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 throughY = scale * X + shift.Weighted: thelogpdfweight paths, scalar and the vectorisedProduct{Weighted}form.Transformed:thinandcumulative, 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-linkquantileandrandexercise the monotone-bisection cdf inversion, the one non-closed-form path.AD gradients:DifferentiationInterface.gradientof everytest/ADFixturesscenario 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
Ratio summary
| c5ff0062ac07a5... | |
|---|---|
| AD gradients/Affine LogNormal scale+shift logpdf/Enzyme forward | 8.73 ± 0.12 μs |
| AD gradients/Affine LogNormal scale+shift logpdf/Enzyme reverse | 3.04 ± 0.051 μs |
| AD gradients/Affine LogNormal scale+shift logpdf/ForwardDiff | 0.743 ± 0.1 μs |
| AD gradients/Affine LogNormal scale+shift logpdf/Mooncake forward | 7.03 ± 0.23 μs |
| AD gradients/Affine LogNormal scale+shift logpdf/Mooncake reverse | 20 ± 1.1 μs |
| AD gradients/Affine LogNormal scale+shift logpdf/ReverseDiff (tape) | 16.4 ± 0.47 μs |
| AD gradients/Modified LogNormal identity-link logpdf/Enzyme forward | 8.78 ± 0.077 μs |
| AD gradients/Modified LogNormal identity-link logpdf/Enzyme reverse | 3.01 ± 0.076 μs |
| AD gradients/Modified LogNormal identity-link logpdf/ForwardDiff | 1.07 ± 0.016 μs |
| AD gradients/Modified LogNormal identity-link logpdf/Mooncake forward | 8.7 ± 0.18 μs |
| AD gradients/Modified LogNormal identity-link logpdf/Mooncake reverse | 0.036 ± 0.0017 ms |
| AD gradients/Modified LogNormal identity-link logpdf/ReverseDiff (tape) | 31.5 ± 0.59 μs |
| AD gradients/Modified LogNormal log-link logpdf/Enzyme forward | 8.6 ± 0.09 μs |
| AD gradients/Modified LogNormal log-link logpdf/Enzyme reverse | 3.54 ± 0.086 μs |
| AD gradients/Modified LogNormal log-link logpdf/ForwardDiff | 0.905 ± 0.094 μs |
| AD gradients/Modified LogNormal log-link logpdf/Mooncake forward | 7.6 ± 0.16 μs |
| AD gradients/Modified LogNormal log-link logpdf/Mooncake reverse | 0.0477 ± 0.0047 ms |
| AD gradients/Modified LogNormal log-link logpdf/ReverseDiff (tape) | 26.2 ± 0.59 μs |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Enzyme forward | 8.26 ± 0.14 μs |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Enzyme reverse | 1.02 ± 0.22 μs |
| AD gradients/Product{Weighted} LogNormal vector logpdf/ForwardDiff | 0.897 ± 0.068 μs |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Mooncake forward | 7.18 ± 0.46 μs |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Mooncake reverse | 0.037 ± 0.003 ms |
| AD gradients/Product{Weighted} LogNormal vector logpdf/ReverseDiff (tape) | 16.4 ± 0.44 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/Enzyme forward | 8.03 ± 0.068 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/Enzyme reverse | 1.97 ± 0.061 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/ForwardDiff | 0.541 ± 0.083 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/Mooncake forward | 6.4 ± 0.61 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/Mooncake reverse | 30.8 ± 8.1 μs |
| AD gradients/Transformed cumulative LogNormal logpdf/ReverseDiff (tape) | 14.8 ± 0.43 μs |
| AD gradients/Transformed thin LogNormal logpdf/Enzyme forward | 8.09 ± 0.084 μs |
| AD gradients/Transformed thin LogNormal logpdf/Enzyme reverse | 1.97 ± 0.066 μs |
| AD gradients/Transformed thin LogNormal logpdf/ForwardDiff | 0.545 ± 0.081 μs |
| AD gradients/Transformed thin LogNormal logpdf/Mooncake forward | 7.7 ± 0.21 μs |
| AD gradients/Transformed thin LogNormal logpdf/Mooncake reverse | 30 ± 7.7 μs |
| AD gradients/Transformed thin LogNormal logpdf/ReverseDiff (tape) | 14.7 ± 0.4 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/Enzyme forward | 8.55 ± 0.1 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/Enzyme reverse | 0.954 ± 0.072 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/ForwardDiff | 0.861 ± 0.14 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/Mooncake forward | 7.37 ± 0.21 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/Mooncake reverse | 20.5 ± 1.2 μs |
| AD gradients/Weighted Affine LogNormal nested logpdf/ReverseDiff (tape) | 18.3 ± 0.49 μs |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Enzyme forward | 8.05 ± 0.075 μs |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Enzyme reverse | 1.3 ± 0.32 μs |
| AD gradients/Weighted LogNormal observation-time weight logpdf/ForwardDiff | 0.591 ± 0.096 μs |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Mooncake forward | 6.19 ± 0.76 μs |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Mooncake reverse | 0.0369 ± 0.0033 ms |
| AD gradients/Weighted LogNormal observation-time weight logpdf/ReverseDiff (tape) | 16.8 ± 0.45 μs |
| AD gradients/Weighted LogNormal scalar logpdf/Enzyme forward | 8.04 ± 0.07 μs |
| AD gradients/Weighted LogNormal scalar logpdf/Enzyme reverse | 1.25 ± 0.34 μs |
| AD gradients/Weighted LogNormal scalar logpdf/ForwardDiff | 0.597 ± 0.091 μs |
| AD gradients/Weighted LogNormal scalar logpdf/Mooncake forward | 6.01 ± 0.7 μs |
| AD gradients/Weighted LogNormal scalar logpdf/Mooncake reverse | 0.0446 ± 0.0036 ms |
| AD gradients/Weighted LogNormal scalar logpdf/ReverseDiff (tape) | 16.9 ± 0.47 μs |
| AD gradients/Weighted Sequential observed-total logpdf/Enzyme forward | 0.155 ± 0.0041 ms |
| AD gradients/Weighted Sequential observed-total logpdf/Enzyme reverse | 0.492 ± 0.033 ms |
| AD gradients/Weighted Sequential observed-total logpdf/ForwardDiff | 0.126 ± 0.0013 ms |
| AD gradients/Weighted Sequential observed-total logpdf/Mooncake forward | 0.588 ± 0.014 ms |
| AD gradients/Weighted Sequential observed-total logpdf/Mooncake reverse | 1.52 ± 0.035 ms |
| AD gradients/Weighted Sequential observed-total logpdf/ReverseDiff (tape) | 4.24 ± 0.51 ms |
| Affine/LogNormal/ccdf | 3.27 ± 0.38 μs |
| Affine/LogNormal/cdf | 3.36 ± 0.37 μs |
| Affine/LogNormal/construction | 3.1 ± 0.01 ns |
| Affine/LogNormal/logpdf | 2.63 ± 0.35 μs |
| Affine/LogNormal/pdf | 3.78 ± 0.2 μs |
| Affine/LogNormal/quantile | 0.488 ± 0.017 μs |
| Affine/LogNormal/rand | 1.27 ± 0.073 μs |
| Baseline/LogNormal/ccdf | 2.66 ± 0.34 μs |
| Baseline/LogNormal/cdf | 2.65 ± 0.34 μs |
| Baseline/LogNormal/construction | 1.55 ± 0.009 ns |
| Baseline/LogNormal/logpdf | 1.67 ± 0.31 μs |
| Baseline/LogNormal/pdf | 2.96 ± 0.32 μs |
| Baseline/LogNormal/quantile | 0.467 ± 0.017 μs |
| Baseline/LogNormal/rand | 1.03 ± 0.03 μs |
| Modified/IdentityLink/ccdf | 7.5 ± 0.018 μs |
| Modified/IdentityLink/cdf | 7.13 ± 0.02 μs |
| Modified/IdentityLink/construction | 3.1 ± 0.01 ns |
| Modified/IdentityLink/logpdf | 10.5 ± 0.051 μs |
| Modified/IdentityLink/pdf | 12.8 ± 0.05 μs |
| Modified/IdentityLink/quantile | 0.107 ± 0.00018 ms |
| Modified/IdentityLink/rand | 0.559 ± 0.015 ms |
| Modified/LogLink/ccdf | 5.76 ± 0.043 μs |
| Modified/LogLink/cdf | 6.11 ± 0.026 μs |
| Modified/LogLink/construction | 2.79 ± 0.01 ns |
| Modified/LogLink/logpdf | 7.99 ± 0.025 μs |
| Modified/LogLink/pdf | 9.29 ± 0.04 μs |
| Modified/LogLink/quantile | 0.922 ± 0.07 μs |
| Modified/LogLink/rand | 5.13 ± 0.14 μs |
| Transformed/cumulative/cdf | 2.64 ± 0.32 μs |
| Transformed/cumulative/construction | 4.02 ± 0.011 ns |
| Transformed/cumulative/logpdf | 1.66 ± 0.31 μs |
| Transformed/cumulative/rand | 1.04 ± 0.032 μs |
| Transformed/thin/cdf | 2.65 ± 0.34 μs |
| Transformed/thin/construction | 4.02 ± 0.01 ns |
| Transformed/thin/logpdf | 1.66 ± 0.31 μs |
| Transformed/thin/rand | 1.04 ± 0.039 μs |
| Weighted/Product/construction | 0.305 ± 0.14 μs |
| Weighted/Product/logpdf | 2.92 ± 0.21 μs |
| Weighted/scalar/construction | 3.41 ± 0.001 ns |
| Weighted/scalar/logpdf | 1.73 ± 0.3 μs |
| time_to_load | 0.594 ± 0.0037 s |
| c5ff0062ac07a5... | |
|---|---|
| AD gradients/Affine LogNormal scale+shift logpdf/Enzyme forward | 0.044 k allocs: 1.52 kB |
| AD gradients/Affine LogNormal scale+shift logpdf/Enzyme reverse | 24 allocs: 0.969 kB |
| AD gradients/Affine LogNormal scale+shift logpdf/ForwardDiff | 7 allocs: 0.484 kB |
| AD gradients/Affine LogNormal scale+shift logpdf/Mooncake forward | 0.07 k allocs: 3.33 kB |
| AD gradients/Affine LogNormal scale+shift logpdf/Mooncake reverse | 0.292 k allocs: 13.5 kB |
| AD gradients/Affine LogNormal scale+shift logpdf/ReverseDiff (tape) | 0.248 k allocs: 10.6 kB |
| AD gradients/Modified LogNormal identity-link logpdf/Enzyme forward | 0.04 k allocs: 1.25 kB |
| AD gradients/Modified LogNormal identity-link logpdf/Enzyme reverse | 14 allocs: 0.609 kB |
| AD gradients/Modified LogNormal identity-link logpdf/ForwardDiff | 7 allocs: 0.359 kB |
| AD gradients/Modified LogNormal identity-link logpdf/Mooncake forward | 0.064 k allocs: 3.06 kB |
| AD gradients/Modified LogNormal identity-link logpdf/Mooncake reverse | 0.455 k allocs: 21.3 kB |
| AD gradients/Modified LogNormal identity-link logpdf/ReverseDiff (tape) | 0.465 k allocs: 17.8 kB |
| AD gradients/Modified LogNormal log-link logpdf/Enzyme forward | 0.04 k allocs: 1.25 kB |
| AD gradients/Modified LogNormal log-link logpdf/Enzyme reverse | 24 allocs: 0.969 kB |
| AD gradients/Modified LogNormal log-link logpdf/ForwardDiff | 7 allocs: 0.359 kB |
| AD gradients/Modified LogNormal log-link logpdf/Mooncake forward | 0.064 k allocs: 3.06 kB |
| AD gradients/Modified LogNormal log-link logpdf/Mooncake reverse | 0.439 k allocs: 0.039 MB |
| AD gradients/Modified LogNormal log-link logpdf/ReverseDiff (tape) | 0.377 k allocs: 14.9 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Enzyme forward | 0.053 k allocs: 2.31 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Enzyme reverse | 16 allocs: 0.922 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/ForwardDiff | 15 allocs: 1.06 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Mooncake forward | 0.116 k allocs: 6.31 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/Mooncake reverse | 0.372 k allocs: 23.5 kB |
| AD gradients/Product{Weighted} LogNormal vector logpdf/ReverseDiff (tape) | 0.239 k allocs: 10 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/Enzyme forward | 0.036 k allocs: 1.11 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/Enzyme reverse | 14 allocs: 0.609 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/ForwardDiff | 7 allocs: 0.266 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/Mooncake forward | 0.058 k allocs: 2.91 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/Mooncake reverse | 0.274 k allocs: 25.6 kB |
| AD gradients/Transformed cumulative LogNormal logpdf/ReverseDiff (tape) | 0.213 k allocs: 9.06 kB |
| AD gradients/Transformed thin LogNormal logpdf/Enzyme forward | 0.036 k allocs: 1.11 kB |
| AD gradients/Transformed thin LogNormal logpdf/Enzyme reverse | 14 allocs: 0.609 kB |
| AD gradients/Transformed thin LogNormal logpdf/ForwardDiff | 7 allocs: 0.266 kB |
| AD gradients/Transformed thin LogNormal logpdf/Mooncake forward | 0.058 k allocs: 2.91 kB |
| AD gradients/Transformed thin LogNormal logpdf/Mooncake reverse | 0.274 k allocs: 25.6 kB |
| AD gradients/Transformed thin LogNormal logpdf/ReverseDiff (tape) | 0.213 k allocs: 9.06 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/Enzyme forward | 0.036 k allocs: 1.38 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/Enzyme reverse | 6 allocs: 0.484 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/ForwardDiff | 7 allocs: 0.516 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/Mooncake forward | 0.08 k allocs: 4.02 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/Mooncake reverse | 0.329 k allocs: 15.6 kB |
| AD gradients/Weighted Affine LogNormal nested logpdf/ReverseDiff (tape) | 0.269 k allocs: 11.3 kB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Enzyme forward | 0.032 k allocs: 1.05 kB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Enzyme reverse | 10 allocs: 1.14 kB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/ForwardDiff | 7 allocs: 0.297 kB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Mooncake forward | 0.068 k allocs: 3.59 kB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/Mooncake reverse | 0.32 k allocs: 0.0353 MB |
| AD gradients/Weighted LogNormal observation-time weight logpdf/ReverseDiff (tape) | 0.239 k allocs: 9.97 kB |
| AD gradients/Weighted LogNormal scalar logpdf/Enzyme forward | 0.032 k allocs: 1.05 kB |
| AD gradients/Weighted LogNormal scalar logpdf/Enzyme reverse | 10 allocs: 1.14 kB |
| AD gradients/Weighted LogNormal scalar logpdf/ForwardDiff | 7 allocs: 0.297 kB |
| AD gradients/Weighted LogNormal scalar logpdf/Mooncake forward | 0.068 k allocs: 3.59 kB |
| AD gradients/Weighted LogNormal scalar logpdf/Mooncake reverse | 0.348 k allocs: 0.0453 MB |
| AD gradients/Weighted LogNormal scalar logpdf/ReverseDiff (tape) | 0.239 k allocs: 9.97 kB |
| AD gradients/Weighted Sequential observed-total logpdf/Enzyme forward | 0.556 k allocs: 21.1 kB |
| AD gradients/Weighted Sequential observed-total logpdf/Enzyme reverse | 1.83 k allocs: 0.0805 MB |
| AD gradients/Weighted Sequential observed-total logpdf/ForwardDiff | 0.159 k allocs: 8.22 kB |
| AD gradients/Weighted Sequential observed-total logpdf/Mooncake forward | 1.37 k allocs: 0.0577 MB |
| AD gradients/Weighted Sequential observed-total logpdf/Mooncake reverse | 6.49 k allocs: 1.33 MB |
| AD gradients/Weighted Sequential observed-total logpdf/ReverseDiff (tape) | 0.0531 M allocs: 2.06 MB |
| Affine/LogNormal/ccdf | 2 allocs: 0.906 kB |
| Affine/LogNormal/cdf | 2 allocs: 0.906 kB |
| Affine/LogNormal/construction | 0 allocs: 0 B |
| Affine/LogNormal/logpdf | 2 allocs: 0.906 kB |
| Affine/LogNormal/pdf | 2 allocs: 0.906 kB |
| Affine/LogNormal/quantile | 2 allocs: 0.219 kB |
| Affine/LogNormal/rand | 2 allocs: 0.906 kB |
| Baseline/LogNormal/ccdf | 2 allocs: 0.906 kB |
| Baseline/LogNormal/cdf | 2 allocs: 0.906 kB |
| Baseline/LogNormal/construction | 0 allocs: 0 B |
| Baseline/LogNormal/logpdf | 2 allocs: 0.906 kB |
| Baseline/LogNormal/pdf | 2 allocs: 0.906 kB |
| Baseline/LogNormal/quantile | 2 allocs: 0.219 kB |
| Baseline/LogNormal/rand | 2 allocs: 0.906 kB |
| Modified/IdentityLink/ccdf | 2 allocs: 0.906 kB |
| Modified/IdentityLink/cdf | 2 allocs: 0.906 kB |
| Modified/IdentityLink/construction | 0 allocs: 0 B |
| Modified/IdentityLink/logpdf | 2 allocs: 0.906 kB |
| Modified/IdentityLink/pdf | 2 allocs: 0.906 kB |
| Modified/IdentityLink/quantile | 2 allocs: 0.219 kB |
| Modified/IdentityLink/rand | 2 allocs: 0.906 kB |
| Modified/LogLink/ccdf | 2 allocs: 0.906 kB |
| Modified/LogLink/cdf | 2 allocs: 0.906 kB |
| Modified/LogLink/construction | 0 allocs: 0 B |
| Modified/LogLink/logpdf | 2 allocs: 0.906 kB |
| Modified/LogLink/pdf | 2 allocs: 0.906 kB |
| Modified/LogLink/quantile | 2 allocs: 0.219 kB |
| Modified/LogLink/rand | 2 allocs: 0.906 kB |
| Transformed/cumulative/cdf | 2 allocs: 0.906 kB |
| Transformed/cumulative/construction | 0 allocs: 0 B |
| Transformed/cumulative/logpdf | 2 allocs: 0.906 kB |
| Transformed/cumulative/rand | 2 allocs: 0.906 kB |
| Transformed/thin/cdf | 2 allocs: 0.906 kB |
| Transformed/thin/construction | 0 allocs: 0 B |
| Transformed/thin/logpdf | 2 allocs: 0.906 kB |
| Transformed/thin/rand | 2 allocs: 0.906 kB |
| Weighted/Product/construction | 3 allocs: 2.45 kB |
| Weighted/Product/logpdf | 6 allocs: 2.72 kB |
| Weighted/scalar/construction | 0 allocs: 0 B |
| Weighted/scalar/logpdf | 2 allocs: 0.906 kB |
| time_to_load | 0.149 k allocs: 11.2 kB |
Per-benchmark timelines
