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 |
|:-------|------:|----:|--------:|------:|-------:|-------:|-------:|-------:|-------:|-------:|------:|------:|------:|
| DF1705 | 0.005 | 690 |   3.45  | 40763 |   6.56 |   8.74 |  18.6  |  14.88 |  14    |  11.2  |  19   | 0.357 |  15.2 |
| DF1001 | 0.01  | 690 |   6.9   | 40763 |  10.37 |  13.82 |  29.4  |  23.52 |  21.5  |  17.2  |  29.5 | 0.372 |  23.6 |
| DF1715 | 0.015 | 690 |  10.35  | 40763 |  14.18 |  18.9  |  40.21 |  32.17 |  29    |  23.2  |  40.5 | 0.397 |  32.4 |
| DF1002 | 0.02  | 690 |  13.8   | 40763 |  17.99 |  23.98 |  51.02 |  40.82 |  36    |  28.8  |  51   | 0.417 |  40.8 |
| DF1003 | 0.03  | 690 |  20.7   | 40763 |  25.61 |  34.14 |  72.64 |  58.11 |  54    |  43.2  |  73   | 0.352 |  58.4 |
| DF1004 | 0.04  | 690 |  27.6   | 40763 |  33.22 |  44.28 |  94.21 |  75.37 |  69.5  |  55.6  |  94.5 | 0.36  |  75.6 |
| DF1005 | 0.05  | 690 |  34.5   | 40763 |  40.84 |  54.44 | 115.83 |  92.66 |  85    |  68    | 116   | 0.365 |  92.8 |
| DF1006 | 0.06  | 690 |  41.4   | 40763 |  48.46 |  64.6  | 137.45 | 109.96 | 100    |  80    | 137.5 | 0.375 | 110   |
| DF1007 | 0.07  | 690 |  48.3   | 40763 |  56.08 |  74.75 | 159.04 | 127.23 | 116.5  |  93.2  | 159   | 0.365 | 127.2 |
| DF1008 | 0.08  | 735 |  58.8   | 40763 |  67.67 |  90.2  | 191.91 | 153.53 | 176    | 140.8  | 192   | 0.091 | 153.6 |
| DF1009 | 0.09  | 735 |  66.15  | 40763 |  75.78 | 101.01 | 214.91 | 171.93 | 198    | 158.4  | 215   | 0.086 | 172   |
| DF1010 | 0.1   | 735 |  73.5   | 40763 |  83.9  | 111.84 | 237.96 | 190.37 | 219    | 175.2  | 238   | 0.087 | 190.4 |
| DF1012 | 0.12  | 735 |  88.2   | 40763 | 100.13 | 133.47 | 283.98 | 227.18 | 261    | 208.8  | 284   | 0.088 | 227.2 |
| DF1015 | 0.15  | 800 | 120     | 40763 | 135.23 | 180.26 | 383.53 | 306.82 | 324    | 259.2  | 385   | 0.188 | 308   |
| DF1020 | 0.2   | 875 | 175     | 40763 | 195.95 | 261.2  | 555.74 | 444.59 | 540    | 432    | 560   | 0.037 | 448   |
| DF1025 | 0.25  | 975 | 243.75  | 40763 | 271.85 | 362.38 | 771.02 | 616.82 | 910    | 728    | 910   | 0     | 728   |
| DF2705 | 0.005 | 600 |   3     | 40763 |   6.07 |   8.09 |  17.21 |  13.77 |  13    |  10.4  |  17.5 | 0.346 |  14   |
| DF2001 | 0.01  | 600 |   6     | 40763 |   9.38 |  12.5  |  26.6  |  21.28 |  19    |  15.2  |  27   | 0.421 |  21.6 |
| DF2715 | 0.015 | 600 |   9     | 40763 |  12.69 |  16.92 |  36    |  28.8  |  25.5  |  20.4  |  36   | 0.412 |  28.8 |
| DF2002 | 0.02  | 600 |  12     | 40763 |  16    |  21.33 |  45.38 |  36.3  |  31.5  |  25.2  |  45.5 | 0.444 |  36.4 |
| DF2003 | 0.03  | 600 |  18     | 40763 |  22.63 |  30.17 |  64.19 |  51.35 |  49    |  39.2  |  64.5 | 0.316 |  51.6 |
| DF2004 | 0.04  | 600 |  24     | 40763 |  29.25 |  38.99 |  82.96 |  66.37 |  63.5  |  50.8  |  83   | 0.307 |  66.4 |
| DF2005 | 0.05  | 600 |  30     | 40763 |  35.87 |  47.81 | 101.72 |  81.38 |  77.5  |  62    | 102   | 0.316 |  81.6 |
| DF2006 | 0.06  | 600 |  36     | 40763 |  42.5  |  56.65 | 120.53 |  96.42 |  91.5  |  73.2  | 120.5 | 0.317 |  96.4 |
| DF2007 | 0.07  | 600 |  42     | 40763 |  49.12 |  65.48 | 139.32 | 111.46 | 105.5  |  84.4  | 140   | 0.327 | 112   |
| DF2008 | 0.08  | 645 |  51.6   | 40763 |  59.72 |  79.61 | 169.38 | 135.5  | 139    | 111.2  | 170   | 0.223 | 136   |
| DF2009 | 0.09  | 645 |  58.05  | 40763 |  66.84 |  89.1  | 189.57 | 151.66 | 176    | 140.8  | 190   | 0.08  | 152   |
| DF2010 | 0.1   | 645 |  64.5   | 40763 |  73.96 |  98.59 | 209.77 | 167.82 | 195    | 156    | 210   | 0.077 | 168   |
| DF2012 | 0.12  | 645 |  77.4   | 40763 |  88.2  | 117.57 | 250.15 | 200.12 | 233    | 186.4  | 250   | 0.073 | 200   |
| DF2015 | 0.15  | 700 | 105     | 40763 | 118.67 | 158.19 | 336.57 | 269.26 | 289    | 231.2  | 340   | 0.176 | 272   |
| DF2020 | 0.2   | 825 | 165     | 40763 | 184.91 | 246.49 | 524.45 | 419.56 | 510    | 408    | 525   | 0.029 | 420   |
| DF2025 | 0.25  | 925 | 231.25  | 40763 | 258.05 | 343.98 | 731.87 | 585.5  | 750    | 600    | 750   | 0     | 600   |
| DF3705 | 0.005 | 485 |   2.425 | 40763 |   5.43 |   7.24 |  15.4  |  12.32 |  11.5  |   9.2  |  15.5 | 0.348 |  12.4 |
| DF3001 | 0.01  | 485 |   4.85  | 40763 |   8.11 |  10.81 |  23    |  18.4  |  16    |  12.8  |  23   | 0.438 |  18.4 |
| DF3715 | 0.015 | 485 |   7.275 | 40763 |  10.79 |  14.38 |  30.6  |  24.48 |  20.5  |  16.4  |  31   | 0.512 |  24.8 |
| DF3002 | 0.02  | 485 |   9.7   | 40763 |  13.46 |  17.94 |  38.17 |  30.54 |  25    |  20    |  38.5 | 0.54  |  30.8 |
| DF3003 | 0.03  | 485 |  14.55  | 40763 |  18.82 |  25.09 |  53.38 |  42.7  |  41    |  32.8  |  53.5 | 0.305 |  42.8 |
| DF3004 | 0.04  | 485 |  19.4   | 40763 |  24.17 |  32.22 |  68.55 |  54.84 |  52    |  41.6  |  69   | 0.327 |  55.2 |
| DF3005 | 0.05  | 485 |  24.25  | 40763 |  29.53 |  39.36 |  83.74 |  66.99 |  63.5  |  50.8  |  84   | 0.323 |  67.2 |
| DF3006 | 0.06  | 485 |  29.1   | 40763 |  34.88 |  46.5  |  98.94 |  79.15 |  74.5  |  59.6  |  99   | 0.329 |  79.2 |
| DF3007 | 0.07  | 485 |  33.95  | 40763 |  40.23 |  53.63 | 114.11 |  91.29 |  85.8  |  68.64 | 114   | 0.329 |  91.2 |
| DF3008 | 0.08  | 610 |  48.8   | 40763 |  56.63 |  75.49 | 160.62 | 128.5  | 126    | 100.8  | 161   | 0.278 | 128.8 |
| DF3009 | 0.09  | 610 |  54.9   | 40763 |  63.36 |  84.46 | 179.7  | 143.76 | 141    | 112.8  | 180   | 0.277 | 144   |
| DF3010 | 0.1   | 610 |  61     | 40763 |  70.1  |  93.44 | 198.81 | 159.05 | 155    | 124    | 199   | 0.284 | 159.2 |
| DF3012 | 0.12  | 610 |  73.2   | 40763 |  83.57 | 111.4  | 237.02 | 189.62 | 186    | 148.8  | 237   | 0.274 | 189.6 |
| DF3015 | 0.15  | 635 |  95.25  | 40763 | 107.91 | 143.84 | 306.04 | 244.83 | 230.5  | 184.4  | 310   | 0.345 | 248   |
| DF3020 | 0.2   | 700 | 140     | 40763 | 157.31 | 209.69 | 446.15 | 356.92 | 415    | 332    | 450   | 0.084 | 360   |
| DF3025 | 0.25  | 765 | 191.25  | 40763 | 213.89 | 285.12 | 606.64 | 485.31 | 600    | 480    | 610   | 0.017 | 488   |
| DF4705 | 0.005 | 410 |   2.05  | 40763 |   5.02 |   6.69 |  14.23 |  11.38 |  11    |   8.8  |  14.5 | 0.318 |  11.6 |
| DF4001 | 0.01  | 410 |   4.1   | 40763 |   7.28 |   9.7  |  20.64 |  16.51 |  15    |  12    |  21   | 0.4   |  16.8 |
| DF4715 | 0.015 | 410 |   6.15  | 40763 |   9.54 |  12.72 |  27.06 |  21.65 |  19    |  15.2  |  27   | 0.421 |  21.6 |
| DF4002 | 0.02  | 410 |   8.2   | 40763 |  11.81 |  15.74 |  33.49 |  26.79 |  23.5  |  18.8  |  33.5 | 0.426 |  26.8 |
| DF4003 | 0.03  | 410 |  12.3   | 40763 |  16.33 |  21.77 |  46.32 |  37.06 |  35.5  |  28.4  |  46.5 | 0.31  |  37.2 |
| DF4004 | 0.04  | 410 |  16.4   | 40763 |  20.86 |  27.81 |  59.17 |  47.34 |  45    |  36    |  59.5 | 0.322 |  47.6 |
| DF4005 | 0.05  | 410 |  20.5   | 40763 |  25.39 |  33.84 |  72    |  57.6  |  54.5  |  43.6  |  72   | 0.321 |  57.6 |
| DF4006 | 0.06  | 410 |  24.6   | 40763 |  29.91 |  39.87 |  84.83 |  67.86 |  64    |  51.2  |  85   | 0.328 |  68   |
| DF4007 | 0.07  | 475 |  33.25  | 40763 |  39.46 |  52.6  | 111.91 |  89.53 |  74    |  59.2  | 112   | 0.514 |  89.6 |
| DF4008 | 0.08  | 475 |  38     | 40763 |  44.71 |  59.6  | 126.81 | 101.45 | 110    |  88    | 127   | 0.155 | 101.6 |
| DF4009 | 0.09  | 475 |  42.75  | 40763 |  49.95 |  66.58 | 141.66 | 113.33 | 122.5  |  98    | 142   | 0.159 | 113.6 |
| DF4010 | 0.1   | 475 |  47.5   | 40763 |  55.19 |  73.57 | 156.53 | 125.22 | 135.5  | 108.4  | 157   | 0.159 | 125.6 |
| DFW001 | 0.01  | 340 |   3.4   | 40763 |   8.17 |  10.89 |  24.2  |  19.36 |  33.18 |  26.54 |  35   | 0.055 |  28   |
| DFW002 | 0.02  | 340 |   6.8   | 40763 |  11.79 |  15.72 |  34.93 |  27.94 |  43.13 |  34.5  |  45   | 0.043 |  36   |



label: D=C*B
labeled_formulas: D=C*B
output: {"Arithmetic-Relationship": ["D=C*B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_688288___xlsx_216d58b302d32b0156af3d29b5c5d71688f1abae.xlsx___line_94