Performance over time

How ModifiedDistributions'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.

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

Tables below show the most recent 1 revision, columns labelled by commit date.

AD gradients

Time

Benchmark	d81ddd1eb1c19f...
Affine LogNormal scale+shift logpdf/Enzyme forward	8.47 ± 0.097 μs
Affine LogNormal scale+shift logpdf/Enzyme reverse	3.04 ± 0.048 μs
Affine LogNormal scale+shift logpdf/ForwardDiff	0.752 ± 0.041 μs
Affine LogNormal scale+shift logpdf/Mooncake forward	6.71 ± 0.12 μs
Affine LogNormal scale+shift logpdf/Mooncake reverse	17.5 ± 0.79 μs
Affine LogNormal scale+shift logpdf/ReverseDiff (tape)	16.4 ± 0.39 μs
Modified LogNormal identity-link logpdf/Enzyme forward	8.78 ± 0.08 μs
Modified LogNormal identity-link logpdf/Enzyme reverse	5.86 ± 1.1 μs
Modified LogNormal identity-link logpdf/ForwardDiff	0.99 ± 0.019 μs
Modified LogNormal identity-link logpdf/Mooncake forward	8.34 ± 0.17 μs
Modified LogNormal identity-link logpdf/Mooncake reverse	0.0437 ± 0.0073 ms
Modified LogNormal identity-link logpdf/ReverseDiff (tape)	0.0322 ± 0.00057 ms
Modified LogNormal log-link logpdf/Enzyme forward	8.58 ± 0.08 μs
Modified LogNormal log-link logpdf/Enzyme reverse	3.56 ± 0.083 μs
Modified LogNormal log-link logpdf/ForwardDiff	0.905 ± 0.093 μs
Modified LogNormal log-link logpdf/Mooncake forward	7.51 ± 0.14 μs
Modified LogNormal log-link logpdf/Mooncake reverse	0.0399 ± 0.0086 ms
Modified LogNormal log-link logpdf/ReverseDiff (tape)	27.6 ± 0.54 μs
Modified discrete logit-link per-bin logpdf/Enzyme forward	13.2 ± 0.62 μs
Modified discrete logit-link per-bin logpdf/Enzyme reverse	14.4 ± 1.2 μs
Modified discrete logit-link per-bin logpdf/ForwardDiff	3.75 ± 0.71 μs
Modified discrete logit-link per-bin logpdf/Mooncake forward	24.4 ± 8.8 μs
Modified discrete logit-link per-bin logpdf/Mooncake reverse	0.127 ± 0.013 ms
Modified discrete logit-link per-bin logpdf/ReverseDiff (tape)	0.0477 ± 0.0027 ms
Modified numeric quadrature clamped additive LogNormal logpdf/Enzyme forward	0.152 ± 0.0022 ms
Modified numeric quadrature clamped additive LogNormal logpdf/ForwardDiff	0.12 ± 0.00033 ms
Modified numeric quadrature clamped additive LogNormal logpdf/Mooncake forward	0.489 ± 0.012 ms
Modified numeric quadrature clamped additive LogNormal logpdf/ReverseDiff (tape)	0.704 ± 0.09 ms
Product{Weighted} LogNormal vector logpdf/Enzyme forward	8.47 ± 0.28 μs
Product{Weighted} LogNormal vector logpdf/Enzyme reverse	1.02 ± 0.22 μs
Product{Weighted} LogNormal vector logpdf/ForwardDiff	0.87 ± 0.061 μs
Product{Weighted} LogNormal vector logpdf/Mooncake forward	7.14 ± 0.8 μs
Product{Weighted} LogNormal vector logpdf/Mooncake reverse	27.6 ± 1.8 μs
Product{Weighted} LogNormal vector logpdf/ReverseDiff (tape)	16.5 ± 0.44 μs
Thinned convolved series sum/Enzyme forward	10.7 ± 0.16 μs
Thinned convolved series sum/Enzyme reverse	14.2 ± 0.19 μs
Thinned convolved series sum/ForwardDiff	3.26 ± 0.037 μs
Thinned convolved series sum/Mooncake forward	12.5 ± 0.41 μs
Thinned convolved series sum/Mooncake reverse	29.2 ± 4.4 μs
Thinned convolved series sum/ReverseDiff (tape)	0.0374 ± 0.00083 ms
Transformed cumulative LogNormal logpdf/Enzyme forward	8.09 ± 0.073 μs
Transformed cumulative LogNormal logpdf/Enzyme reverse	2.02 ± 0.069 μs
Transformed cumulative LogNormal logpdf/ForwardDiff	0.513 ± 0.039 μs
Transformed cumulative LogNormal logpdf/Mooncake forward	5.57 ± 0.17 μs
Transformed cumulative LogNormal logpdf/Mooncake reverse	23.7 ± 6.9 μs
Transformed cumulative LogNormal logpdf/ReverseDiff (tape)	14.8 ± 0.38 μs
Transformed series_transform LogNormal logpdf/Enzyme forward	8.12 ± 0.08 μs
Transformed series_transform LogNormal logpdf/Enzyme reverse	1.99 ± 0.073 μs
Transformed series_transform LogNormal logpdf/ForwardDiff	0.513 ± 0.041 μs
Transformed series_transform LogNormal logpdf/Mooncake forward	5.44 ± 0.19 μs
Transformed series_transform LogNormal logpdf/Mooncake reverse	23.9 ± 7 μs
Transformed series_transform LogNormal logpdf/ReverseDiff (tape)	15 ± 0.39 μs
Transformed thin LogNormal logpdf/Enzyme forward	8.05 ± 0.065 μs
Transformed thin LogNormal logpdf/Enzyme reverse	1.99 ± 0.07 μs
Transformed thin LogNormal logpdf/ForwardDiff	0.515 ± 0.048 μs
Transformed thin LogNormal logpdf/Mooncake forward	5.53 ± 0.17 μs
Transformed thin LogNormal logpdf/Mooncake reverse	23.7 ± 6.9 μs
Transformed thin LogNormal logpdf/ReverseDiff (tape)	14.8 ± 0.37 μs
Weighted Affine LogNormal nested logpdf/Enzyme forward	8.31 ± 0.094 μs
Weighted Affine LogNormal nested logpdf/Enzyme reverse	0.942 ± 0.074 μs
Weighted Affine LogNormal nested logpdf/ForwardDiff	0.791 ± 0.04 μs
Weighted Affine LogNormal nested logpdf/Mooncake forward	7.32 ± 0.16 μs
Weighted Affine LogNormal nested logpdf/Mooncake reverse	19.3 ± 0.78 μs
Weighted Affine LogNormal nested logpdf/ReverseDiff (tape)	18.5 ± 0.45 μs
Weighted LogNormal observation-time weight logpdf/Enzyme forward	8.04 ± 0.062 μs
Weighted LogNormal observation-time weight logpdf/Enzyme reverse	1.26 ± 0.32 μs
Weighted LogNormal observation-time weight logpdf/ForwardDiff	0.546 ± 0.038 μs
Weighted LogNormal observation-time weight logpdf/Mooncake forward	6.03 ± 0.58 μs
Weighted LogNormal observation-time weight logpdf/Mooncake reverse	30.2 ± 3.2 μs
Weighted LogNormal observation-time weight logpdf/ReverseDiff (tape)	16.9 ± 0.38 μs
Weighted LogNormal scalar logpdf/Enzyme forward	8.03 ± 0.065 μs
Weighted LogNormal scalar logpdf/Enzyme reverse	1.27 ± 0.32 μs
Weighted LogNormal scalar logpdf/ForwardDiff	0.546 ± 0.05 μs
Weighted LogNormal scalar logpdf/Mooncake forward	6.05 ± 0.61 μs
Weighted LogNormal scalar logpdf/Mooncake reverse	0.0365 ± 0.0035 ms
Weighted LogNormal scalar logpdf/ReverseDiff (tape)	16.9 ± 0.39 μs
Weighted Sequential observed-total logpdf/Enzyme forward	0.116 ± 0.004 ms
Weighted Sequential observed-total logpdf/Enzyme reverse	0.348 ± 0.026 ms
Weighted Sequential observed-total logpdf/ForwardDiff	0.0837 ± 0.001 ms
Weighted Sequential observed-total logpdf/Mooncake forward	0.416 ± 0.02 ms
Weighted Sequential observed-total logpdf/Mooncake reverse	1.29 ± 0.1 ms
Weighted Sequential observed-total logpdf/ReverseDiff (tape)	2.52 ± 0.32 ms

Memory

Benchmark	d81ddd1eb1c19f...
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	0.291 k allocs: 13.4 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	0.484 k allocs: 0.0415 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	0.438 k allocs: 0.039 MB
Modified LogNormal log-link logpdf/ReverseDiff (tape)	0.377 k allocs: 14.9 kB
Modified discrete logit-link per-bin logpdf/Enzyme forward	0.307 k allocs: 13.9 kB
Modified discrete logit-link per-bin logpdf/Enzyme reverse	0.145 k allocs: 14.3 kB
Modified discrete logit-link per-bin logpdf/ForwardDiff	0.062 k allocs: 5.36 kB
Modified discrete logit-link per-bin logpdf/Mooncake forward	0.779 k allocs: 0.0345 MB
Modified discrete logit-link per-bin logpdf/Mooncake reverse	1.25 k allocs: 0.107 MB
Modified discrete logit-link per-bin logpdf/ReverseDiff (tape)	0.84 k allocs: 0.0357 MB
Modified numeric quadrature clamped additive LogNormal logpdf/Enzyme forward	0.205 k allocs: 6.88 kB
Modified numeric quadrature clamped additive LogNormal logpdf/ForwardDiff	0.056 k allocs: 1.75 kB
Modified numeric quadrature clamped additive LogNormal logpdf/Mooncake forward	0.397 k allocs: 13.7 kB
Modified numeric quadrature clamped additive LogNormal logpdf/ReverseDiff (tape)	8.65 k allocs: 0.347 MB
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	0.262 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	0.273 k allocs: 25.6 kB
Transformed cumulative LogNormal logpdf/ReverseDiff (tape)	0.213 k allocs: 9.06 kB
Transformed series_transform LogNormal logpdf/Enzyme forward	0.036 k allocs: 1.11 kB
Transformed series_transform LogNormal logpdf/Enzyme reverse	14 allocs: 0.609 kB
Transformed series_transform LogNormal logpdf/ForwardDiff	7 allocs: 0.266 kB
Transformed series_transform LogNormal logpdf/Mooncake forward	0.058 k allocs: 2.91 kB
Transformed series_transform LogNormal logpdf/Mooncake reverse	0.273 k allocs: 25.6 kB
Transformed series_transform 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	0.273 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	2.01 k allocs: 0.0974 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	d81ddd1eb1c19f...
LogNormal/ccdf	3.27 ± 0.37 μs
LogNormal/cdf	3.37 ± 0.37 μs
LogNormal/construction	3.1 ± 0.01 ns
LogNormal/logpdf	2.67 ± 0.33 μs
LogNormal/pdf	4.08 ± 0.36 μs
LogNormal/quantile	0.493 ± 0.018 μs
LogNormal/rand	1.27 ± 0.076 μs

Memory

Benchmark	d81ddd1eb1c19f...
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	d81ddd1eb1c19f...
LogNormal/ccdf	2.65 ± 0.33 μs
LogNormal/cdf	2.64 ± 0.34 μs
LogNormal/construction	1.55 ± 0.01 ns
LogNormal/logpdf	1.66 ± 0.29 μs
LogNormal/pdf	2.96 ± 0.33 μs
LogNormal/quantile	0.469 ± 0.018 μs
LogNormal/rand	1.03 ± 0.032 μs

Memory

Benchmark	d81ddd1eb1c19f...
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	d81ddd1eb1c19f...
IdentityLink/ccdf	7.52 ± 0.022 μs
IdentityLink/cdf	7.2 ± 0.022 μs
IdentityLink/construction	2.79 ± 0.01 ns
IdentityLink/logpdf	10.5 ± 0.059 μs
IdentityLink/pdf	12.7 ± 0.06 μs
IdentityLink/quantile	0.11 ± 0.00017 ms
IdentityLink/rand	0.579 ± 0.015 ms
LogLink/ccdf	5.77 ± 0.038 μs
LogLink/cdf	6.14 ± 0.026 μs
LogLink/construction	3.1 ± 0.01 ns
LogLink/logpdf	8.04 ± 0.027 μs
LogLink/pdf	9.36 ± 0.049 μs
LogLink/quantile	0.918 ± 0.076 μs
LogLink/rand	5.14 ± 0.14 μs

Memory

Benchmark	d81ddd1eb1c19f...
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	d81ddd1eb1c19f...
cumulative/cdf	2.64 ± 0.35 μs
cumulative/construction	3.1 ± 0.01 ns
cumulative/logpdf	1.65 ± 0.29 μs
cumulative/rand	1.03 ± 0.032 μs
thin/cdf	2.64 ± 0.34 μs
thin/construction	3.1 ± 0.01 ns
thin/logpdf	1.66 ± 0.31 μs
thin/rand	1.03 ± 0.034 μs

Memory

Benchmark	d81ddd1eb1c19f...
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	d81ddd1eb1c19f...
Product/construction	0.223 ± 0.08 μs
Product/logpdf	2.96 ± 0.24 μs
scalar/construction	3.1 ± 0.01 ns
scalar/logpdf	1.7 ± 0.31 μs

Memory

Benchmark	d81ddd1eb1c19f...
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	d81ddd1eb1c19f...
time_to_load	0.609 ± 0.0046 s

Memory

Benchmark	d81ddd1eb1c19f...
time_to_load	0.149 k allocs: 11.2 kB

Per-benchmark timelines

<details> <summary>Show 7 plots</summary>

</details>

About these 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.