocs: 0.906 kB
LogNormal/pdf	2 allocs: 0.906 kB
LogNormal/quantile	2 allocs: 0.219 kB
LogNormal/rand	2 allocs: 0.906 kB

Modified

Time

Benchmark	b105916a72bb9c...
IdentityLink/ccdf	7.53 ± 0.028 μs
IdentityLink/cdf	7.2 ± 0.028 μs
IdentityLink/construction	3.1 ± 0.01 ns
IdentityLink/logpdf	10.5 ± 0.06 μs
IdentityLink/pdf	12.7 ± 0.06 μs
IdentityLink/quantile	0.111 ± 0.0002 ms
IdentityLink/rand	0.58 ± 0.015 ms
LogLink/ccdf	5.8 ± 0.06 μs
LogLink/cdf	6.17 ± 0.048 μs
LogLink/construction	3.1 ± 0.01 ns
LogLink/logpdf	8.02 ± 0.033 μs
LogLink/pdf	9.35 ± 0.05 μs
LogLink/quantile	0.929 ± 0.073 μs
LogLink/rand	5.13 ± 0.14 μs

Memory

Benchmark	b105916a72bb9c...
IdentityLink/ccdf	2 allocs: 0.906 kB
IdentityLink/cdf	2 allocs: 0.906 kB
IdentityLink/construction	0 allocs: 0 B
IdentityLink/logpdf	2 allocs: 0.906 kB
IdentityLink/pdf	2 allocs: 0.906 kB
IdentityLink/quantile	2 allocs: 0.219 kB
IdentityLink/rand	2 allocs: 0.906 kB
LogLink/ccdf	2 allocs: 0.906 kB
LogLink/cdf	2 allocs: 0.906 kB
LogLink/construction	0 allocs: 0 B
LogLink/logpdf	2 allocs: 0.906 kB
LogLink/pdf	2 allocs: 0.906 kB
LogLink/quantile	2 allocs: 0.219 kB
LogLink/rand	2 allocs: 0.906 kB

Transformed

Time

Benchmark	b105916a72bb9c...
cumulative/cdf	2.66 ± 0.33 μs
cumulative/construction	2.79 ± 0.01 ns
cumulative/logpdf	1.67 ± 0.28 μs
cumulative/rand	1.03 ± 0.033 μs
thin/cdf	2.66 ± 0.35 μs
thin/construction	2.79 ± 0.01 ns
thin/logpdf	1.69 ± 0.3 μs
thin/rand	1.03 ± 0.034 μs

Memory

Benchmark	b105916a72bb9c...
cumulative/cdf	2 allocs: 0.906 kB
cumulative/construction	0 allocs: 0 B
cumulative/logpdf	2 allocs: 0.906 kB
cumulative/rand	2 allocs: 0.906 kB
thin/cdf	2 allocs: 0.906 kB
thin/construction	0 allocs: 0 B
thin/logpdf	2 allocs: 0.906 kB
thin/rand	2 allocs: 0.906 kB

Weighted

Time

Benchmark	b105916a72bb9c...
Product/construction	0.309 ± 0.23 μs
Product/logpdf	2.99 ± 0.24 μs
scalar/construction	2.79 ± 0.009 ns
scalar/logpdf	1.72 ± 0.31 μs

Memory

Benchmark	b105916a72bb9c...
Product/construction	3 allocs: 2.45 kB
Product/logpdf	6 allocs: 2.72 kB
scalar/construction	0 allocs: 0 B
scalar/logpdf	2 allocs: 0.906 kB

time_to_load

Time

Benchmark	b105916a72bb9c...
time_to_load	0.766 ± 0.013 s

Memory

Benchmark	b105916a72bb9c...
time_to_load	0.149 k allocs: 11.2 kB

Per-benchmark timelines

<details> <summary>Show 6 plots</summary>

</details>

</details>