Reuse direct reverse mode autodiff specializations for known laplace distributions

[ishaan-arora-1]

I've implemented a fix for the issue. I found that we can bypass the expensive nested autodiff by providing specialized diff() and third_diff() methods directly within the likelihood functors like neg_binomial_2_log.

I think this should be a good fix considering we've added type traits (e.g., has_custom_diff) to compile-time dispatch these specialized methods without breaking the generic autodiff fallback for other distributions. Computations derived from the original implementation (commit 3f310e7) were adapted to match the current API structure, which should bring back the performance gains.

Resolves #3287

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_regr/gp_regr.stan	0.09	0.09	1.04	4.23% faster
gp_regr/gen_gp_data.stan	0.02	0.02	1.08	7.07% faster
arK/arK.stan	1.81	1.71	1.05	5.2% faster
eight_schools/eight_schools.stan	0.06	0.05	1.06	5.87% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.89	8.37	1.06	5.81% faster
pkpd/one_comp_mm_elim_abs.stan	19.84	18.66	1.06	5.95% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.24	1.06	5.94% faster
sir/sir.stan	70.65	65.88	1.07	6.76% faster
gp_pois_regr/gp_pois_regr.stan	2.85	2.77	1.03	2.91% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.7	2.57	1.05	4.81% faster
irt_2pl/irt_2pl.stan	4.14	3.92	1.06	5.42% faster
arma/arma.stan	0.29	0.27	1.09	8.26% faster
garch/garch.stan	0.43	0.44	0.99	-1.41% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.12	10.64% faster
performance.compilation	234.77	224.81	1.04	4.24% faster
Mean result: 1.0583549459280994

---

Jenkins Console Log
Blue Ocean
Commit hash: 19930437e3538fa8e0be8b788055ba897f63efce

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU:
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Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
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NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
Vulnerability Gather data sampling: Mitigation; Microcode
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Vulnerability Vmscape: Mitigation; IBPB before exit to userspace
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++:
g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
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Clang:
clang version 10.0.0-4ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin

[SteveBronder]

This is cool! Can you do a benchmark of this vs the old version to see what the difference in performance is?

[SteveBronder]

Also, do the benchmark first, but if the benchmark works then I think I'd prefer having two overloads instead of an if constexpr here as the if statements / nested if statements can be a bit much for readability. See the example below

https://godbolt.org/z/bjhrdKo4E

I have this repo for benchmarking stan stuff that may be useful, but we also have google benchmark

https://github.com/SteveBronder/stan-perf