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:
|   D |         E |     F |        G |        H |   I |        J |    K |         L |        M |       N |       O |
|----:|----------:|------:|---------:|---------:|----:|---------:|-----:|----------:|---------:|--------:|--------:|
|   1 | 0.527     | 47.58 | 25.0747  | 0.801476 | 0.4 | 0.32059  |  0.4 |  0.32059  | 0.801476 | 82.3526 | 77.4403 |
|   2 | 0.524673  | 47.18 | 24.7541  | 0.801034 | 0.4 | 0.320414 |  0.8 |  0.641004 | 0.801255 | 82.3785 | 77.4662 |
|   3 | 0.52231   | 46.78 | 24.4337  | 0.800586 | 0.4 | 0.320234 |  1.2 |  0.961238 | 0.801032 | 82.4049 | 77.4927 |
|   4 | 0.51991   | 46.38 | 24.1134  | 0.80013  | 0.4 | 0.320052 |  1.6 |  1.28129  | 0.800807 | 82.4319 | 77.5196 |
|   5 | 0.517472  | 45.98 | 23.7934  | 0.799667 | 0.4 | 0.319867 |  2   |  1.60116  | 0.800579 | 82.4593 | 77.547  |
|   6 | 0.514996  | 45.58 | 23.4735  | 0.799196 | 0.4 | 0.319679 |  2.4 |  1.92084  | 0.800348 | 82.4873 | 77.575  |
|   7 | 0.51248   | 45.18 | 23.1538  | 0.798717 | 0.4 | 0.319487 |  2.8 |  2.24032  | 0.800115 | 82.5158 | 77.6035 |
|   8 | 0.509923  | 44.78 | 22.8343  | 0.798229 | 0.4 | 0.319292 |  3.2 |  2.55961  | 0.79988  | 82.5449 | 77.6326 |
|   9 | 0.507324  | 44.38 | 22.515   | 0.797732 | 0.4 | 0.319093 |  3.6 |  2.87871  | 0.799641 | 82.5745 | 77.6623 |
|  10 | 0.504683  | 43.98 | 22.196   | 0.797225 | 0.4 | 0.31889  |  4   |  3.1976   | 0.799399 | 82.6048 | 77.6926 |
|  11 | 0.501998  | 43.58 | 21.8771  | 0.796708 | 0.4 | 0.318683 |  4.4 |  3.51628  | 0.799155 | 82.6358 | 77.7235 |
|  12 | 0.499268  | 43.18 | 21.5584  | 0.79618  | 0.4 | 0.318472 |  4.8 |  3.83475  | 0.798907 | 82.6674 | 77.7551 |
|  13 | 0.496492  | 42.78 | 21.2399  | 0.795641 | 0.4 | 0.318256 |  5.2 |  4.15301  | 0.798656 | 82.6996 | 77.7874 |
|  14 | 0.493668  | 42.38 | 20.9217  | 0.79509  | 0.4 | 0.318036 |  5.6 |  4.47104  | 0.798401 | 82.7326 | 77.8204 |
|  15 | 0.490796  | 41.98 | 20.6036  | 0.794526 | 0.4 | 0.31781  |  6   |  4.78885  | 0.798142 | 82.7664 | 77.8541 |
|  16 | 0.487874  | 41.58 | 20.2858  | 0.793948 | 0.4 | 0.317579 |  6.4 |  5.10643  | 0.79788  | 82.8009 | 77.8886 |
|  17 | 0.484901  | 41.18 | 19.9682  | 0.793357 | 0.4 | 0.317343 |  6.8 |  5.42378  | 0.797614 | 82.8362 | 77.9239 |
|  18 | 0.481876  | 40.78 | 19.6509  | 0.79275  | 0.4 | 0.3171   |  7.2 |  5.74088  | 0.797344 | 82.8724 | 77.9601 |
|  19 | 0.478796  | 40.38 | 19.3338  | 0.792128 | 0.4 | 0.316851 |  7.6 |  6.05773  | 0.797069 | 82.9094 | 77.9972 |
|  20 | 0.475661  | 39.98 | 19.0169  | 0.791488 | 0.4 | 0.316595 |  8   |  6.37432  | 0.79679  | 82.9474 | 78.0351 |
|  21 | 0.472469  | 39.58 | 18.7003  | 0.790831 | 0.4 | 0.316332 |  8.4 |  6.69066  | 0.796507 | 82.9863 | 78.074  |
|  22 | 0.469219  | 39.18 | 18.384   | 0.790154 | 0.4 | 0.316062 |  8.8 |  7.00672  | 0.796218 | 83.0262 | 78.114  |
|  23 | 0.465909  | 38.78 | 18.0679  | 0.789457 | 0.4 | 0.315783 |  9.2 |  7.3225   | 0.795924 | 83.0672 | 78.1549 |
|  24 | 0.462537  | 38.38 | 17.7522  | 0.788739 | 0.4 | 0.315496 |  9.6 |  7.638    | 0.795625 | 83.1093 | 78.197  |
|  25 | 0.459101  | 37.98 | 17.4367  | 0.787998 | 0.4 | 0.315199 | 10   |  7.95319  | 0.795319 | 83.1525 | 78.2402 |
|  26 | 0.4556    | 37.58 | 17.1215  | 0.787232 | 0.4 | 0.314893 | 10.4 |  8.26809  | 0.795008 | 83.1969 | 78.2846 |
|  27 | 0.452033  | 37.18 | 16.8066  | 0.78644  | 0.4 | 0.314576 | 10.8 |  8.58266  | 0.794691 | 83.2426 | 78.3303 |
|  28 | 0.448396  | 36.78 | 16.492   | 0.785621 | 0.4 | 0.314248 | 11.2 |  8.89691  | 0.794367 | 83.2896 | 78.3773 |
|  29 | 0.444688  | 36.38 | 16.1777  | 0.784773 | 0.4 | 0.313909 | 11.6 |  9.21082  | 0.794036 | 83.338  | 78.4257 |
|  30 | 0.440907  | 35.98 | 15.8638  | 0.783893 | 0.4 | 0.313557 | 12   |  9.52438  | 0.793698 | 83.3878 | 78.4756 |
|  31 | 0.437051  | 35.58 | 15.5503  | 0.782979 | 0.4 | 0.313192 | 12.4 |  9.83757  | 0.793352 | 83.4393 | 78.527  |
|  32 | 0.433118  | 35.18 | 15.2371  | 0.78203  | 0.4 | 0.312812 | 12.8 | 10.1504   | 0.792999 | 83.4923 | 78.58   |
|  33 | 0.429105  | 34.78 | 14.9243  | 0.781043 | 0.4 | 0.312417 | 13.2 | 10.4628   | 0.792636 | 83.547  | 78.6347 |
|  34 | 0.42501   | 34.38 | 14.6119  | 0.780016 | 0.4 | 0.312006 | 13.6 | 10.7748   | 0.792265 | 83.6036 | 78.6913 |
|  35 | 0.420831  | 33.98 | 14.2999  | 0.778946 | 0.4 | 0.311578 | 14   | 11.0864   | 0.791885 | 83.662  | 78.7498 |
|  36 | 0.416566  | 33.58 | 13.9883  | 0.77783  | 0.4 | 0.311132 | 14.4 | 11.3975   | 0.791494 | 83.7225 | 78.8102 |
|  37 | 0.41221   | 33.18 | 13.6771  | 0.776665 | 0.4 | 0.310666 | 14.8 | 11.7082   | 0.791093 | 83.7851 | 78.8729 |
|  38 | 0.407763  | 32.78 | 13.3665  | 0.775448 | 0.4 | 0.310179 | 15.2 | 12.0184   | 0.790682 | 83.85   | 78.9377 |
|  39 | 0.403221  | 32.38 | 13.0563  | 0.774176 | 0.4 | 0.30967  | 15.6 | 12.328    | 0.790258 | 83.9173 | 79.005  |
|  40 | 0.398581  | 31.98 | 12.7466  | 0.772844 | 0.4 | 0.309138 | 16   | 12.6372   | 0.789823 | 83.9871 | 79.0748 |
|  41 | 0.393841  | 31.58 | 12.4375  | 0.77145  | 0.4 | 0.30858  | 16.4 | 12.9457   | 0.789375 | 84.0596 | 79.1473 |
|  42 | 0.388996  | 31.18 | 12.1289  | 0.769989 | 0.4 | 0.307996 | 16.8 | 13.2537   | 0.788913 | 84.135  | 79.2227 |
|  43 | 0.384045  | 30.78 | 11.8209  | 0.768457 | 0.4 | 0.307383 | 17.2 | 13.5611   | 0.788438 | 84.2134 | 79.3011 |
|  44 | 0.378984  | 30.38 | 11.5135  | 0.766849 | 0.4 | 0.30674  | 17.6 | 13.8679   | 0.787947 | 84.295  | 79.3828 |
|  45 | 0.373809  | 29.98 | 11.2068  | 0.765161 | 0.4 | 0.306064 | 18   | 14.1739   | 0.787441 | 84.3801 | 79.4679 |
|  46 | 0.368517  | 29.58 | 10.9007  | 0.763387 | 0.4 | 0.305355 | 18.4 | 14.4793   | 0.786918 | 84.4689 | 79.5567 |
|  47 | 0.363104  | 29.18 | 10.5954  | 0.761522 | 0.4 | 0.304609 | 18.8 | 14.7839   | 0.786377 | 84.5617 | 79.6494 |
|  48 | 0.357567  | 28.78 | 10.2908  | 0.75956  | 0.4 | 0.303824 | 19.2 | 15.0877   | 0.785819 | 84.6586 | 79.7463 |
|  49 | 0.351901  | 28.38 |  9.98694 | 0.757495 | 0.4 | 0.302998 | 19.6 | 15.3907   | 0.785241 | 84.76   | 79.8478 |
|  50 | 0.346102  | 27.98 |  9.68394 | 0.755322 | 0.4 | 0.302129 | 20   | 15.6928   | 0.784642 | 84.8663 | 79.954  |
|  51 | 0.340167  | 27.58 |  9.38181 | 0.753032 | 0.4 | 0.301213 | 20.4 | 15.9941   | 0.784023 | 84.9777 | 80.0654 |
|  52 | 0.334091  | 27.18 |  9.0806  | 0.750619 | 0.4 | 0.300248 | 20.8 | 16.2943   | 0.78338  | 85.0946 | 80.1823 |
|  53 | 0.32787   | 26.78 |  8.78035 | 0.748075 | 0.4 | 0.29923  | 21.2 | 16.5935   | 0.782714 | 85.2174 | 80.3052 |
|  54 | 0.321498  | 26.38 |  8.48112 | 0.745391 | 0.4 | 0.298156 | 21.6 | 16.8917   | 0.782023 | 85.3467 | 80.4344 |
|  55 | 0.314972  | 25.98 |  8.18297 | 0.742559 | 0.4 | 0.297024 | 22   | 17.1887   | 0.781305 | 85.4828 | 80.5705 |
|  56 | 0.308286  | 25.58 |  7.88594 | 0.739568 | 0.4 | 0.295827 | 22.4 | 17.4845   | 0.78056  | 85.6262 | 80.714  |
|  57 | 0.301434  | 25.18 |  7.59012 | 0.736408 | 0.4 | 0.294563 | 22.8 | 17.7791   | 0.779785 | 85.7777 | 80.8654 |
|  58 | 0.294413  | 24.78 |  7.29555 | 0.733066 | 0.4 | 0.293226 | 23.2 | 18.0723   | 0.77898  | 85.9377 | 81.0254 |
|  59 | 0.287216  | 24.38 |  7.00233 | 0.729528 | 0.4 | 0.291811 | 23.6 | 18.3641   | 0.778142 | 86.1069 | 81.1946 |
|  60 | 0.279838  | 23.98 |  6.71052 | 0.725779 | 0.4 | 0.290311 | 24   | 18.6545   | 0.777269 | 86.2862 | 81.3739 |
|  61 | 0.272273  | 23.58 |  6.4202  | 0.7218   | 0.4 | 0.28872  | 24.4 | 18.9432   | 0.77636  | 86.4762 | 81.5639 |
|  62 | 0.264516  | 23.18 |  6.13148 | 0.71757  | 0.4 | 0.287028 | 24.8 | 19.2302   | 0.775411 | 86.678  | 81.7657 |
|  63 | 0.256561  | 22.78 |  5.84446 | 0.713064 | 0.4 | 0.285226 | 25.2 | 19.5154   | 0.774422 | 86.8923 | 81.9801 |
|  64 | 0.248402  | 22.38 |  5.55923 | 0.708251 | 0.4 | 0.283301 | 25.6 | 19.7987   | 0.773388 | 87.1204 | 82.2081 |
|  65 | 0.240033  | 21.98 |  5.27593 | 0.703094 | 0.4 | 0.281238 | 26   | 20.08     | 0.772306 | 87.3633 | 82.451  |
|  66 | 0.23145   | 21.58 |  4.99469 | 0.697547 | 0.4 | 0.279019 | 26.4 | 20.359    | 0.771174 | 87.6222 | 82.7099 |
|  67 | 0.222647  | 21.18 |  4.71567 | 0.691555 | 0.4 | 0.276622 | 26.8 | 20.6356   | 0.769985 | 87.8985 | 82.9862 |
|  68 | 0.213621  | 20.78 |  4.43905 | 0.685047 | 0.4 | 0.274019 | 27.2 | 20.9096   | 0.768736 | 88.1935 | 83.2812 |
|  69 | 0.204369  | 20.38 |  4.16503 | 0.677938 | 0.4 | 0.271175 | 27.6 | 21.1808   | 0.76742  | 88.5088 | 83.5965 |
|  70 | 0.194888  | 19.98 |  3.89386 | 0.67012  | 0.4 | 0.268048 | 28   | 21.4489   | 0.76603  | 88.846  | 83.9337 |
|  71 | 0.185179  | 19.58 |  3.62581 | 0.661459 | 0.4 | 0.264584 | 28.4 | 21.7134   | 0.764558 | 89.2065 | 84.2942 |
|  72 | 0.175246  | 19.18 |  3.36123 | 0.651791 | 0.4 | 0.260717 | 28.8 | 21.9742   | 0.762991 | 89.5922 | 84.6799 |
|  73 | 0.165096  | 18.78 |  3.10051 | 0.640914 | 0.4 | 0.256366 | 29.2 | 22.2305   | 0.761319 | 90.0045 | 85.0922 |
|  74 | 0.154741  | 18.38 |  2.84414 | 0.628582 | 0.4 | 0.251433 | 29.6 | 22.4819   | 0.759525 | 90.4449 | 85.5326 |
|  75 | 0.1442    | 17.98 |  2.59271 | 0.614503 | 0.4 | 0.245801 | 30   | 22.7278   | 0.757592 | 90.9145 | 86.0022 |
|  76 | 0.133499  | 17.58 |  2.34691 | 0.598336 | 0.4 | 0.239334 | 30.4 | 22.9671   | 0.755496 | 91.4142 | 86.502  |
|  77 | 0.122676  | 17.18 |  2.10757 | 0.579693 | 0.4 | 0.231877 | 30.8 | 23.199    | 0.753213 | 91.9441 | 87.0319 |
|  78 | 0.111782  | 16.78 |  1.8757  | 0.558159 | 0.4 | 0.223263 | 31.2 | 23.4222   | 0.750712 | 92.5034 | 87.5911 |
|  79 | 0.100881  | 16.38 |  1.65243 | 0.533313 | 0.4 | 0.213325 | 31.6 | 23.6356   | 0.74796  | 93.0901 | 88.1778 |
|  80 | 0.0900569 | 15.98 |  1.43911 | 0.50478  | 0.4 | 0.201912 | 32   | 23.8375   | 0.744921 | 93.7004 | 88.7881 |



label: J=H*I
M=L/K
labeled_formulas: J=H*I
M=L/K
output: {"Arithmetic-Relationship": ["J=H*I", "M=L/K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_26700___xlsx_cc5466b1166fd6a35e8defdb4bb46be5349e04b4.xlsx___line_430