Bugfix common subexpression elimination in kernel generator

[t4c1]

Summary

Kernel generator used to merge subexpressions even if they were indexed differently (such as taking two blocks of same subexpression). This fixes the bug by making copies of expressions that have changed indexing. Since only expressions are copied and underlying matrices are not this is relatively cheap.

Tests

Added a new test that demonstrates the bug.

Side Effects

None.

Checklist

• Math issue Implement OpenCL kernel generator #1342

• Copyright holder: Tadej Ciglarič

  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

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_pois_regr/gp_pois_regr.stan	4.91	4.93	0.99	-0.52% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.02	0.02	0.99	-1.27% slower
eight_schools/eight_schools.stan	0.09	0.09	0.98	-2.29% slower
gp_regr/gp_regr.stan	0.22	0.22	1.0	0.24% faster
irt_2pl/irt_2pl.stan	6.07	6.08	1.0	-0.06% slower
performance.compilation	88.21	87.08	1.01	1.28% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	7.35	7.33	1.0	0.23% faster
pkpd/one_comp_mm_elim_abs.stan	20.35	21.01	0.97	-3.28% slower
sir/sir.stan	91.06	89.06	1.02	2.2% faster
gp_regr/gen_gp_data.stan	0.04	0.05	0.98	-2.53% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.99	2.99	1.0	-0.13% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.31	0.33	0.96	-3.9% slower
arK/arK.stan	1.82	1.74	1.04	4.3% faster
arma/arma.stan	0.77	0.77	1.0	0.14% faster
garch/garch.stan	0.52	0.53	0.99	-1.46% slower
Mean result: 0.995752772649

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Jenkins Console Log
Blue Ocean
Commit hash: 496161e

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Machine information

ProductName: Mac OS X ProductVersion: 10.11.6 BuildVersion: 15G22010

CPU:
Intel(R) Xeon(R) CPU E5-1680 v2 @ 3.00GHz

G++:
Configured with: --prefix=/Applications/Xcode.app/Contents/Developer/usr --with-gxx-include-dir=/usr/include/c++/4.2.1
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

Clang:
Apple LLVM version 7.0.2 (clang-700.1.81)
Target: x86_64-apple-darwin15.6.0
Thread model: posix

[rok-cesnovar]

Looks good. Thanks for the test.