Make sure reduce_sum_static only evaluates inputs once

[SteveBronder]

Summary

Fixes #3304 . Minimal alternative to #3305 which makes sure that expressions passed to reduce_sum_static are only evaluated once.

Tests

./runTest.py test/unit/math/prim/functor/reduce_sum_static_expression_test.cpp
./runTests.py test/unit/math/rev/functor/reduce_sum_static_expression_test.cpp

Thanks @tmchow !

Checklist

• Copyright holder: Trevin Chow & Steve Bronder

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested

[WardBrian]

test/unit/math/rev/functor/reduce_sum_static_expression_test.cpp at line 28:

	[rev-tests] Reverse-mode tests in test/unit/math/rev must use a cleanup fixture. Replace raw TEST(...) with TEST_F(AgradRev, ...) or another approved fixture-based form.

Huh, glad we have this check, would've totally missed it...

[SteveBronder]

Thank you past Steve 🙏

[WardBrian]

Locally, one of the new tests fails:
[ FAILED ] StanMathPrim_reduce_sum_static.eigen_expression_arg_evaluated_once

[SteveBronder]

Ah I was running locally with only stan threads on. Fixed for stan threads being on and off

[stan-buildbot]

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
stat_comp_benchmarks/benchmarks/gp_regr/gp_regr.stan	0.23	0.23	1.0	-0.33% slower
stat_comp_benchmarks/benchmarks/gp_regr/gen_gp_data.stan	0.06	0.06	0.98	-2.05% slower
stat_comp_benchmarks/benchmarks/low_dim_gauss_mix/low_dim_gauss_mix.stan	6.36	6.43	0.99	-1.18% slower
stat_comp_benchmarks/benchmarks/low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	1.02	1.5% faster
stat_comp_benchmarks/benchmarks/irt_2pl/irt_2pl.stan	9.09	9.03	1.01	0.72% faster
stat_comp_benchmarks/benchmarks/gp_pois_regr/gp_pois_regr.stan	4.48	4.48	1.0	-0.1% slower
stat_comp_benchmarks/benchmarks/sir/sir.stan	167.21	167.94	1.0	-0.44% slower
stat_comp_benchmarks/benchmarks/garch/garch.stan	0.89	0.89	1.0	-0.27% slower
stat_comp_benchmarks/benchmarks/arma/arma.stan	0.7	0.7	0.99	-0.79% slower
stat_comp_benchmarks/benchmarks/pkpd/one_comp_mm_elim_abs.stan	42.81	43.36	0.99	-1.28% slower
stat_comp_benchmarks/benchmarks/pkpd/sim_one_comp_mm_elim_abs.stan	0.58	0.58	0.99	-0.61% slower
stat_comp_benchmarks/benchmarks/low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	20.97	21.06	1.0	-0.42% slower
stat_comp_benchmarks/benchmarks/eight_schools/eight_schools.stan	0.11	0.11	0.99	-1.32% slower
stat_comp_benchmarks/benchmarks/arK/arK.stan	3.19	3.22	0.99	-0.81% slower
performance.compilation	380.92	393.94	0.97	-3.42% slower
Mean result: 0.9929692911079996

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Commit hash: 29fbe6930a05f7ff146352e9a28187f983c52d08

Machine information

Distributor ID:	Ubuntu
Description:	Ubuntu 20.04.3 LTS
Release:	20.04
Codename:	focal

CPU:

Architecture:                            x86_64
CPU op-mode(s):                          32-bit, 64-bit
Byte Order:                              Little Endian
Address sizes:                           43 bits physical, 48 bits virtual
CPU(s):                                  256
On-line CPU(s) list:                     0-255
Thread(s) per core:                      2
Core(s) per socket:                      64
Socket(s):                               2
NUMA node(s):                            2
Vendor ID:                               AuthenticAMD
CPU family:                              23
Model:                                   49
Model name:                              AMD EPYC 7742 64-Core Processor
Stepping:                                0
Frequency boost:                         enabled
CPU MHz:                                 1497.196
CPU max MHz:                             3416.0681
CPU min MHz:                             1500.0000
BogoMIPS:                                4491.55
Virtualization:                          AMD-V
L1d cache:                               4 MiB
L1i cache:                               4 MiB
L2 cache:                                64 MiB
L3 cache:                                512 MiB
NUMA node0 CPU(s):                       0-63,128-191
NUMA node1 CPU(s):                       64-127,192-255
Vulnerability Gather data sampling:      Not affected
Vulnerability Indirect target selection: Not affected
Vulnerability Itlb multihit:             Not affected
Vulnerability L1tf:                      Not affected
Vulnerability Mds:                       Not affected
Vulnerability Meltdown:                  Not affected
Vulnerability Mmio stale data:           Not affected
Vulnerability Reg file data sampling:    Not affected
Vulnerability Retbleed:                  Mitigation; untrained return thunk; SMT enabled with STIBP protection
Vulnerability Spec rstack overflow:      Mitigation; Safe RET
Vulnerability Spec store bypass:         Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1:                Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:                Mitigation; Retpolines; IBPB conditional; STIBP always-on; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds:                     Not affected
Vulnerability Tsa:                       Not affected
Vulnerability Tsx async abort:           Not affected
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 mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip rdpid overflow_recov succor smca sev sev_es

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
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang:

clang version 10.0.0-4ubuntu1 
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin