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 |
|:--------|------:|---------:|---------:|---------:|---------:|--------:|
| CM2.3   |  2.3  | 11.6547  |  75.3458 | 12.7042  | 0.917388 | 5.93076 |
| CM2.4   |  2.4  | 11.3122  |  73.8504 | 12.3051  | 0.919315 | 6.00163 |
| CM2.9   |  2.9  |  9.41224 |  64.3253 | 10.8226  | 0.869686 | 5.94362 |
| CM4.0   |  4    |  9.2498  |  62.5062 |  9.6202  | 0.961498 | 6.4974  |
| CM5.2   |  5.2  |  9.26782 |  60.4558 |  9.58774 | 0.966632 | 6.30553 |
| CM6.05  |  6.05 |  7.43206 |  53.7168 |  8.46174 | 0.878313 | 6.34819 |
| CM7.2   |  7.2  |  7.95837 |  57.07   | 11.0817  | 0.718157 | 5.14995 |
| CM8.1   |  8.1  |  8.2676  |  62.6661 | 11.0984  | 0.744936 | 5.64641 |
| CM8.5   |  8.5  |  8.39263 |  63.2177 | 12.3564  | 0.679214 | 5.1162  |
| CM9.2   |  9.2  |  8.28972 |  58.7467 |  9.31201 | 0.890217 | 6.3087  |
| CM9.7   |  9.7  | 10.6312  |  72.9669 | 11.6923  | 0.909247 | 6.24058 |
| CM10.5  | 10.5  |  9.21008 |  68.0723 | 11.8487  | 0.777307 | 5.74513 |
| CM11.4  | 11.4  |  9.0742  |  68.2716 |  9.89458 | 0.917088 | 6.8999  |
| CM12.6  | 12.6  |  6.14826 |  43.712  |  7.18471 | 0.855742 | 6.08403 |
| CM13.3  | 13.3  |  7.39904 |  53.249  |  7.91104 | 0.935279 | 6.73096 |
| CM13.6  | 13.6  |  7.52776 |  54.762  |  8.82254 | 0.853242 | 6.20705 |
| CM14.0  | 14    |  7.6627  |  56.8901 |  8.73308 | 0.877434 | 6.51432 |
| CM15.5  | 15.5  |  7.34357 |  53.456  |  7.74376 | 0.94832  | 6.9031  |
| CM16.1  | 16.1  |  8.05564 |  54.4208 |  9.27102 | 0.868906 | 5.86999 |
| CM16.9  | 16.9  |  8.92632 |  65.3406 | 11.8541  | 0.753012 | 5.51205 |
| CM17.5  | 17.5  |  8.88707 |  68.3458 | 11.1844  | 0.794595 | 6.11081 |
| CM18.5  | 18.5  |  8.63885 |  73.3994 | 11.6316  | 0.742706 | 6.31034 |
| CM19.6  | 19.6  |  8.66332 |  60.934  |  9.98689 | 0.86747  | 6.10141 |
| CM19.9  | 19.9  |  8.45085 |  68.1976 | 11.3346  | 0.745583 | 6.01678 |
| CM21.4  | 21.4  | 14.4906  |  93.0331 | 13.3349  | 1.08666  | 6.97664 |
| CM22.4  | 22.4  | 15.469   |  97.5591 | 13.8138  | 1.11983  | 7.06245 |
| CM23.7  | 23.7  | 15.3883  | 100.723  | 13.4398  | 1.14498  | 7.49442 |
| CM25.3  | 25.3  | 15.9279  | 103.188  | 13.4821  | 1.18141  | 7.65367 |
| CM25.7  | 25.7  | 11.261   |  77.3055 | 11.6714  | 0.964837 | 6.6235  |
| CM26.1  | 26.1  | 13.4514  |  92.5593 | 14.3814  | 0.935327 | 6.43602 |
| CM27.2  | 27.2  | 13.6313  |  90.9951 | 12.423   | 1.09727  | 7.32476 |
| CM28.3  | 28.3  | 10.6882  |  75.0117 | 11.0152  | 0.970315 | 6.80983 |
| CM29.4  | 29.4  | 10.746   |  72.2788 | 11.0254  | 0.974661 | 6.55566 |
| CM30.4  | 30.4  | 13.5662  |  92.606  | 12.6253  | 1.07452  | 7.33494 |
| CM30.6  | 30.6  | 11.5561  |  78.4865 | 11.0495  | 1.04585  | 7.10315 |
| CM31.4  | 31.4  | 11.0866  |  82.4993 | 11.657   | 0.951073 | 7.07725 |
| CM32.3  | 32.3  | 10.8903  |  79.201  | 11.776   | 0.924786 | 6.72564 |
| CM32.9  | 32.9  | 11.4721  |  80.8951 | 11.2121  | 1.02319  | 7.21499 |
| CM33.4  | 33.4  | 11.082   |  77.2137 | 11.382   | 0.973638 | 6.78383 |
| CM34.5  | 34.5  | 11.2376  |  77.8921 | 10.837   | 1.03697  | 7.18762 |
| CM35.0  | 35    | 12.056   |  83.6219 | 11.6158  | 1.0379   | 7.19897 |
| CM35.5  | 35.5  | 12.037   |  82.8183 | 11.6968  | 1.02908  | 7.08041 |
| CM36.3  | 36.3  | 12.4847  |  86.1973 | 11.3404  | 1.10091  | 7.60091 |
| CM36.85 | 36.85 | 10.3838  |  74.5211 | 10.6488  | 0.97512  | 6.99809 |
| CM37.5  | 37.5  | 11.2542  |  80.2662 | 11.1613  | 1.00833  | 7.19149 |
| CM40.2  | 40.2  |  7.14454 |  47.8243 |  7.06427 | 1.01136  | 6.76989 |
| CM40.7  | 40.7  |  8.70772 |  65.4242 | 10.5281  | 0.827089 | 6.21422 |
| CM41.4  | 41.4  | 11.229   |  76.2175 | 11.5384  | 0.973183 | 6.60554 |
| CM41.9  | 41.9  | 11.4097  |  83.0977 | 12.4997  | 0.9128   | 6.648   |
| CM42.6  | 42.6  | 10.456   |  75.5209 | 11.8554  | 0.881956 | 6.37015 |
| CM43.0  | 43    | 10.1911  |  80.6892 | 14.2975  | 0.712788 | 5.64361 |
| CM43.6  | 43.6  |  8.99952 |  64.2708 |  9.77206 | 0.920945 | 6.577   |
| CM44.1  | 44.1  |  8.84724 |  64.05   | 10.2368  | 0.864258 | 6.25684 |
| CM44.7  | 44.7  |  9.56927 |  65.4819 | 10.8519  | 0.88181  | 6.03416 |
| CM45.2  | 45.2  |  9.23531 |  62.9005 |  9.08474 | 1.01657  | 6.92376 |
| CM45.9  | 45.9  |  8.61353 |  59.0042 |  9.22378 | 0.933839 | 6.39696 |
| CM46.6  | 46.6  |  8.82323 |  62.8118 | 10.1622  | 0.86824  | 6.18092 |
| CM47.3  | 47.3  |  8.84875 |  61.1386 |  8.79858 | 1.0057   | 6.94869 |
| CM48.3  | 48.3  |  9.77711 |  70.9951 | 11.6659  | 0.838095 | 6.08571 |
| CM49.1  | 49    |  8.7103  |  60.7121 |  9.63033 | 0.904465 | 6.30426 |
| CM49.7  | 49.7  |  8.48308 |  59.4516 |  9.29337 | 0.912809 | 6.3972  |
| CM50.8  | 50.8  |  8.21996 |  56.9777 |  8.6415  | 0.95122  | 6.5935  |
| CM52.45 | 52.45 |  9.57898 |  74.6641 | 10.9374  | 0.875799 | 6.82648 |
| CM53.0  | 53    |  8.18637 |  69.065  | 10.6123  | 0.771402 | 6.508   |
| CM53.7  | 53.7  | 10.2204  |  68.9323 | 10.5833  | 0.965714 | 6.51333 |
| CM54.8  | 54.8  | 10.0381  |  66.0979 |  9.94706 | 1.00916  | 6.64496 |
| CM55.6  | 55.6  | 13.0987  |  82.7966 | 11.4475  | 1.14425  | 7.23274 |
| CM56.5  | 56.5  | 10.4697  |  71.958  | 10.3897  | 1.0077   | 6.92589 |
| CM57.2  | 57.2  |  8.87576 |  70.2648 | 10.128   | 0.87636  | 6.93769 |
| CM57.65 | 57.65 |  9.37314 |  64.8417 |  9.04303 | 1.0365   | 7.17035 |
| CM58.4  | 58.4  | 10.0122  |  69.5832 | 10.3235  | 0.969844 | 6.74027 |
| CM59.3  | 59.3  |  9.82996 |  70.0672 | 10.6982  | 0.918843 | 6.54944 |
| CM60.5  | 60.5  |  6.54475 |  43.2514 |  5.73417 | 1.14136  | 7.54276 |
| CM61.45 | 61.45 |  7.44773 |  48.7916 |  7.67859 | 0.969935 | 6.35425 |
| CM62.2  | 62.2  |  7.07401 |  52.3136 | 13.5268  | 0.522963 | 3.86741 |
| CM64.1  | 64.1  |  7.5828  |  46.8243 |  5.83292 | 1.3      | 8.02759 |
| CM64.6  | 64.6  |  7.69153 |  62.8193 |  8.69256 | 0.884841 | 7.22679 |
| CM65.25 | 65.25 |  5.57387 |  31.4619 |  4.323   | 1.28935  | 7.27778 |
| CM65.8  | 65.8  |  4.57868 |  25.8628 |  4.22567 | 1.08354  | 6.12039 |
| CM66.5  | 66.5  |  7.46133 |  51.9773 |  8.34863 | 0.89372  | 6.22585 |
| CM67.5  | 67.5  |  7.66364 |  57.1371 |  7.11338 | 1.07736  | 8.03235 |
| CM69.5  | 69.5  |  7.07727 |  47.4087 |  7.58779 | 0.932718 | 6.24802 |



label: F=C/E
G=D/E
labeled_formulas: F=C/E
G=D/E
output: {"Arithmetic-Relationship": ["F=C/E", "G=D/E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_451432___xlsx_3fe7495104303a251d1efc6452b1ea7ff47af3da.xlsx___line_304