Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| A   | B                                             |                C |   D |                E |   F |   G |   H |           I |                J |           K |   L |   M |   N |   O |           P |                Q |                R |   S |   T |   U |   V |           W |
|:----|:----------------------------------------------|-----------------:|----:|-----------------:|----:|----:|----:|------------:|-----------------:|------------:|----:|----:|----:|----:|------------:|-----------------:|-----------------:|----:|----:|----:|----:|------------:|
| C0  | Alamance Community College                    |      2.14055e+06 |   0 | 994205           |   0 |   0 |   0 | 5.6902e+07  |      3.78491e+06 | 7.23854e+06 |   0 |   0 |   0 |   0 | 1.71194e+07 | 940221           |      2.84995e+06 |   0 |   0 |   0 |   0 | 5.01506e+07 |
| C1  | South Piedmont Community College              |      3.79255e+06 |   0 |      1.81779e+07 |   0 |   0 |   0 | 3.39265e+07 | 761329           | 5.56764e+06 |   0 |   0 |   0 |   0 | 1.27194e+07 | 529133           |      2.54084e+06 |   0 |   0 |   0 |   0 | 4.64366e+07 |
| C2  | Asheville-Buncombe Tech Community College     |      5.95821e+06 |   0 |      1.40108e+07 |   0 |   0 |   0 | 1.54995e+08 |      1.10075e+07 | 1.81265e+07 |   0 |   0 |   0 |   0 | 4.15211e+07 |      3.15968e+06 |      1.01286e+07 |   0 |   0 |   0 |   0 | 1.49289e+08 |
| C3  | Beaufort County Community College             | 573900           |   0 |      2.85207e+06 |   0 |   0 |   0 | 2.30503e+07 |      1.5843e+06  | 5.52368e+06 |   0 |   0 |   0 |   0 | 9.87664e+06 | 720014           |      2.9491e+06  |   0 |   0 |   0 |   0 | 2.00385e+07 |
| C4  | Bladen Community College                      |  78163.6         |   0 |      0           |   0 |   0 |   0 | 1.83517e+07 | 776215           | 2.25094e+06 |   0 |   0 |   0 |   0 | 5.44368e+06 | 413614           | 825249           |   0 |   0 |   0 |   0 | 1.47745e+07 |
| C6  | Brunswick Community College                   |      1.03696e+06 |   0 |  88420           |   0 |   0 |   0 | 5.21739e+07 |      5.29924e+06 | 4.38212e+06 |   0 |   0 |   0 |   0 | 1.54979e+07 |      1.24294e+06 |      1.93305e+06 |   0 |   0 |   0 |   0 | 4.43067e+07 |
| C7  | Caldwell Community College and Tech Institute |      7.36588e+06 |   0 |      5.25007e+06 |   0 |   0 |   0 | 4.54928e+07 |      2.12327e+06 | 1.15943e+07 |   0 |   0 |   0 |   0 | 1.9599e+07  | 953484           |      7.90335e+06 |   0 |   0 |   0 |   0 | 4.33704e+07 |
| C8  | Cape Fear Community College                   |      1.74699e+07 |   0 | 710887           |   0 |   0 |   0 | 2.64335e+08 |      1.00533e+07 | 1.96934e+07 |   0 |   0 |   0 |   0 | 5.31825e+07 |      4.52743e+06 |      9.14246e+06 |   0 |   0 |   0 |   0 | 2.4541e+08  |
| C9  | Carteret Community College                    |      4.38621e+06 |   0 |      5.03557e+06 |   0 |   0 |   0 | 2.4423e+07  |      1.71351e+06 | 4.19653e+06 |   0 |   0 |   0 |   0 | 8.44158e+06 | 598890           |      1.58192e+06 |   0 |   0 |   0 |   0 | 2.91325e+07 |
| CA  | Catawba Valley Community College              |      3.0446e+06  |   0 | 878991           |   0 |   0 |   0 | 7.2844e+07  |      8.5364e+06  | 1.33245e+07 |   0 |   0 |   0 |   0 | 1.81474e+07 |      1.25173e+06 |      5.00151e+06 |   0 |   0 |   0 |   0 | 7.42279e+07 |
| CB  | Central Carolina Community College            |      4.34687e+06 |   0 |  44250           |   0 |   0 |   0 | 7.75456e+07 |      2.03003e+06 | 9.78939e+06 |   0 |   0 |   0 |   0 | 2.35145e+07 | 421984           |      4.85059e+06 |   0 |   0 |   0 |   0 | 6.49691e+07 |
| CD  | Cleveland Community College                   |      1.04252e+06 |   0 | 916876           |   0 |   0 |   0 | 2.62961e+07 |      1.23455e+06 | 1.13716e+07 |   0 |   0 |   0 |   0 | 1.30812e+07 | 532167           |      5.24435e+06 |   0 |   0 |   0 |   0 | 2.20039e+07 |
| CE  | Coastal Carolina Community College            |      1.48196e+06 |   0 |      2.56697e+06 |   0 |   0 |   0 | 3.63496e+07 |      1.72903e+07 | 1.13789e+07 |   0 |   0 |   0 |   0 | 1.86473e+07 |      4.37942e+06 |      6.10908e+06 |   0 |   0 |   0 |   0 | 3.99319e+07 |
| CF  | College of the Albemarle                      |      1.83601e+06 |   0 |      0           |   0 |   0 |   0 | 4.24336e+07 |      1.02962e+06 | 5.69291e+06 |   0 |   0 |   0 |   0 | 1.52731e+07 | 413354           |      3.35535e+06 |   0 |   0 |   0 |   0 | 3.19504e+07 |
| CH  | Davidson County Community College             | 258694           |   0 | 306784           |   0 |   0 |   0 | 5.66331e+07 |      2.96689e+06 | 8.18262e+06 |   0 |   0 |   0 |   0 | 2.21527e+07 | 891888           |      4.2136e+06  |   0 |   0 |   0 |   0 | 4.10899e+07 |
| CJ  | Durham Technical Community College            |      2.77403e+06 |   0 |      1.06938e+07 |   0 |   0 |   0 | 5.3197e+07  |      2.17216e+06 | 4.47817e+06 |   0 |   0 |   0 |   0 | 1.78361e+07 | 554353           |      2.42591e+06 |   0 |   0 |   0 |   0 | 5.24988e+07 |
| CK  | Edgecombe Community College                   |      1.10982e+06 |   0 |      6.76225e+06 |   0 |   0 |   0 | 3.55134e+07 |      1.12082e+06 | 6.30338e+06 |   0 |   0 |   0 |   0 | 1.00153e+07 | 389382           |      3.20237e+06 |   0 |   0 |   0 |   0 | 3.72026e+07 |
| CL  | Fayetteville Technical Community College      |      8.72535e+06 |   0 | 866230           |   0 |   0 |   0 | 8.62046e+07 |      1.6196e+06  | 2.59823e+07 |   0 |   0 |   0 |   0 | 2.76379e+07 | 679191           |      8.53207e+06 |   0 |   0 |   0 |   0 | 8.65489e+07 |
| CM  | Forsyth Technical Community College           |      5.1658e+06  |   0 |      9.65608e+06 |   0 |   0 |   0 | 1.24829e+08 |      4.37379e+06 | 1.78239e+07 |   0 |   0 |   0 |   0 | 3.2242e+07  |      1.35731e+06 |      7.42209e+06 |   0 |   0 |   0 |   0 | 1.20827e+08 |
| CP  | Guilford Technical Community College          |      2.20875e+07 |   0 |      1.12452e+07 |   0 |   0 |   0 | 2.32599e+08 |      2.42531e+07 | 4.69574e+07 |   0 |   0 |   0 |   0 | 5.77323e+07 |      5.06707e+06 |      1.75723e+07 |   0 |   0 |   0 |   0 | 2.5677e+08  |
| CQ  | Halifax Community College                     | 194800           |   0 | 422530           |   0 |   0 |   0 | 1.82118e+07 | 592177           | 3.26204e+06 |   0 |   0 |   0 |   0 | 8.66698e+06 | 201910           |      2.15979e+06 |   0 |   0 |   0 |   0 | 1.16546e+07 |
| CR  | Haywood Community College                     |      5.23958e+06 |   0 | 343401           |   0 |   0 |   0 | 4.15058e+07 |      3.69735e+06 | 8.23797e+06 |   0 |   0 |   0 |   0 | 1.3775e+07  | 995763           |      5.76058e+06 |   0 |   0 |   0 |   0 | 3.84927e+07 |
| CT  | James Sprunt Community College                | 172764           |   0 |      2.03132e+06 |   0 |   0 |   0 | 1.36283e+07 |      2.37583e+06 | 2.0077e+06  |   0 |   0 |   0 |   0 | 6.1315e+06  | 602699           |      1.07531e+06 |   0 |   0 |   0 |   0 | 1.24064e+07 |
| CU  | Johnston Community College                    |      5.45622e+06 |   0 | 863569           |   0 |   0 |   0 | 6.57095e+07 |      7.92691e+06 | 1.11727e+07 |   0 |   0 |   0 |   0 | 1.88584e+07 |      2.25665e+06 |      7.88275e+06 |   0 |   0 |   0 |   0 | 6.2131e+07  |
| CV  | Lenoir Community College                      |      1.70053e+06 |   0 |   7126.38        |   0 |   0 |   0 | 3.42314e+07 |      4.47612e+06 | 1.22588e+07 |   0 |   0 |   0 |   0 | 1.49245e+07 |      1.58797e+06 |      4.7855e+06  |   0 |   0 |   0 |   0 | 3.1376e+07  |
| CW  | Martin Community College                      | 166280           |   0 |      2.44077e+06 |   0 |   0 |   0 | 6.77882e+06 |      3.95611e+06 | 2.80713e+06 |   0 |   0 |   0 |   0 | 4.59975e+06 |      1.20173e+06 |      1.40075e+06 |   0 |   0 |   0 |   0 | 8.94687e+06 |
| CX  | Mayland Community College                     | 838445           |   0 |      2.23138e+06 |   0 |   0 |   0 | 1.75332e+07 | 568312           | 4.91659e+06 |   0 |   0 |   0 |   0 | 4.72337e+06 | 287437           |      1.51221e+06 |   0 |   0 |   0 |   0 | 1.95649e+07 |
| CY  | McDowell Technical Community College          | 439873           |   0 |      2.95462e+06 |   0 |   0 |   0 | 1.12944e+07 | 653107           | 2.27414e+06 |   0 |   0 |   0 |   0 | 5.90191e+06 | 419597           | 817522           |   0 |   0 |   0 |   0 | 1.04772e+07 |
| CZ  | Mitchell Community College                    |      2.94715e+06 |   0 |      9.42921e+06 |   0 |   0 |   0 | 3.09479e+07 |      2.14797e+06 | 5.34259e+06 |   0 |   0 |   0 |   0 | 1.02489e+07 | 722799           |      2.34571e+06 |   0 |   0 |   0 |   0 | 3.74974e+07 |
| D1  | Nash Community College                        |      1.84594e+06 |   0 | 107990           |   0 |   0 |   0 | 3.91873e+07 |      3.24009e+06 | 9.78142e+06 |   0 |   0 |   0 |   0 | 1.37935e+07 |      1.86263e+06 |      4.17999e+06 |   0 |   0 |   0 |   0 | 3.43266e+07 |
| D3  | Piedmont Community College                    | 194856           |   0 |  58500           |   0 |   0 |   0 | 1.76393e+07 |      3.17572e+06 | 4.26e+06    |   0 |   0 |   0 |   0 | 7.98742e+06 | 994662           |      2.06724e+06 |   0 |   0 |   0 |   0 | 1.4279e+07  |
| D4  | Pitt Community College                        |      6.38444e+06 |   0 | 790165           |   0 |   0 |   0 | 9.45275e+07 |      3.48406e+06 | 1.48621e+07 |   0 |   0 |   0 |   0 | 1.93657e+07 | 825365           |      4.65726e+06 |   0 |   0 |   0 |   0 | 9.52e+07    |
| D7  | Roanoke-Chowan Community College              |  34805           |   0 | 177652           |   0 |   0 |   0 | 1.16947e+07 | 242311           | 1.87489e+06 |   0 |   0 |   0 |   0 | 7.37711e+06 | 240219           |      1.0812e+06  |   0 |   0 |   0 |   0 | 5.32585e+06 |
| D8  | Robeson Community College                     | 513738           |   0 |      2.20962e+06 |   0 |   0 |   0 | 2.62881e+07 |      6.60415e+06 | 1.00009e+07 |   0 |   0 |   0 |   0 | 1.20032e+07 |      2.25235e+06 |      6.47193e+06 |   0 |   0 |   0 |   0 | 2.48889e+07 |
| D9  | Rockingham Community College                  | 650164           |   0 | 705886           |   0 |   0 |   0 | 2.75889e+07 |      3.42665e+06 | 4.41045e+06 |   0 |   0 |   0 |   0 | 9.46368e+06 |   5543.89        |      2.55145e+06 |   0 |   0 |   0 |   0 | 2.47613e+07 |
| DA  | Rowan-Cabarrus Community College              |      3.07412e+06 |   0 |      1.1211e+07  |   0 |   0 |   0 | 9.01225e+07 |      2.34469e+06 | 1.37977e+07 |   0 |   0 |   0 |   0 | 1.57892e+07 | 651905           |      6.0057e+06  |   0 |   0 |   0 |   0 | 9.81032e+07 |
| DB  | Sampson Community College                     | 147037           |   0 | 148696           |   0 |   0 |   0 | 2.06294e+07 |      1.39116e+06 | 6.1244e+06  |   0 |   0 |   0 |   0 | 8.24812e+06 | 454601           |      3.00587e+06 |   0 |   0 |   0 |   0 | 1.67321e+07 |
| DC  | Sandhills Community College                   | 699243           |   0 |      1.47108e+06 |   0 |   0 |   0 | 7.21773e+07 |      2.07416e+06 | 6.30391e+06 |   0 |   0 |   0 |   0 | 2.3543e+07  | 974197           |      3.801e+06   |   0 |   0 |   0 |   0 | 5.44075e+07 |
| DD  | Southeastern Community College                | 981101           |   0 |      5.37997e+06 |   0 |   0 |   0 | 2.141e+07   | 960616           | 6.5613e+06  |   0 |   0 |   0 |   0 | 7.66172e+06 | 324144           |      2.65373e+06 |   0 |   0 |   0 |   0 | 2.46534e+07 |
| DE  | Southwestern Community College                |      2.62828e+06 |   0 |      1.1767e+07  |   0 |   0 |   0 | 3.58741e+07 |      4.02465e+06 | 7.79626e+06 |   0 |   0 |   0 |   0 | 1.32886e+07 |      1.67376e+06 |      5.05549e+06 |   0 |   0 |   0 |   0 | 4.20724e+07 |
| DF  | Stanly Community College                      | 705187           |   0 | 754915           |   0 |   0 |   0 | 2.05001e+07 |      1.94245e+06 | 6.00213e+06 |   0 |   0 |   0 |   0 | 8.34366e+06 |      1.22721e+06 |      2.37608e+06 |   0 |   0 |   0 |   0 | 1.79578e+07 |
| DG  | Surry Community College                       | 932655           |   0 | 615651           |   0 |   0 |   0 | 3.6862e+07  | 756173           | 6.06602e+06 |   0 |   0 |   0 |   0 | 1.44595e+07 | 508487           |      3.06963e+06 |   0 |   0 |   0 |   0 | 2.71949e+07 |
| DH  | Tri-County Community College                  | 501488           |   0 |      0           |   0 |   0 |   0 | 1.57138e+07 |      1.21004e+06 | 3.18284e+06 |   0 |   0 |   0 |   0 | 5.74178e+06 | 297216           |      2.09958e+06 |   0 |   0 |   0 |   0 | 1.24696e+07 |
| DJ  | Vance-Granville Community College             | 963221           |   0 |      2.49602e+06 |   0 |   0 |   0 | 3.61772e+07 |      2.33674e+06 | 7.87903e+06 |   0 |   0 |   0 |   0 | 1.54185e+07 | 936594           |      4.10791e+06 |   0 |   0 |   0 |   0 | 2.93892e+07 |
| DK  | Wake Technical Community College              |      2.33509e+07 |   0 |      6.4973e+07  |   0 |   0 |   0 | 4.02245e+08 |      3.4286e+07  | 2.48514e+07 |   0 |   0 |   0 |   0 | 7.30473e+07 |      4.39127e+06 |      6.87618e+06 |   0 |   0 |   0 |   0 | 4.65391e+08 |
| DL  | Wayne Community College                       |      1.65302e+06 |   0 |      7.16243e+06 |   0 |   0 |   0 | 3.77632e+07 |      1.99065e+06 | 1.17202e+07 |   0 |   0 |   0 |   0 | 1.86204e+07 | 392106           |      3.88535e+06 |   0 |   0 |   0 |   0 | 3.73917e+07 |
| DP  | Wilson Community College                      | 904015           |   0 |      0           |   0 |   0 |   0 | 1.64886e+07 | 947187           | 5.12063e+06 |   0 |   0 |   0 |   0 | 7.28353e+06 | 701823           |      2.61841e+06 |   0 |   0 |   0 |   0 | 1.28567e+07 |



labeled_formulas: F=C*D
G=C*D
H=C*D
L=C*D
M=C*D
N=C*D
O=C*D
S=C*D
T=C*D
U=C*D
V=C*D
L=C*F
S=C*F
L=C*G
S=C*G
L=C*H
S=C*H
M=C*L
N=C*L
O=C*L
S=C*L
T=C*L
U=C*L
V=C*L
S=C*M
S=C*N
S=C*O
T=C*S
U=C*S
V=C*S
F=D*E
G=D*E
H=D*E
L=D*E
M=D*E
N=D*E
O=D*E
S=D*E
T=D*E
U=D*E
V=D*E
F=D*I
F=D*J
F=D*K
F=D*P
F=D*Q
F=D*R
F=D*W
G=D*I
G=D*J
F=(C*D)*E
G=(C*D)*E
H=(C*D)*E
L=(C*D)*E
M=(C*D)*E
N=(C*D)*E
O=(C*D)*E
S=(C*D)*E
T=(C*D)*E
U=(C*D)*E
V=(C*D)*E
F=(C*D)*I
F=(C*D)*J
F=(C*D)*K
F=(C*D)*P
F=(C*D)*Q
F=(C*D)*R
F=(C*D)*W
G=(C*D)*I
G=(C*D)*J
G=(C*D)*K
G=(C*D)*P
G=(C*D)*Q
G=(C*D)*R
G=(C*D)*W
H=(C*D)*I
H=(C*D)*J
H=(C*D)*K
H=(C*D)*P
H=(C*D)*Q
H=(C*D)*R
H=(C*D)*W
L=(C*D)*I
M=(C*D)*I
N=(C*D)*I
O=(C*D)*I
S=(C*D)*I
T=(C*D)*I
U=(C*D)*I
V=(C*D)*I
L=(C*D)*J
M=(C*D)*J
N=(C*D)*J
O=(C*D)*J
S=(C*D)*J
T=(C*D)*J
U=(C*D)*J
V=(C*D)*J
L=(C*D)*K
M=(C*D)*K
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_132040___xlsx_2499b4060163ab547c434a4706be5fecfbdb3f8d.xlsx___line_129