SymReg
General purpose
Let give some symbols like x1 and x2.
The algorithm will consider first the linear combinations a*x1+b and c*x2+d, then extra start symbolic expressions defined with extraExpressions.
Set verbose to true to get some information during regression.
Then the first iteration starts:
- We apply the unary operators defined with
un_ops, for examplee*log(a*x1+b)+fandg*log(c*x2+d)+h. - We apply then the binary operators defined with
bin_ops, for examplei*(a*x1+b+c*x2+d)+jsame ask*x1+l*x2+m, etc. We can skip some combinations according to symmetric binary operators.
We can define the depth of operators with operatorDepth.
At each combination, we compute an optimal expression. If paramValues is empty, we search optimal parameters with ceres, else we use a discrete optimizer.
If discreteParams is true, parameters will be rounded to admissible values after ceres optimization.
We process like that until the computed loss is less than epsLoss.
eps is used to round numeric values and compare with other expressions for example.
It is possible to call user callback during process with callback.
Installation
Linux
sudo apt update
sudo apt install -y cmake make git libcurl4-openssl-dev libboost-dev libqt6charts6-dev libmlpack-dev libensmallen-dev libarmadillo-dev libstb-dev pybind11-dev graphviz libgraphviz-dev libqt6svg6-dev build-essential python3-sympy
sudo apt install -y libgoogle-glog-dev libeigen3-dev libsuitesparse-dev
cd ~
mkdir symreg_ws
cd symreg_ws
git clone https://github.com/Julien-Livet/SymReg.git
git clone --recursive https://ceres-solver.googlesource.com/ceres-solver
cd ceres-solver
mkdir build
cd build
cmake .. -DBUILD_TESTING=OFF
make -j$(nproc)
sudo make install
cd ../../SymReg
mkdir build
cd build
cmake ..
make -j$(nproc)
sudo make install
./benchmark 0
./primes_demo
ctest -V
time ./test_symreg --gtest_filter=TestSymReg.Line
cd ..
pip install --break-system-packages -e .
Windows with MSYS2 UCRT64
In MSYS2 UCRT64 prompt:
pacman -Syu
pacman -Sy git
pacman -Sy mingw-w64-ucrt-x86_64-cmake
pacman -Sy mingw-w64-ucrt-x86_64-ninja
pacman -Sy mingw-w64-ucrt-x86_64-toolchain base-devel
pacman -Sy mingw-w64-ucrt-x86_64-gcc mingw-w64-ucrt-x86_64-gdb
pacman -Sy mingw-w64-ucrt-x86_64-boost
pacman -Sy mingw-w64-ucrt-x86_64-qt6
pacman -Sy mingw-w64-ucrt-x86_64-armadillo
pacman -Sy mingw-w64-ucrt-x86_64-ensmallen
pacman -Sy mingw-w64-ucrt-x86_64-python
pacman -Sy mingw-w64-ucrt-x86_64-pybind11
pacman -Sy mingw-w64-ucrt-x86_64-graphviz
pacman -Sy mingw-w64-ucrt-x86_64-mlpack
pacman -Sy mingw-w64-ucrt-x86_64-eigen3
pacman -Sy mingw-w64-ucrt-x86_64-ceres-solver
pacman -Sy mingw-w64-ucrt-x86_64-blas
pacman -Sy mingw-w64-ucrt-x86_64-lapack
pacman -Sy mingw-w64-ucrt-x86_64-suitesparse
pacman -Sy mingw-w64-ucrt-x86_64-python-pip
pacman -Sy mingw-w64-ucrt-x86_64-python-pytest
pacman -Sy mingw-w64-ucrt-x86_64-python-numpy
cd ~
mkdir symreg_ws
cd symreg_ws
git clone https://github.com/DrTimothyAldenDavis/SuiteSparse.git
cd SuiteSparse
mkdir build
cd build
cmake -DCMAKE_INSTALL_PREFIX=/ucrt64 -DBLAS_LIBRARIES=/ucrt64/lib/libblas.dll.a -DLAPACK_LIBRARIES=/ucrt64/lib/liblapack.dll.a ..
ninja -j$(nproc)
ninja install
cd ../..
git clone https://github.com/mlpack/mlpack.git
cd mlpack
mkdir build
cd build
cmake -DCMAKE_INSTALL_PREFIX=/ucrt64 ..
ninja -j$(nproc)
ninja install
cd ../..
git clone https://github.com/Julien-Livet/SymReg.git
git clone https://github.com/Julien-Livet/Sym.git
cd Sym
mkdir build
cd build
cmake -DCMAKE_INSTALL_PREFIX=/ucrt64 ..
ninja -j$(nproc)
ninja install
cd ../../SymReg
mkdir build
cd build
cmake -DCMAKE_INSTALL_PREFIX=/ucrt64 -DBLAS_LIBRARIES=/ucrt64/lib/libblas.dll.a -DLAPACK_LIBRARIES=/ucrt64/lib/liblapack.dll.a -DPython3_EXECUTABLE=/ucrt64/bin/python -DPython3_LIBRARY=/ucrt64/lib/libpython3.12.dll.a -DPython3_INCLUDE_DIR=/ucrt64/include/python3.12 ..
ninja -j$(nproc)
ninja install
cd ..
mkdir symreg
cp build/*pyd symreg
pip install --break-system-packages -e .
cd scripts
pytest -s test_symreg.py
Copy following DLL files from MSYS2 UCRT64 bin folder to launch executables from Windows Explorer: libarmadillo.dll libopenblas.dll libblas.dll libceres-4.dll libcurl-4.dll libgcc_s_seh-1.dll libglog-2.dll libgvc-6.dll libstdc++-6.dll libwinpthread-1.dll Qt6Charts.dll Qt6Core.dll Qt6Gui.dll Qt6OpenGL.dll Qt6Svg.dll Qt6Widgets.dll zlib1.dll
In CMD prompt:
D:
cd D:\Programmes\msys64\home\Julien\symreg_ws\SymReg\build
benchmark.exe 0
primes_demo.exe
ctest -V
test_symreg.exe --gtest_filter=TestSymReg.Line
Benchmark with 0% of noise
| Test name | MSE | Expression time | Test time | Input symbolic expression | Found symbolic expression |
|---|---|---|---|---|---|
| 5x1Add7x2Addx3Add8 | 8.38789e-14 | 4ms | 5ms | 5.2*x1+7.3*x2+x3+8.6 |
5.2*x1 + 7.3*x2 + x3 + 8.6 |
| LinearFit | 3.44176e-16 | 0ms | 0ms | 2*x+3 |
2.0*x + 3.0 |
| LogFit | 0 | 1ms | 1ms | 2*log(3*x+4)+5 |
2.0*log(3.0*x + 4.0) + 5.0 |
| Test1 | 4.03717e-15 | 0ms | 0ms | x**2+x+1 |
x + x**2.0 + 1.0 |
| Test2 | 4.1359e-24 | 19ms | 19ms | exp(x)*sin(x) |
exp(x)*sin(x) |
| Test3 | 2.15704e-32 | 2ms | 2ms | x / (1 + x**2) |
x/(x**2.0 + 1.0)**1.0 |
| Test4 | 7.25338e-22 | 2ms | 4ms | x**2+y**2 |
x**2.0 + y**2.0 |
| Test5 | 3.35266e-30 | 21ms | 23ms | log(x)+sin(x) |
log(x) + sin(x) |
| Test6 | 4.84764e-32 | 991ms | 992ms | exp(-0.5*x**2)/sqrt(2*pi) |
0.4*exp(-0.5*x**2.0) |
| PySR | 1.21677e-22 | 1196ms | 1438ms | 2.5382*cos(x3)+x0**2-0.5 |
x0**2.0 + 2.5*cos(x3) - 0.5 |
| GPLearn | 1.02851e-21 | 3ms | 6ms | x0**2-x1**2+x1-1 |
x0**2.0 + x1 - 1.0*x1**2.0 - 1.0 |
| x1Mulx2 | 1.1832e-15 | 0ms | 0ms | x1*x2 |
x1*x2 |
| Nguyen1 | 3.28779e-20 | 1ms | 2ms | x+x**2+x**3 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 |
| Nguyen2 | 4.19683e-20 | 0ms | 1ms | x+x**2+x**3+x**4 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 |
| Nguyen3 | 2.4968e-20 | 24ms | 50ms | x+x**2+x**3+x**4+x**5 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 + 1.0*x**5.0 |
| Nguyen4 | 1.24337e-22 | 92ms | 115ms | x+x**2+x**3+x**4+x**5+x**6 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 + 1.0*x**5.0 + 1.0*x**6.0 |
| Nguyen5 | 1.97215e-31 | 891ms | 898ms | sin(x**2)*cos(x)-1 |
sin(x**2.0)*cos(x) - 1.0 |
| Nguyen6 | 1.10934e-31 | 56ms | 60ms | sin(x)+sin(x+x**2) |
sin(x) + sin(x + x**2.0) |
| Nguyen7 | 1.50377e-30 | 246ms | 250ms | log(x+1)+log(x**2+1) |
log(x + 1.0) + log(x**2.0 + 1.0) |
| Nguyen8 | 0 | 0ms | 0ms | sqrt(x) |
x**0.5 |
| Nguyen9 | 0 | 255ms | 267ms | sin(x1)+sin(x2**2) |
sin(x1) + sin(x2**2.0) |
| Nguyen10 | 0 | 9ms | 11ms | 2*sin(x1)*cos(x2) |
2.0*sin(x1)*cos(x2) |
| Keijzer10 | 0 | 2ms | 3ms | x1**x2 |
x1**x2 |
| d_bacres1 | 8.92493e-20 | 0ms | 541ms | 20-x-(x*y/(1+0.5*x**2)) |
-1.7*x*y/(0.8*x**2.0 + 1.7)**1.0 - 1.0*x + 20.0 |
| d_bacres2 | 4.34292e-21 | 639ms | 1059ms | 10-(x*y/(1+0.5*x**2)) |
10.0 - 298.6/(208.0*x**2.0/(x*y)**1.0 + 416.0/(x*y)**1.0)**1.0 |
| d_barmag1 | 1.42591e-27 | 4031ms | 4409ms | 0.5*sin(x-y)-sin(x) |
-1.0*sin(x) + 0.5*sin(x - 1.0*y) |
| d_barmag2 | 7.61955e-28 | 4441ms | 4805ms | 0.5*sin(y-x)-sin(y) |
-1.0*sin(y) - 0.5*sin(x - 1.0*y) |
| d_glider1 | 1.07305e-25 | 16170ms | 16475ms | -0.05*x**2-sin(y) |
-1.0*sin(y) |
| d_glider2 | 1.5599e-15 | 11ms | 347ms | x-cy/x |
(-1.0*cy + x**2.0)/x**1.0 |
| d_lv1 | 7.55206e-27 | 10ms | 269ms | 3*x-2*x*y-x**2 |
-2.0*x*y + 3.0*x - 1.0*x**2.0 |
| d_lv2 | 8.13647e-27 | 48ms | 364ms | 2*y-x*y-y**2 |
-1.0*x*y + 2.0*y - 1.0*y**2.0 |
| d_shearflow1 | 4.12295e-27 | 21ms | 296ms | cos(x)*cot(y) |
cos(x)*cot(y) |
| d_shearflow2 | 6.10506e-19 | 359ms | 844ms | (cy**2+0.1*sy**2)*sx |
sx*(1.0*cy**2.0 + 0.1*sy**2.0) |
| d_vdp1 | 2.31375e-13 | 58ms | 335ms | 10*(y-(1/3*(x**3-x))) |
3.3*x - 3.3*x**3.0 + 10.0*y |
| d_vdp2 | 4.09897e-25 | 0ms | 637ms | -0.1*x |
-0.1*x |
Benchmark with 0.1% of noise
| Test name | MSE | Expression time | Test time | Input symbolic expression | Found symbolic expression |
|---|---|---|---|---|---|
| 5x1Add7x2Addx3Add8 | 0.00378479 | 20ms | 50ms | 5.2*x1+7.3*x2+x3+8.6 |
5.2*x1 + 7.3*x2 + 1.0*x3 + 8.6 |
| LinearFit | 1.14303e-05 | 0ms | 0ms | 2*x+3 |
2.0*x + 3.0 |
| LogFit | 0.0022121 | 17ms | 18ms | 2*log(3*x+4)+5 |
2.0*log(3.0*x + 4.0) + 5.0 |
| Test1 | 0.0644484 | 14ms | 15ms | x**2+x+1 |
1.0*x + 1.0*x**2.0 + 1.0 |
| Test2 | 82.7865 | 196ms | 1868ms | exp(x)*sin(x) |
exp(x)*sin(x) - 0.1 |
| Test3 | 1.70665e-06 | 15ms | 2191ms | x / (1 + x**2) |
x/(x**2.0 + 1.0)**1.0 |
| Test4 | 1.25972e-05 | 265ms | 505ms | x**2+y**2 |
1.0*x**2.0 + 1.0*y**2.0 |
| Test5 | 0.000162595 | 712ms | 2398ms | log(x)+sin(x) |
log(x) + sin(x) |
| Test6 | 4.90219e-07 | 5504ms | 13467ms | exp(-0.5*x**2)/sqrt(2*pi) |
0.4*exp(-0.5*x**2.0) |
| PySR | 0.000143323 | 1588ms | 6972ms | 2.5382*cos(x3)+x0**2-0.5 |
1.0*x0**2.0 + 2.5*cos(1.0*x3) - 0.4 |
| GPLearn | 4.26414e-05 | 284ms | 507ms | x0**2-x1**2+x1-1 |
1.0*x0**2.0 + 1.0*x1 - 1.0*x1**2.0 - 1.0 |
| x1Mulx2 | 2.45325e-06 | 0ms | 0ms | x1*x2 |
1.0*x1*x2 |
| Nguyen1 | 2.62823e-05 | 802ms | 908ms | x+x**2+x**3 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 |
| Nguyen2 | 3.18715e-05 | 652ms | 885ms | x+x**2+x**3+x**4 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 |
| Nguyen3 | 6.71155e-05 | 935ms | 1042ms | x+x**2+x**3+x**4+x**5 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 + 1.0*x**5.0 |
| Nguyen4 | 4.23057e-05 | 866ms | 977ms | x+x**2+x**3+x**4+x**5+x**6 |
1.0*x + 1.0*x**2.0 + 1.0*x**3.0 + 1.0*x**4.0 + 1.0*x**5.0 + 1.1*x**6.0 + 0.1*x**7.0 - 0.1*x**9.0 |
| Nguyen5 | 2.08185e-05 | 1500ms | 1531ms | sin(x**2)*cos(x)-1 |
sin(x**2.0)*cos(x) - 1.0 |
| Nguyen6 | 4.39748e-05 | 219ms | 227ms | sin(x)+sin(x+x**2) |
sin(x) + sin(x + x**2.0) |
| Nguyen7 | 7.69403e-05 | 401ms | 1115ms | log(x+1)+log(x**2+1) |
log(x + 1.0) + log(x**2.0 + 1.0) |
| Nguyen8 | 3.76766e-05 | 0ms | 1ms | sqrt(x) |
x**0.5 |
| Nguyen9 | 1.51535e-05 | 339ms | 619ms | sin(x1)+sin(x2**2) |
sin(x1) + sin(x2**2.0) |
| Nguyen10 | 2.14083e-05 | 36ms | 767ms | 2*sin(x1)*cos(x2) |
2.0*sin(x1)*cos(x2) |
| Keijzer10 | 3.67798e-05 | 6ms | 15438ms | x1**x2 |
x1**x2 |
| d_bacres1 | 0.0155473 | 430ms | 1293ms | 20-x-(x*y/(1+0.5*x**2)) |
-1.1*x*y/(0.5*x**2.0 - 0.1/(10.0 - 0.7*x)**1.0 + 0.9)**1.0 - 1.02*x + 0.5/(0.5*x**2.0 - 0.1/(10.0 - 0.7*x)**1.0 + 0.9)**1.0 + 20.6 |
| d_bacres2 | 0.0127714 | 197ms | 541ms | 10-(x*y/(1+0.5*x**2)) |
-0.6*y/(0.3*x + 0.1)**1.0 + 0.1*y/(-3.5*x + 1.6*x**2.0 + 1.9)**1.0 - 0.3/(0.3*x + 0.1)**1.0 + 5.9/(-3.5*x + 1.6*x**2.0 + 1.9)**1.0 + 10.0 |
| d_barmag1 | 0.00167878 | 10299ms | 40760ms | 0.5*sin(x-y)-sin(x) |
-1.0*sin(x) + 0.5*sin(x - 1.0*y) |
| d_barmag2 | 0.000946167 | 29806ms | 77585ms | 0.5*sin(y-x)-sin(y) |
-1.0*sin(y) - 0.5*sin(x - 1.0*y) |
| d_glider1 | 0.0164986 | 18617ms | 19017ms | -0.05*x**2-sin(y) |
-1.0*sin(y) |
| d_glider2 | 0.0154252 | 42ms | 336ms | x-cy/x |
1.0*(-cy + x**2.0)/x**1.0 |
| d_lv1 | 0.00831714 | 7196ms | 7750ms | 3*x-2*x*y-x**2 |
-2.0*x*y + 3.0*x - 1.0*x**2.0 |
| d_lv2 | 0.00166309 | 4129ms | 4496ms | 2*y-x*y-y**2 |
-1.0*x*y + 2.0*y - 1.0*y**2.0 |
| d_shearflow1 | 0.000936923 | 118ms | 61044ms | cos(x)*cot(y) |
cos(x)*cot(y) |
| d_shearflow2 | 1.62147 | 9ms | 325ms | (cy**2+0.1*sy**2)*sx |
1.1*cy**2.0*sx |
| d_vdp1 | 0.0325666 | 37ms | 389ms | 10*(y-(1/3*(x**3-x))) |
3.3*x - 3.3*x**3.0 + 10.0*y |
| d_vdp2 | 2.84792e-06 | 98ms | 414ms | -0.1*x |
-0.1*x |
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Release files for symregpy 0.1.0
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