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 |
|:----------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|
| Allbrook Close        |   0 |   0 |   0 |   5 |   4 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  12 |   0 |   0 |  12 |  33 |  12 |
| Boucher Close         |   0 |   0 |   0 |   9 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |  15 |   0 |   0 |   5 |  31 |  17 |
| Church Lane           |   0 |   0 |   0 |   9 |  26 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  29 |   0 |   0 |   0 |  64 |  29 |
| Clavering Close       |   0 |   0 |   0 |   3 |   6 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   7 |   0 |   0 |   3 |  21 |   9 |
| Clifton Road          |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  34 |   0 |   0 |   0 |  36 |  34 |
| Clive Road            |   0 |   0 |   1 |  16 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  50 |   0 |   0 |   0 |  68 |  51 |
| Clonmel Road          |   0 |   0 |   1 |  26 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |  94 |   0 |   0 |   0 | 127 |  95 |
| Downside              |   0 |   0 |   0 |   6 |   0 |   0 |   0 |   0 |   0 |   0 |   5 |   0 |   1 |   6 |   0 |   0 |   0 |  18 |  11 |
| Elmtree Road          |   0 |   0 |   0 |   4 |  32 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 |  48 |   0 |   0 |   0 |  86 |  48 |
| Fulwell Road          |   0 |   0 |   1 |   9 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   2 | 139 |   0 |   0 |   0 | 155 | 140 |
| Hawkesley Close       |   0 |   0 |   0 |   5 |   6 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  11 |   0 |   0 |   1 |  23 |  11 |
| Preston Close         |   0 |   0 |   0 |   7 |   0 |   0 |   0 |   0 |   0 |   0 |   4 |   0 |   0 |   8 |   0 |   0 |  11 |  30 |  12 |
| Railway Road          |   0 |   0 |   0 |  12 |   7 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  79 |   0 |   0 |  60 | 158 |  79 |
| Shacklegate Lane      |   0 |   0 |   0 |   7 |  80 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |  83 |   0 |   0 |   0 | 171 |  83 |
| Shaftesbury Way       |   0 |   0 |   0 |  46 |   4 |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |  42 |   0 |   0 |  17 | 111 |  44 |
| Somerset Gardens      |   0 |   0 |   0 |   4 |   0 |   0 |   0 |   0 |   0 |   0 |   9 |   0 |   0 |  26 |   0 |   0 |   0 |  39 |  35 |
| Somerset Road         |   0 |   0 |   1 |  10 |  10 |   6 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |  69 |   0 |   0 |   0 |  97 |  70 |
| Spencer Road          |   0 |   0 |   0 |  27 |   5 |   2 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |  74 |   0 |   0 |   3 | 112 |  74 |
| Strawberry Hill Close |   0 |   0 |   0 |   2 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  24 |   0 |   0 |  12 |  41 |  24 |
| Stuart Grove          |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  12 |   0 |   0 |  10 |  23 |  12 |
| Sutherland Grove      |   0 |   0 |   1 |  10 |   3 |   4 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |  55 |   0 |   0 |   2 |  77 |  56 |
| Sydney Road           |   0 |   0 |   0 |   3 |   1 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  32 |   0 |   0 |   0 |  36 |  32 |
| Vicarage Road         |   0 |   0 |   0 |   4 |   4 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  28 |   0 |   0 |   0 |  36 |  28 |
| Walpole Crescent      |   0 |   0 |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  31 |   0 |   0 |   0 |  33 |  31 |
| Walpole Gardens       |   0 |   0 |   0 |  14 |   6 |   1 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |  79 |   0 |   0 |   0 | 101 |  79 |
| Walpole Place         |   0 |   0 |   0 |   7 |   0 |   4 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |  14 |  26 |   1 |
| Walpole Road          |   0 |   0 |   0 |   5 |   2 |   2 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  69 |   0 |   0 |   2 |  80 |  69 |
| Wellesley Crescent    |   0 |   0 |   0 |   9 |   3 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  40 |   0 |   0 |  46 |  98 |  40 |
| Wellesley Road        |   0 |   0 |   0 |  29 |  21 |  14 |   0 |   0 |   0 |   2 |   0 |   0 |   0 | 114 |   0 |   0 |   2 | 182 | 114 |
| Winchendon Road       |   0 |   0 |   0 |   4 |   2 |   0 |   0 |   0 |   0 |   1 |   0 |   0 |   0 |  87 |   0 |   0 |   0 |  94 |  87 |
| York Road             |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |  89 |   0 |   0 |   2 |  91 |  89 |



labeled_formulas: C=B*D
C=B*E
C=B*F
C=B*G
H=B*C
C=B*I
J=B*C
C=B*K
C=B*N
C=B*O
Q=B*C
C=B*S
C=B*T
H=B*D
B=D*I
J=B*D
B=D*L
M=B*D
P=B*D
Q=B*D
H=B*E
J=B*E
M=B*E
Q=B*E
H=B*F
J=B*F
M=B*F
Q=B*F
H=B*G
B=G*I
J=B*G
B=G*L
M=B*G
P=B*G
Q=B*G
H=B*I
J=B*H
H=B*K
H=B*L
M=B*H
H=B*N
H=B*O
H=B*P
Q=B*H
H=B*R
H=B*S
H=B*T
J=B*I
B=I*K
I=B*L
C=(B*D)*E
C=(B*D)*F
C=(B*D)*G
H=(B*C)*D
C=(B*D)*J
C=(B*D)*K
C=(B*D)*N
C=(B*D)*O
C=(B*D)*Q
C=(B*D)*S
C=(B*D)*T
C=(B*E)*F
C=(B*E)*G
H=(B*C)*E
C=(B*E)*I
J=(B*C)*E
C=(B*E)*K
C=(B*E)*N
C=(B*E)*O
Q=(B*C)*E
C=(B*E)*S
C=(B*E)*T
C=(B*F)*G
H=(B*C)*F
C=(B*F)*I
J=(B*C)*F
C=(B*F)*K
C=(B*F)*N
C=(B*F)*O
Q=(B*C)*F
C=(B*F)*S
C=(B*F)*T
C=(B*G)*I
C=(B*G)*J
C=(B*G)*K
C=(B*G)*N
C=(B*G)*O
C=(B*G)*Q
C=(B*G)*S
C=(B*G)*T
H=(B*C)*J
H=(B*C)*K
H=(B*C)*O
H=(B*C)*Q
H=(B*C)*S
H=(B*C)*T
C=(B*I)*J
C=(B*I)*K
C=(B*I)*N
C=(B*I)*O
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_155724___xlsx_e769bd9c9d257a148990e5ac101b2b52fb326143.xlsx___line_754