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:
| B                  |   C |   D |   E |   F |   G |   H |   I |   J |   K |   L | M       | N       | O                  | P                  | Q                  | R                  | S                  | T                  | U       | V                  |
|:-------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|:--------|:--------|:-------------------|:-------------------|:-------------------|:-------------------|:-------------------|:-------------------|:--------|:-------------------|
| Alpine             |   0 |   0 |   0 |   3 |   0 |   3 |   5 |   3 |   9 |   3 | 0       | 0       | 0                  | 33.333333333333329 | 0                  | 33.333333333333329 | 55.555555555555557 | 33.333333333333329 | 100     | 33.333333333333329 |
| Ararat             |   0 |   0 |   0 |   0 |   0 |   4 |   6 |  10 |  25 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 16                 | 24                 | 40                 | 100     | 0                  |
| Ballarat           |   0 |   0 |   7 |  23 |  22 |  45 |  76 |  84 | 258 |  52 | 0       | 0       | 2.7131782945736433 | 8.9147286821705425 | 8.5271317829457356 | 17.441860465116278 | 29.457364341085274 | 32.558139534883722 | 100     | 20.155038759689923 |
| Banyule            |   0 |   0 |   0 |   5 |   5 |   7 |  17 |  27 |  66 |  10 | 0       | 0       | 0                  | 7.5757575757575761 | 7.5757575757575761 | 10.606060606060606 | 25.757575757575758 | 40.909090909090914 | 100     | 15.151515151515152 |
| Bass Coast         |   0 |   0 |   3 |   6 |   7 |  15 |  22 |  23 |  77 |  16 | 0       | 0       | 3.8961038961038961 | 7.7922077922077921 | 9.0909090909090917 | 19.480519480519483 | 28.571428571428569 | 29.870129870129869 | 100     | 20.779220779220779 |
| Bayside            |   0 |   0 |   0 |   0 |   0 |   3 |   4 |  14 |  27 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 11.111111111111111 | 14.814814814814813 | 51.851851851851848 | 100     | 0                  |
| Benalla            |   0 |   0 |   0 |   5 |   8 |  16 |  11 |  15 |  50 |  13 | 0       | 0       | 0                  | 10                 | 16                 | 32                 | 22                 | 30                 | 100     | 26                 |
| Boroondara         |   0 |   0 |   0 |   3 |   0 |   4 |  11 |  21 |  38 |   3 | 0       | 0       | 0                  | 7.8947368421052628 | 0                  | 10.526315789473683 | 28.947368421052634 | 55.26315789473685  | 100     | 7.8947368421052628 |
| Buloke             |   0 |   0 |   0 |   0 |   0 |   0 |  10 |   6 |  12 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 0                  | 83.333333333333343 | 50                 | 100     | 0                  |
| Campaspe           |   0 |   0 |   0 |   3 |   4 |  14 |  34 |  41 |  95 |   7 | 0       | 0       | 0                  | 3.1578947368421053 | 4.2105263157894735 | 14.736842105263156 | 35.789473684210527 | 43.15789473684211  | 100     | 7.3684210526315788 |
| Central Goldfields |   0 |   0 |   0 |   0 |   0 |  11 |  11 |  12 |  34 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 32.352941176470587 | 32.352941176470587 | 35.294117647058826 | 100     | 0                  |
| Colac-Otway        |   0 |   0 |   0 |   0 |   4 |  10 |  13 |  17 |  45 |   4 | 0       | 0       | 0                  | 0                  | 8.8888888888888893 | 22.222222222222221 | 28.888888888888886 | 37.777777777777779 | 100     | 8.8888888888888893 |
| Corangamite        |   0 |   0 |   0 |   0 |   3 |   3 |  13 |  20 |  37 |   3 | 0       | 0       | 0                  | 0                  | 8.1081081081081088 | 8.1081081081081088 | 35.135135135135137 | 54.054054054054056 | 100     | 8.1081081081081088 |
| Darebin            |   0 |   0 |   0 |   5 |  11 |  14 |  31 |  33 |  94 |  16 | 0       | 0       | 0                  | 5.3191489361702127 | 11.702127659574469 | 14.893617021276595 | 32.978723404255319 | 35.106382978723403 | 100     | 17.021276595744681 |
| East Gippsland     |   0 |   0 |   6 |   4 |   8 |  14 |  27 |  34 |  91 |  18 | 0       | 0       | 6.593406593406594  | 4.395604395604396  | 8.791208791208792  | 15.384615384615385 | 29.670329670329672 | 37.362637362637365 | 100     | 19.780219780219781 |
| Frankston          |   0 |   0 |   5 |  17 |  17 |  38 |  70 | 102 | 253 |  39 | 0       | 0       | 1.9762845849802373 | 6.7193675889328066 | 6.7193675889328066 | 15.019762845849801 | 27.66798418972332  | 40.316205533596836 | 100     | 15.41501976284585  |
| Gannawarra         |   0 |   0 |   0 |   0 |   5 |   6 |   5 |   8 |  23 |   5 | 0       | 0       | 0                  | 0                  | 21.739130434782609 | 26.086956521739129 | 21.739130434782609 | 34.782608695652172 | 100     | 21.739130434782609 |
| Glen Eira          |   0 |   0 |   0 |   0 |   0 |   4 |  17 |  10 |  35 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 11.428571428571429 | 48.571428571428569 | 28.571428571428569 | 100     | 0                  |
| Glenelg            |   0 |   0 |   0 |   0 |   4 |   3 |   9 |  18 |  45 |   4 | 0       | 0       | 0                  | 0                  | 8.8888888888888893 | 6.666666666666667  | 20                 | 40                 | 100     | 8.8888888888888893 |
| Golden Plains      |   0 |   0 |   0 |   0 |   0 |   7 |   7 |   0 |  14 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 50                 | 50                 | 0                  | 100     | 0                  |
| Greater Shepparton |   0 |   0 |   4 |   8 |  25 |  37 |  41 |  70 | 188 |  37 | 0       | 0       | 2.1276595744680851 | 4.2553191489361701 | 13.297872340425531 | 19.680851063829788 | 21.808510638297875 | 37.234042553191486 | 100     | 19.680851063829785 |
| Hepburn            |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   8 |  16 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 0                  | 0                  | 50                 | 100     | 0                  |
| Hindmarsh          |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 | #DIV/0! | #DIV/0! | #DIV/0!            | #DIV/0!            | #DIV/0!            | #DIV/0!            | #DIV/0!            | #DIV/0!            | #DIV/0! | #DIV/0!            |
| Hobsons Bay        |   0 |   0 |   6 |   3 |  12 |  15 |  12 |  34 |  74 |  21 | 0       | 0       | 8.1081081081081088 | 4.0540540540540544 | 16.216216216216218 | 20.27027027027027  | 16.216216216216218 | 45.945945945945951 | 100     | 28.378378378378379 |
| Horsham            |   0 |   0 |   0 |   4 |   5 |  12 |  14 |  27 |  64 |   9 | 0       | 0       | 0                  | 6.25               | 7.8125             | 18.75              | 21.875             | 42.1875            | 100     | 14.0625            |
| Hume               |   0 |   0 |   8 |  14 |  32 |  75 |  84 | 159 | 372 |  54 | 0       | 0       | 2.1505376344086025 | 3.763440860215054  | 8.6021505376344098 | 20.161290322580644 | 22.58064516129032  | 42.741935483870968 | 100     | 14.516129032258066 |
| Indigo             |   0 |   0 |   0 |   0 |   3 |   0 |   5 |   4 |  10 |   3 | 0       | 0       | 0                  | 0                  | 30                 | 0                  | 50                 | 40                 | 100     | 30                 |
| Kingston           |   0 |   0 |   0 |   4 |  12 |  11 |  16 |  33 |  75 |  16 | 0       | 0       | 0                  | 5.3333333333333339 | 16                 | 14.666666666666666 | 21.333333333333336 | 44                 | 100     | 21.333333333333336 |
| Loddon             |   0 |   0 |   0 |   0 |   0 |   4 |   6 |   3 |  15 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 26.666666666666668 | 40                 | 20                 | 100     | 0                  |
| Macedon Ranges     |   0 |   0 |   0 |   4 |   0 |   3 |   6 |  19 |  37 |   4 | 0       | 0       | 0                  | 10.810810810810811 | 0                  | 8.1081081081081088 | 16.216216216216218 | 51.351351351351347 | 100     | 10.810810810810811 |
| Manningham         |   0 |   0 |   0 |   0 |   3 |   3 |   5 |  12 |  30 |   3 | 0       | 0       | 0                  | 0                  | 10                 | 10                 | 16.666666666666664 | 40                 | 100     | 10                 |
| Mansfield          |   0 |   0 |   0 |   0 |   0 |   0 |   6 |   5 |  10 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 0                  | 60                 | 50                 | 100     | 0                  |
| Maribyrnong        |   0 |   0 |   0 |   4 |   3 |  15 |  17 |  16 |  54 |   7 | 0       | 0       | 0                  | 7.4074074074074066 | 5.5555555555555554 | 27.777777777777779 | 31.481481481481481 | 29.629629629629626 | 100     | 12.962962962962962 |
| Maroondah          |   0 |   0 |   0 |   3 |   9 |  11 |  23 |  29 |  86 |  12 | 0       | 0       | 0                  | 3.4883720930232558 | 10.465116279069768 | 12.790697674418606 | 26.744186046511626 | 33.720930232558139 | 100     | 13.953488372093023 |
| Melbourne          |   0 |   0 |   0 |   5 |   3 |   8 |  13 |  14 |  46 |   8 | 0       | 0       | 0                  | 10.869565217391305 | 6.5217391304347823 | 17.391304347826086 | 28.260869565217391 | 30.434782608695656 | 100     | 17.391304347826086 |
| Melton             |   0 |   0 |   9 |   4 |  17 |  45 |  64 | 111 | 255 |  30 | 0       | 0       | 3.5294117647058822 | 1.5686274509803921 | 6.666666666666667  | 17.647058823529413 | 25.098039215686274 | 43.529411764705884 | 100     | 11.764705882352942 |
| Mildura            |   0 |   0 |   4 |  13 |  18 |  18 |  38 |  50 | 142 |  35 | 0       | 0       | 2.8169014084507045 | 9.1549295774647899 | 12.676056338028168 | 12.676056338028168 | 26.760563380281688 | 35.2112676056338   | 100     | 24.647887323943664 |
| Mitchell           |   0 |   0 |   0 |   3 |   3 |  10 |  28 |  36 |  89 |   6 | 0       | 0       | 0                  | 3.3707865168539324 | 3.3707865168539324 | 11.235955056179774 | 31.460674157303369 | 40.449438202247187 | 100     | 6.7415730337078648 |
| Moira              |   0 |   0 |   0 |   4 |  14 |   8 |  27 |  31 |  85 |  18 | 0       | 0       | 0                  | 4.7058823529411766 | 16.470588235294116 | 9.4117647058823533 | 31.764705882352938 | 36.470588235294116 | 100     | 21.176470588235293 |
| Monash             |   0 |   0 |   0 |   5 |   5 |  16 |  15 |  18 |  60 |  10 | 0       | 0       | 0                  | 8.3333333333333321 | 8.3333333333333321 | 26.666666666666668 | 25                 | 30                 | 100     | 16.666666666666664 |
| Moonee Valley      |   0 |   0 |   0 |   5 |   0 |   6 |  15 |  17 |  43 |   5 | 0       | 0       | 0                  | 11.627906976744185 | 0                  | 13.953488372093023 | 34.883720930232556 | 39.534883720930232 | 100     | 11.627906976744185 |
| Moorabool          |   0 |   0 |   0 |   0 |   5 |   9 |  17 |   6 |  36 |   5 | 0       | 0       | 0                  | 0                  | 13.888888888888889 | 25                 | 47.222222222222221 | 16.666666666666664 | 100     | 13.888888888888889 |
| Moreland           |   0 |   0 |   3 |   3 |   7 |  20 |  42 |  50 | 125 |  13 | 0       | 0       | 2.4                | 2.4                | 5.6000000000000005 | 16                 | 33.6               | 40                 | 100     | 10.4               |
| Mount Alexander    |   0 |   0 |   0 |   3 |   0 |   4 |  12 |  10 |  24 |   3 | 0       | 0       | 0                  | 12.5               | 0                  | 16.666666666666664 | 50                 | 41.666666666666671 | 100     | 12.5               |
| Moyne              |   0 |   0 |   0 |   0 |   4 |   7 |   5 |  18 |  37 |   4 | 0       | 0       | 0                  | 0                  | 10.810810810810811 | 18.918918918918919 | 13.513513513513514 | 48.648648648648653 | 100     | 10.810810810810811 |
| Murrindindi        |   0 |   0 |   0 |   0 |   0 |   0 |   7 |   4 |  11 |   0 | 0       | 0       | 0                  | 0                  | 0                  | 0                  | 63.636363636363633 | 36.363636363636367 | 100     | 0                  |
| Nillumbik          |   0 |   0 |   0 |   0 |   4 |   6 |   0 |  10 |  14 |   4 | 0       | 0       | 0                  | 0                  | 28.571428571428569 | 42.857142857142854 | 0                  | 71.428571428571431 | 100     | 28.571428571428569 |
| Northern Grampians |   0 |   0 |   0 |   0 |   4 |   7 |   5 |  17 |  28 |   4 | 0       | 0       | 0                  | 0                  | 14.285714285714285 | 25                 | 17.857142857142858 | 60.714285714285708 | 100     | 14.285714285714285 |
| Port Phillip       |   0 |   0 |   0 |   7 |   7 |   7 |   9 |  11 |  39 |  14 | 0       | 0       | 0                  | 17.948717948717949 | 17.948717948717949 | 17.948717948717949 | 23.076923076923077 | 28.205128205128204 | 100     | 35.897435897435898 |



labeled_formulas: D=C*E
D=C*F
D=C*G
D=C*H
D=C*I
D=C*J
D=C*K
D=C*L
D=(E-F)*C
D=(C*E)*G
D=(C*E)*H
D=(C*E)*I
D=(C*E)*J
D=(C*E)*K
D=(C*E)*L
D=(C*F)*G
D=(C*F)*H
D=(C*F)*I
D=(C*F)*J
D=(C*F)*K
D=(C*F)*L
D=(C*G)*H
D=(C*G)*I
D=(C*G)*J
D=(C*G)*K
D=(C*G)*L
C=(H-I)*D
D=(C*H)*J
D=(C*H)*K
C=(H-L)*D
D=(C*I)*J
D=(C*I)*K
D=(C*I)*L
D=(C*J)*K
D=(C*J)*L
D=(C*K)*L
L=(E+F)+G
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_103458___xlsx_effcc50c4f48f7adfb806e328a81aa6fc41a0796.xlsx___line_463