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 |
|----:|----------:|----:|----------:|-----------:|----------:|----:|----------:|---------:|
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  0        |   0 | 10425.8   | 72.4017  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  0.787402 |  20 | 10425.8   | 72.4017  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  0.787402 |  20 | 10425.8   | 72.4017  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  1.5748   |  40 | 10425.8   | 72.4017  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  1.5748   |  40 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  2.55906  |  65 |  9437.88  | 65.5408  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  2.55906  |  65 | 10425.8   | 72.4017  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  3.34646  |  85 | 10425.8   | 72.4017  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  3.34646  |  85 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  4.33071  | 110 |  9437.88  | 65.5408  |
|  30 |   2       |   2 |   4       |  61.8124   |  4.33071  | 110 |  8444.37  | 58.6415  |
|  30 |   2       |   2 |   4       |  61.8124   |  5.51181  | 140 |  8444.37  | 58.6415  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  5.51181  | 140 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  6.49606  | 165 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  6.49606  | 165 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  7.48031  | 190 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  7.48031  | 190 |  9437.88  | 65.5408  |
|  25 |   1.66667 |   2 |   3.33333 |  75.8156   |  8.46457  | 215 |  9437.88  | 65.5408  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  8.46457  | 215 | 10425.8   | 72.4017  |
|  20 |   1.33333 |   2 |   2.66667 |  97.3415   |  9.25197  | 235 | 10425.8   | 72.4017  |
|  15 |   1       |   2 |   2       | 134.347    |  9.25197  | 235 | 10597     | 73.5906  |
|  15 |   1       |   2 |   2       | 134.347    |  9.84252  | 250 | 10597     | 73.5906  |
|  15 |   1.875   |   2 |   3.75    |  66.4458   |  9.84252  | 250 |  8803.72  | 61.1369  |
|  15 |   1.875   |   2 |   3.75    |  66.4458   | 10.4331   | 265 |  8803.72  | 61.1369  |
|  10 |   3.33333 |   2 |   6.66667 |  34.8823   | 10.4331   | 265 |  5756.46  | 39.9754  |
|  10 |   3.33333 |   2 |   6.66667 |  34.8823   | 10.8268   | 275 |  5756.46  | 39.9754  |
|  15 |   5       |   2 |  10       |  22.1505   | 10.8268   | 275 |  4129.63  | 28.678   |
|  15 |   5       |   2 |  10       |  22.1505   | 11.4173   | 290 |  4129.63  | 28.678   |
|  10 |  10       |   2 |  20       |  10.1913   | 11.4173   | 290 |  2393.33  | 16.6204  |
|  10 |  10       |   2 |  20       |  10.1913   | 11.811    | 300 |  2393.33  | 16.6204  |
|  10 |  10       |   2 |  20       |  10.1913   | 11.811    | 300 |  2393.33  | 16.6204  |
|  10 |  10       |   2 |  20       |  10.1913   | 12.2047   | 310 |  2393.33  | 16.6204  |
| 120 | 120       |   2 | 240       |   0.630298 | 12.2047   | 310 |   860.134 |  5.97315 |
| 120 | 120       |   2 | 240       |   0.630298 | 16.9291   | 430 |   860.134 |  5.97315 |
|  55 |  55       |   2 | 110       |   1.51016  | 16.9291   | 430 |  1006.61  |  6.99037 |
|  55 |  55       |   2 | 110       |   1.51016  | 19.0945   | 485 |  1006.61  |  6.99037 |
|  40 |  40       |   2 |  80       |   2.15736  | 19.0945   | 485 |  1113.66  |  7.73377 |
|  40 |  40       |   2 |  80       |   2.15736  | 20.6693   | 525 |  1113.66  |  7.73377 |
|  30 |  30       |   2 |  60       |   2.97751  | 20.6693   | 525 |  1248.47  |  8.66994 |
|  30 |  30       |   2 |  60       |   2.97751  | 21.8504   | 555 |  1248.47  |  8.66994 |
|  25 |  25       |   2 |  50       |   3.65205  | 21.8504   | 555 |  1358.63  |  9.43495 |
|  25 |  25       |   2 |  50       |   3.65205  | 22.8346   | 580 |  1358.63  |  9.43495 |
|  40 |  20       |   2 |  40       |   4.68895  | 22.8346   | 580 |  1526.72  | 10.6023  |
|  40 |  20       |   2 |  40       |   4.68895  | 24.4094   | 620 |  1526.72  | 10.6023  |
|  35 |  17.5     |   2 |  35       |   5.44536  | 24.4094   | 620 |  1648.39  | 11.4471  |
|  35 |  17.5     |   2 |  35       |   5.44536  | 25.7874   | 655 |  1648.39  | 11.4471  |
|  35 |  17.5     |   2 |  35       |   5.44536  | 25.7874   | 655 |  1648.39  | 11.4471  |
|  35 |  17.5     |   2 |  35       |   5.44536  | 27.1654   | 690 |  1648.39  | 11.4471  |
|  30 |  15       |   2 |  30       |   6.47153  | 27.1654   | 690 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 28.3465   | 720 |  1812.15  | 12.5844  |
|  40 |  20       |   2 |  40       |   4.68895  | 28.3465   | 720 |  1526.72  | 10.6023  |
|  40 |  20       |   2 |  40       |   4.68895  | 29.9213   | 760 |  1526.72  | 10.6023  |
|  30 |  15       |   2 |  30       |   6.47153  | 29.9213   | 760 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 31.1024   | 790 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 31.1024   | 790 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |
|  30 |  15       |   2 |  30       |   6.47153  | 32.2835   | 820 |  1812.15  | 12.5844  |



label: D=B*C
labeled_formulas: D=B*C
output: {"Arithmetic-Relationship": ["D=B*C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_379481___xlsx_640717ff4abc6adf2df941f14bf7cae9b6885c05.xlsx___line_269