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 |
|------:|----:|----------:|-------:|----:|----:|----:|-------:|------:|------:|----:|-------:|-------:|----:|-------:|-------:|---------:|----------:|-----------------:|----:|
| 36273 |   1 |   3.21256 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |   2 |   3.33312 |      0 |   0 |   0 |   0 |  53760 |     0 |  3328 |   0 |      0 |  57088 |   0 |    0   |      0 |  57088   |      0    | 190281           |   0 |
| 36273 |   4 |   2.75514 |      0 |   0 |   0 |   0 |  55472 | 61184 |    21 |   0 |      0 | 116677 |   0 | 6118.4 |      0 | 122795   |      0    | 338319           |   0 |
| 36273 |   5 |  10.3788  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |   6 |   3.14164 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |   8 |   3.36148 |      0 |   0 |   0 |   0 |  20096 |     0 |     0 |   0 |      0 |  20096 |   0 |    0   |      0 |  20096   |      0    |  67552.4         |   0 |
| 36273 |  10 |   5.54929 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  13 |   2.69486 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  15 |   6.84353 |      0 |   0 |   0 |   0 |      0 | 36192 |     0 |   0 |      0 |  36192 |   0 | 3619.2 |      0 |  39811.2 |      0    | 272449           |   0 |
| 36273 |  18 |   3.6026  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  20 |   3.43595 |      0 |   0 |   0 |   0 |    912 |     0 |     0 |   0 |      0 |    912 |   0 |    0   |      0 |    912   |      0    |   3133.58        |   0 |
| 36273 |  21 |   3.70898 |      0 |   0 |   0 |   0 |  23424 |     0 | 24394 |   0 |      0 |  47818 |   0 |    0   |      0 |  47818   |      0    | 177356           |   0 |
| 36273 |  22 |   3.09554 |      0 |   0 |   0 |   0 |  16160 |     0 |     0 |   0 |      0 |  16160 |   0 |    0   |      0 |  16160   |      0    |  50024           |   0 |
| 36273 |  23 |   3.34375 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  26 |   3.38985 |  34464 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |  34464 |      0 |   0 |    0   |  34464 |      0   | 116828    |      0           |   0 |
| 36273 |  27 |   0       |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  31 |  68.1829  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  32 | 120.417   |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  36 |  72.1702  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 36273 |  39 |  98.0877  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |   1 |   3.21256 |   1360 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |   1360 |      0 |   0 |    0   |   1360 |      0   |   4369.08 |      0           |   0 |
| 23582 |   2 |   3.33312 |      0 |   0 |   0 |   0 |      0 |     0 |    60 |   0 |      0 |     60 |   0 |    0   |      0 |     60   |      0    |    199.987       |   0 |
| 23582 |   5 |  10.3788  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |   6 |   3.14164 |      0 |   0 |   0 |   0 |      0 |     0 |    56 |   0 |      0 |     56 |   0 |    0   |      0 |     56   |      0    |    175.932       |   0 |
| 23582 |   8 |   3.36148 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  10 |   5.54929 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  13 |   2.69486 |   7440 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |   7440 |      0 |   0 |    0   |   7440 |      0   |  20049.8  |      0           |   0 |
| 23582 |  15 |   6.84353 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  17 |   4.96067 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  18 |   3.6026  |      0 |   0 |   0 |   0 | 279472 |     0 |     0 |   0 |      0 | 279472 |   0 |    0   |      0 | 279472   |      0    |      1.00683e+06 |   0 |
| 23582 |  20 |   3.43595 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  21 |   3.70898 |      0 |   0 |   0 |   0 |      0 |     0 |  1640 |   0 |      0 |   1640 |   0 |    0   |      0 |   1640   |      0    |   6082.73        |   0 |
| 23582 |  22 |   3.09554 |      0 |   0 |   0 |   0 |   1120 |     0 |     0 |   0 |      0 |   1120 |   0 |    0   |      0 |   1120   |      0    |   3467.01        |   0 |
| 23582 |  25 |   2.53884 | 148416 |   0 |   0 |   0 |      0 |     0 |     0 |   0 | 148416 |      0 |   0 |    0   | 148416 |      0   | 376805    |      0           |   0 |
| 23582 |  27 |   0       |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  31 |  68.1829  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  32 | 120.417   |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  36 |  72.1702  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23582 |  39 |  98.0877  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |   1 |   3.21256 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |   2 |   3.33312 |      0 |   0 |   0 |   0 |      0 |     0 | 11232 |   0 |      0 |  11232 |   0 |    0   |      0 |  11232   |      0    |  37437.6         |   0 |
| 23485 |   5 |  10.3788  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |   6 |   3.14164 |      0 |   0 |   0 |   0 |  12048 |     0 | 15808 |   0 |      0 |  27856 |   0 |    0   |      0 |  27856   |      0    |  87513.5         |   0 |
| 23485 |   8 |   3.36148 |      0 |   0 |   0 |   0 |      0 |     0 | 34080 |   0 |      0 |  34080 |   0 |    0   |      0 |  34080   |      0    | 114559           |   0 |
| 23485 |  10 |   5.54929 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  13 |   2.69486 |   3456 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |   3456 |      0 |   0 |    0   |   3456 |      0   |   9313.44 |      0           |   0 |
| 23485 |  14 |   4.53517 |      0 |   0 |   0 |   0 | 481744 |     0 |     0 |   0 |      0 | 481744 |   0 |    0   |      0 | 481744   |      0    |      2.18479e+06 |   0 |
| 23485 |  15 |   6.84353 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  17 |   4.96067 |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  18 |   3.6026  |      0 |   0 |   0 |   0 | 114736 |     0 |     0 |   0 |      0 | 114736 |   0 |    0   |      0 | 114736   |      0    | 413348           |   0 |
| 23485 |  20 |   3.43595 |      0 |   0 |   0 |   0 |  32848 |     0 |     0 |   0 |      0 |  32848 |   0 |    0   |      0 |  32848   |      0    | 112864           |   0 |
| 23485 |  21 |   3.70898 |      0 |   0 |   0 |   0 |      0 |     0 | 27472 |   0 |      0 |  27472 |   0 |    0   |      0 |  27472   |      0    | 101893           |   0 |
| 23485 |  22 |   3.09554 |      0 |   0 |   0 |   0 |    432 |     0 |  7440 |   0 |      0 |   7872 |   0 |    0   |      0 |   7872   |      0    |  24368.1         |   0 |
| 23485 |  23 |   3.34375 |  12672 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |  12672 |      0 |   0 |    0   |  12672 |      0   |  42372.1  |      0           |   0 |
| 23485 |  24 |   3.07781 |   5952 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |   5952 |      0 |   0 |    0   |   5952 |      0   |  18319.2  |      0           |   0 |
| 23485 |  25 |   2.53884 | 137856 |   0 |   0 |   0 |      0 |     0 |     0 |   0 | 137856 |      0 |   0 |    0   | 137856 |      0   | 349995    |      0           |   0 |
| 23485 |  27 |   0       |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  31 |  68.1829  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  32 | 120.417   |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  36 |  72.1702  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |
| 23485 |  39 |  98.0877  |      0 |   0 |   0 |   0 |      0 |     0 |     0 |   0 |      0 |      0 |   0 |    0   |      0 |      0   |      0    |      0           |   0 |



label: P=L+N
Q=M+O
R=C*P
S=C*Q
labeled_formulas: P=L+N
Q=M+O
R=C*P
S=C*Q
F=A*E
G=A*E
N=A*E
T=A*E
G=A*F
K=A*F
N=A*F
T=A*F
K=A*G
N=A*G
T=A*G
T=A*K
T=A*N
F=B*E
G=B*E
N=B*E
T=B*E
G=B*F
K=B*F
N=B*F
T=B*F
K=B*G
N=B*G
T=B*G
T=B*K
T=B*N
R=C*D
F=C*E
G=C*E
N=C*E
T=C*E
G=C*F
K=C*F
N=C*F
T=C*F
K=C*G
N=C*G
T=C*K
R=C*L
T=C*N
F=D*E
G=D*E
E=D*H
E=D*I
E=D*J
E=D*K
L=D+E
N=D*E
E=D*O
P=D+E
F=(A+B)*E
G=(A+B)*E
N=(A+B)*E
T=(A+B)*E
G=(A+B)*F
K=(A+B)*F
N=(A+B)*F
T=(A+B)*F
K=(A+B)*G
N=(A+B)*G
T=(A+B)*G
T=(A+B)*K
T=(A+B)*N
F=(A+C)*E
G=(A+C)*E
N=(A+C)*E
T=(A+C)*E
G=(A+C)*F
K=(A+C)*F
N=(A+C)*F
T=(A+C)*F
K=(A+C)*G
N=(A+C)*G
T=(A+C)*G
T=(A+C)*K
T=(A+C)*N
F=(A*D)*E
G=(A*D)*E
E=(A*D)*H
E=(A*D)*I
E=(A*D)*J
E=(A*D)*K
L=(A*E)+D
N=(A+D)*E
E=(A*D)*O
P=(A*E)+D
T=(A*D)*E
F=(A*D)*H
F=(A*D)*I
F=(A*D)*J
L=(A*F)+D
F=(A*D)*M
F=(A*D)*N
F=(A*D)*O
P=(A*F)+D
F=(A*D)*Q
F=(A*D)*S
T=(A+D)*F
G=(A*D)*H
G=(A*D)*I
output: {"Arithmetic-Relationship": ["P=L+N", "Q=M+O", "R=C*P", "S=C*Q"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_488135___xlsx_840bbae1a6d22e32de4ce779579259644270d00a.xlsx___line_375