improved univariate transforms on fast ldf

[penelopeysm]

Proof of principle. All these are run specifically on linked varinfo because that's what the optimisation affects.

# trivial        before this PR                        after this PR                        v0.38.9
eval      ----   14.664 ns (1 allocs: 32 bytes)        5.585 ns                             163.035 ns (7 allocs: 224 bytes)    
grad (FD) ----   43.595 ns (4 allocs: 144 bytes)       50.415 ns (3 allocs: 96 bytes)       324.728 ns (14 allocs: 544 bytes)   
grad (RD) ----   2.718 μs (52 allocs: 1.781 KiB)       3.107 μs (46 allocs: 1.578 KiB)      4.042 μs (82 allocs: 3.125 KiB)     
grad (MC) ----   319.596 ns (6 allocs: 256 bytes)      111.164 ns (2 allocs: 64 bytes)      1.194 μs (27 allocs: 1.281 KiB)     
grad (EN) ----   172.721 ns (6 allocs: 208 bytes)      73.662 ns (2 allocs: 64 bytes)       483.607 ns (20 allocs: 688 bytes)   
                                                                                                                                   
# eight-schools  before this PR                        after this PR                        v0.38.9
eval      ----   241.115 ns (7 allocs: 352 bytes)      159.574 ns (4 allocs: 256 bytes)     760.417 ns (22 allocs: 1.094 KiB)   
grad (FD) ----   886.719 ns (13 allocs: 2.812 KiB)     777.027 ns (11 allocs: 2.594 KiB)    1.476 μs (28 allocs: 4.828 KiB)     
grad (RD) ----   38.250 μs (593 allocs: 21.641 KiB)    43.750 μs (574 allocs: 20.938 KiB)   43.000 μs (639 allocs: 26.359 KiB)  
grad (MC) ----   1.511 μs (18 allocs: 976 bytes)       1.037 μs (10 allocs: 656 bytes)      4.910 μs (68 allocs: 3.859 KiB)     
grad (EN) ----   998.600 ns (33 allocs: 1.469 KiB)     605.429 ns (13 allocs: 832 bytes)    1.942 μs (59 allocs: 2.797 KiB)     
                                                                                                                                   
# badvarnames    before this PR                        after this PR                        v0.38.9
eval      ----   611.104 ns (22 allocs: 864 bytes)     315.217 ns (2 allocs: 224 bytes)     1.635 μs (66 allocs: 2.531 KiB)     
grad (FD) ----   3.530 μs (51 allocs: 8.656 KiB)       1.949 μs (11 allocs: 4.281 KiB)      5.475 μs (143 allocs: 18.641 KiB)   
grad (RD) ----   47.541 μs (893 allocs: 31.812 KiB)    50.792 μs (754 allocs: 26.859 KiB)   57.167 μs (1076 allocs: 40.078 KiB) 
grad (MC) ----   2.842 μs (68 allocs: 2.344 KiB)       1.221 μs (6 allocs: 672 bytes)       8.319 μs (200 allocs: 8.250 KiB)    
grad (EN) ----   2.633 μs (85 allocs: 4.469 KiB)       477.800 ns (10 allocs: 1.656 KiB)    3.589 μs (144 allocs: 8.641 KiB)    
                                                                                                                                   
# submodel       before this PR                        after this PR                        v0.38.9
eval      ----   124.658 ns (3 allocs: 96 bytes)       57.435 ns                            613.000 ns (19 allocs: 848 bytes)   
grad (FD) ----   229.321 ns (6 allocs: 304 bytes)      187.931 ns (3 allocs: 112 bytes)     920.966 ns (26 allocs: 1.594 KiB)   
grad (RD) ----   10.667 μs (165 allocs: 5.781 KiB)     11.729 μs (147 allocs: 5.156 KiB)    16.375 μs (235 allocs: 9.547 KiB)   
grad (MC) ----   729.158 ns (12 allocs: 432 bytes)     302.182 ns (2 allocs: 80 bytes)      5.667 μs (74 allocs: 3.000 KiB)     
grad (EN) ----   661.111 ns (25 allocs: 928 bytes)     278.971 ns (3 allocs: 128 bytes)     2.420 μs (70 allocs: 2.750 KiB)     
                                                                                                                                   
# demo3          before this PR                        after this PR                        v0.38.9
eval      ----   306.122 ns (12 allocs: 528 bytes)     298.242 ns (12 allocs: 528 bytes)    835.794 ns (23 allocs: 1.031 KiB)  
grad (FD) ----   555.288 ns (17 allocs: 1.094 KiB)     562.098 ns (17 allocs: 1.094 KiB)    1.141 μs (32 allocs: 2.219 KiB)    
grad (RD) ----   15.917 μs (253 allocs: 9.297 KiB)     17.375 μs (253 allocs: 9.297 KiB)    20.292 μs (315 allocs: 12.641 KiB) 
grad (MC) ----   1.839 μs (28 allocs: 1.250 KiB)       1.613 μs (26 allocs: 1.125 KiB)      3.810 μs (64 allocs: 3.266 KiB)    
grad (EN) ----   1.378 μs (32 allocs: 1.406 KiB)       1.377 μs (32 allocs: 1.406 KiB)      1.922 μs (52 allocs: 2.281 KiB)   

demo3 has no real difference because it only uses multivariates I believe.

[github-actions]

Benchmark Report

• this PR's head: acff2745eca12b8925731f91998f8675b89122ee
• base branch: accb515201d8391dea61ccbf87969a09a5db7978

Computer Information

Julia Version 1.11.7
Commit f2b3dbda30a (2025-09-08 12:10 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

Benchmark Results

┌───────────────────────┬───────┬─────────────┬────────────────┬────────┬───────────────────────────────┬────────────────────────────┬─────────────────────────────────┐
│                       │       │             │                │        │       t(eval) / t(ref)        │     t(grad) / t(eval)      │        t(grad) / t(ref)         │
│                       │       │             │                │        │ ─────────┬──────────┬──────── │ ───────┬─────────┬──────── │ ──────────┬───────────┬──────── │
│                 Model │   Dim │  AD Backend │        VarInfo │ Linked │     base │  this PR │ speedup │   base │ this PR │ speedup │      base │   this PR │ speedup │
├───────────────────────┼───────┼─────────────┼────────────────┼────────┼──────────┼──────────┼─────────┼────────┼─────────┼─────────┼───────────┼───────────┼─────────┤
│               Dynamic │    10 │    mooncake │          typed │   true │   321.48 │   335.93 │    0.96 │   9.88 │    9.40 │    1.05 │   3177.49 │   3158.89 │    1.01 │
│                   LDA │    12 │ reversediff │          typed │   true │  2265.54 │  2451.08 │    0.92 │   5.44 │    5.31 │    1.03 │  12333.29 │  13004.41 │    0.95 │
│   Loop univariate 10k │ 10000 │    mooncake │          typed │   true │ 90006.79 │ 67684.66 │    1.33 │   3.94 │    3.94 │    1.00 │ 354505.36 │ 266947.27 │    1.33 │
├───────────────────────┼───────┼─────────────┼────────────────┼────────┼──────────┼──────────┼─────────┼────────┼─────────┼─────────┼───────────┼───────────┼─────────┤
│    Loop univariate 1k │  1000 │    mooncake │          typed │   true │  6875.12 │  4406.34 │    1.56 │   4.88 │    5.76 │    0.85 │  33565.90 │  25384.00 │    1.32 │
│      Multivariate 10k │ 10000 │    mooncake │          typed │   true │ 27948.32 │ 30323.59 │    0.92 │  10.29 │   10.09 │    1.02 │ 287575.18 │ 305983.56 │    0.94 │
│       Multivariate 1k │  1000 │    mooncake │          typed │   true │  3132.04 │  3272.50 │    0.96 │   9.43 │    9.44 │    1.00 │  29534.24 │  30892.10 │    0.96 │
├───────────────────────┼───────┼─────────────┼────────────────┼────────┼──────────┼──────────┼─────────┼────────┼─────────┼─────────┼───────────┼───────────┼─────────┤
│ Simple assume observe │     1 │ forwarddiff │          typed │  false │     3.33 │     1.34 │    2.50 │   2.91 │    7.09 │    0.41 │      9.70 │      9.48 │    1.02 │
│           Smorgasbord │   201 │ forwarddiff │          typed │  false │  1061.92 │   997.98 │    1.06 │ 125.31 │   67.36 │    1.86 │ 133063.76 │  67223.75 │    1.98 │
│           Smorgasbord │   201 │      enzyme │          typed │   true │  1482.56 │  1196.90 │    1.24 │   5.01 │    4.86 │    1.03 │   7425.70 │   5822.25 │    1.28 │
├───────────────────────┼───────┼─────────────┼────────────────┼────────┼──────────┼──────────┼─────────┼────────┼─────────┼─────────┼───────────┼───────────┼─────────┤
│           Smorgasbord │   201 │    mooncake │          typed │   true │  1947.42 │  1226.46 │    1.59 │   4.06 │    5.32 │    0.76 │   7899.03 │   6525.85 │    1.21 │
│           Smorgasbord │   201 │ reversediff │          typed │   true │  1492.89 │  1208.51 │    1.24 │  88.38 │  109.83 │    0.80 │ 131935.68 │ 132734.26 │    0.99 │
│           Smorgasbord │   201 │ forwarddiff │   typed_vector │   true │  1464.59 │  1195.94 │    1.22 │  57.01 │  151.18 │    0.38 │  83497.92 │ 180803.35 │    0.46 │
├───────────────────────┼───────┼─────────────┼────────────────┼────────┼──────────┼──────────┼─────────┼────────┼─────────┼─────────┼───────────┼───────────┼─────────┤
│           Smorgasbord │   201 │ forwarddiff │        untyped │   true │  1461.15 │  1199.86 │    1.22 │  57.96 │   81.02 │    0.72 │  84694.73 │  97209.90 │    0.87 │
│           Smorgasbord │   201 │ forwarddiff │ untyped_vector │   true │  1460.39 │  1204.64 │    1.21 │  55.97 │   81.47 │    0.69 │  81731.87 │  98143.20 │    0.83 │
│              Submodel │     1 │    mooncake │          typed │   true │     7.37 │     5.29 │    1.39 │   4.51 │    4.54 │    0.99 │     33.24 │     24.03 │    1.38 │
└───────────────────────┴───────┴─────────────┴────────────────┴────────┴──────────┴──────────┴─────────┴────────┴─────────┴─────────┴───────────┴───────────┴─────────┘

[codecov]

Codecov Report

❌ Patch coverage is 64.04494% with 32 lines in your changes missing coverage. Please review.
✅ Project coverage is 76.74%. Comparing base (accb515) to head (acff274).

Files with missing lines	Patch %	Lines
src/utils.jl	64.04%	32 Missing ⚠️

Additional details and impacted files

@@                  Coverage Diff                  @@
##           py/type-stability    #1147      +/-   ##
=====================================================
- Coverage              77.17%   76.74%   -0.44%     
=====================================================
  Files                     40       40              
  Lines                   3733     3801      +68     
=====================================================
+ Hits                    2881     2917      +36     
- Misses                   852      884      +32     

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[github-actions]

DynamicPPL.jl documentation for PR #1147 is available at:
https://TuringLang.github.io/DynamicPPL.jl/previews/PR1147/