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 |
|-------:|---------:|--------:|----------:|
| 1054   | 0.000404 | 99.6457 | 246648    |
| 1054.1 | 0.000411 | 99.6108 | 242362    |
| 1054.2 | 0.000418 | 99.5759 | 238220    |
| 1054.3 | 0.000425 | 99.5411 | 234214    |
| 1054.4 | 0.000432 | 99.5066 | 230339    |
| 1054.5 | 0.00044  | 99.4726 | 226074    |
| 1054.6 | 0.000447 | 99.4392 | 222459    |
| 1054.7 | 0.000455 | 99.4065 | 218476    |
| 1054.8 | 0.000463 | 99.3747 | 214632    |
| 1054.9 | 0.000471 | 99.3437 | 210921    |
| 1055   | 0.000479 | 99.3138 | 207336    |
| 1055.1 | 0.000487 | 99.2851 | 203871    |
| 1055.2 | 0.000496 | 99.2575 | 200116    |
| 1055.3 | 0.000504 | 99.2311 | 196887    |
| 1055.4 | 0.000513 | 99.206  | 193384    |
| 1055.5 | 0.000522 | 99.1823 | 190004    |
| 1055.6 | 0.000531 | 99.16   | 186742    |
| 1055.7 | 0.00054  | 99.1391 | 183591    |
| 1055.8 | 0.00055  | 99.1196 | 180217    |
| 1055.9 | 0.00056  | 99.1016 | 176967    |
| 1056   | 0.000569 | 99.0851 | 174139    |
| 1056.1 | 0.000579 | 99.07   | 171105    |
| 1056.2 | 0.00059  | 99.0565 | 167892    |
| 1056.3 | 0.0006   | 99.0445 | 165074    |
| 1056.4 | 0.000611 | 99.0339 | 162085    |
| 1056.5 | 0.000622 | 99.0249 | 159204    |
| 1056.6 | 0.000633 | 99.0173 | 156425    |
| 1056.7 | 0.000644 | 99.0111 | 153744    |
| 1056.8 | 0.000655 | 99.0064 | 151155    |
| 1056.9 | 0.000667 | 99.0031 | 148430    |
| 1057   | 0.000679 | 99.0012 | 145804    |
| 1057.1 | 0.000691 | 99.0007 | 143272    |
| 1057.2 | 0.000704 | 99.0014 | 140627    |
| 1057.3 | 0.000716 | 99.0035 | 138273    |
| 1057.4 | 0.000729 | 99.0068 | 135812    |
| 1057.5 | 0.000742 | 99.0114 | 133439    |
| 1057.6 | 0.000756 | 99.0171 | 130975    |
| 1057.7 | 0.00077  | 99.024  | 128603    |
| 1057.8 | 0.000783 | 99.032  | 126478    |
| 1057.9 | 0.000798 | 99.041  | 124112    |
| 1058   | 0.000812 | 99.0511 | 121984    |
| 1058.1 | 0.000827 | 99.0621 | 119785    |
| 1058.2 | 0.000842 | 99.0741 | 117665    |
| 1058.3 | 0.000858 | 99.0869 | 115486    |
| 1058.4 | 0.000873 | 99.1006 | 113517    |
| 1058.5 | 0.000889 | 99.1151 | 111491    |
| 1058.6 | 0.000906 | 99.1303 | 109415    |
| 1058.7 | 0.000922 | 99.1462 | 107534    |
| 1058.8 | 0.00094  | 99.1628 | 105492    |
| 1058.9 | 0.000957 | 99.18   | 103636    |
| 1059   | 0.000975 | 99.1977 | 101741    |
| 1059.1 | 0.000993 | 99.2159 |  99915.4  |
| 1059.2 | 0.001011 | 99.2347 |  98155    |
| 1059.3 | 0.00103  | 99.2538 |  96362.9  |
| 1059.4 | 0.001049 | 99.2733 |  94636.1  |
| 1059.5 | 0.001069 | 99.2932 |  92884.1  |
| 1059.6 | 0.001089 | 99.3133 |  91196.8  |
| 1059.7 | 0.001109 | 99.3337 |  89570.5  |
| 1059.8 | 0.00113  | 99.3542 |  87924.1  |
| 1059.9 | 0.001151 | 99.375  |  86337.9  |
| 1060   | 0.001173 | 99.3958 |  84736.4  |
| 1060.1 | 0.001195 | 99.4168 |  83193.9  |
| 1060.2 | 0.001218 | 99.4377 |  81640.2  |
| 1060.3 | 0.001241 | 99.4587 |  80144    |
| 1060.4 | 0.001265 | 99.4796 |  78640    |
| 1060.5 | 0.001289 | 99.5005 |  77192    |
| 1060.6 | 0.001313 | 99.5213 |  75796.8  |
| 1060.7 | 0.001338 | 99.5419 |  74396    |
| 1060.8 | 0.001364 | 99.5623 |  72992.9  |
| 1060.9 | 0.00139  | 99.5825 |  71642.1  |
| 1061   | 0.001417 | 99.6025 |  70291.1  |
| 1061.1 | 0.001444 | 99.6222 |  68990.5  |
| 1061.2 | 0.001472 | 99.6416 |  67691.3  |
| 1061.3 | 0.0015   | 99.6607 |  66440.5  |
| 1061.4 | 0.001529 | 99.6795 |  65192.6  |
| 1061.5 | 0.001559 | 99.6978 |  63949.9  |
| 1061.6 | 0.001589 | 99.7158 |  62753.8  |
| 1061.7 | 0.00162  | 99.7334 |  61563.8  |
| 1061.8 | 0.001652 | 99.7505 |  60381.6  |
| 1061.9 | 0.001684 | 99.7671 |  59244.1  |
| 1062   | 0.001717 | 99.7833 |  58114.9  |
| 1062.1 | 0.001751 | 99.7989 |  56995.4  |
| 1062.2 | 0.001785 | 99.814  |  55918.2  |
| 1062.3 | 0.00182  | 99.8286 |  54850.9  |
| 1062.4 | 0.001856 | 99.8427 |  53794.6  |
| 1062.5 | 0.001893 | 99.8562 |  52750.2  |
| 1062.6 | 0.00193  | 99.8691 |  51745.7  |
| 1062.7 | 0.001968 | 99.8815 |  50752.8  |
| 1062.8 | 0.002007 | 99.8932 |  49772.4  |
| 1062.9 | 0.002047 | 99.9044 |  48805.3  |
| 1063   | 0.002088 | 99.9149 |  47852    |
| 1063.1 | 0.00213  | 99.9249 |  46913.1  |
| 1063.2 | 0.002172 | 99.9342 |  46010.2  |
| 1063.3 | 0.002216 | 99.9429 |  45100.6  |
| 1063.4 | 0.00226  | 99.951  |  44226.1  |
| 1063.5 | 0.002306 | 99.9584 |  43347.1  |
| 1063.6 | 0.002352 | 99.9653 |  42502.2  |
| 1063.7 | 0.0024   | 99.9715 |  41654.8  |
| 1063.8 | 0.002448 | 99.977  |  40840.3  |
| 1063.9 | 0.002498 | 99.982  |  40024.8  |
| 1064   | 0.002548 | 99.9863 |  39241.1  |
| 1064.1 | 0.0026   | 99.9901 |  38457.7  |
| 1064.2 | 0.002653 | 99.9932 |  37690.6  |
| 1064.3 | 0.002707 | 99.9957 |  36939.7  |
| 1064.4 | 0.002763 | 99.9976 |  36191.7  |
| 1064.5 | 0.002819 | 99.9989 |  35473.2  |
| 1064.6 | 0.002877 | 99.9996 |  34758.3  |
| 1064.7 | 0.002937 | 99.9998 |  34048.3  |
| 1064.8 | 0.002997 | 99.9994 |  33366.5  |
| 1064.9 | 0.003059 | 99.9984 |  32689.9  |
| 1065   | 0.003122 | 99.9969 |  32029.8  |
| 1065.1 | 0.003187 | 99.9949 |  31375.9  |
| 1065.2 | 0.003253 | 99.9923 |  30738.5  |
| 1065.3 | 0.003321 | 99.9892 |  30108.2  |
| 1065.4 | 0.00339  | 99.9856 |  29494.3  |
| 1065.5 | 0.003461 | 99.9816 |  28888.1  |
| 1065.6 | 0.003534 | 99.9771 |  28290.1  |
| 1065.7 | 0.003608 | 99.9721 |  27708.4  |
| 1065.8 | 0.003684 | 99.9666 |  27135.4  |
| 1065.9 | 0.003761 | 99.9608 |  26578.2  |
| 1066   | 0.003841 | 99.9545 |  26023    |
| 1066.1 | 0.003922 | 99.9479 |  25483.9  |
| 1066.2 | 0.004005 | 99.9408 |  24954    |
| 1066.3 | 0.00409  | 99.9334 |  24433.6  |
| 1066.4 | 0.004177 | 99.9257 |  23922.8  |
| 1066.5 | 0.004266 | 99.9176 |  23421.8  |
| 1066.6 | 0.004357 | 99.9092 |  22930.7  |
| 1066.7 | 0.00445  | 99.9005 |  22449.5  |
| 1066.8 | 0.004546 | 99.8915 |  21973.5  |
| 1066.9 | 0.004643 | 99.8823 |  21512.4  |
| 1067   | 0.004743 | 99.8728 |  21056.9  |
| 1067.1 | 0.004846 | 99.8631 |  20607.3  |
| 1067.2 | 0.004951 | 99.8531 |  20168.3  |
| 1067.3 | 0.005058 | 99.843  |  19739.6  |
| 1067.4 | 0.005168 | 99.8327 |  19317.5  |
| 1067.5 | 0.00528  | 99.8223 |  18905.7  |
| 1067.6 | 0.005395 | 99.8117 |  18500.8  |
| 1067.7 | 0.005513 | 99.8009 |  18102.8  |
| 1067.8 | 0.005634 | 99.7901 |  17712.1  |
| 1067.9 | 0.005757 | 99.7792 |  17331.8  |
| 1068   | 0.005884 | 99.7681 |  16955.8  |
| 1068.1 | 0.006013 | 99.7571 |  16590.2  |
| 1068.2 | 0.006146 | 99.746  |  16229.4  |
| 1068.3 | 0.006282 | 99.7348 |  15876.3  |
| 1068.4 | 0.006421 | 99.7237 |  15530.9  |
| 1068.5 | 0.006564 | 99.7126 |  15190.8  |
| 1068.6 | 0.00671  | 99.7014 |  14858.6  |
| 1068.7 | 0.006859 | 99.6904 |  14534.2  |
| 1068.8 | 0.007013 | 99.6793 |  14213.5  |
| 1068.9 | 0.00717  | 99.6684 |  13900.7  |
| 1069   | 0.00733  | 99.6575 |  13595.8  |
| 1069.1 | 0.007495 | 99.6467 |  13295.1  |
| 1069.2 | 0.007664 | 99.636  |  13000.5  |
| 1069.3 | 0.007837 | 99.6254 |  12712.2  |
| 1069.4 | 0.008015 | 99.615  |  12428.6  |
| 1069.5 | 0.008196 | 99.6047 |  12152.8  |
| 1069.6 | 0.008383 | 99.5946 |  11880.5  |
| 1069.7 | 0.008574 | 99.5847 |  11614.7  |
| 1069.8 | 0.008769 | 99.5749 |  11355.3  |
| 1069.9 | 0.00897  | 99.5654 |  11099.8  |
| 1070   | 0.009176 | 99.556  |  10849.6  |
| 1070.1 | 0.009386 | 99.5469 |  10605.9  |
| 1070.2 | 0.009602 | 99.538  |  10366.4  |
| 1070.3 | 0.009824 | 99.5293 |  10131.2  |
| 1070.4 | 0.010051 | 99.5209 |   9901.59 |
| 1070.5 | 0.010284 | 99.5127 |   9676.46 |
| 1070.6 | 0.010523 | 99.5048 |   9455.94 |
| 1070.7 | 0.010768 | 99.4972 |   9240.08 |
| 1070.8 | 0.011019 | 99.4899 |   9028.94 |
| 1070.9 | 0.011277 | 99.4828 |   8821.75 |
| 1071   | 0.011541 | 99.4761 |   8619.36 |
| 1071.1 | 0.011812 | 99.4696 |   8421.07 |
| 1071.2 | 0.01209  | 99.4635 |   8226.92 |
| 1071.3 | 0.012375 | 99.4577 |   8036.98 |
| 1071.4 | 0.012668 | 99.4521 |   7850.66 |
| 1071.5 | 0.012968 | 99.447  |   7668.64 |
| 1071.6 | 0.013276 | 99.4421 |   7490.37 |
| 1071.7 | 0.013592 | 99.4376 |   7315.89 |
| 1071.8 | 0.013916 | 99.4334 |   7145.26 |
| 1071.9 | 0.014249 | 99.4296 |   6978    |
| 1072   | 0.01459  | 99.4261 |   6814.67 |
| 1072.1 | 0.014941 | 99.4229 |   6654.37 |
| 1072.2 | 0.0153   | 99.4201 |   6498.05 |
| 1072.3 | 0.015669 | 99.4177 |   6344.87 |
| 1072.4 | 0.016048 | 99.4156 |   6194.89 |
| 1072.5 | 0.016437 | 99.4138 |   6048.17 |
| 1072.6 | 0.016837 | 99.4125 |   5904.4  |
| 1072.7 | 0.017247 | 99.4114 |   5763.98 |
| 1072.8 | 0.017668 | 99.4107 |   5626.6  |
| 1072.9 | 0.0181   | 99.4104 |   5492.29 |
| 1073   | 0.018544 | 99.4104 |   5360.78 |
| 1073.1 | 0.018999 | 99.4108 |   5232.42 |
| 1073.2 | 0.019467 | 99.4115 |   5106.67 |
| 1073.3 | 0.019948 | 99.4125 |   4983.58 |
| 1073.4 | 0.020442 | 99.4139 |   4863.22 |
| 1073.5 | 0.020949 | 99.4156 |   4745.6  |
| 1073.6 | 0.02147  | 99.4177 |   4630.54 |
| 1073.7 | 0.022005 | 99.4201 |   4518.07 |
| 1073.8 | 0.022555 | 99.4228 |   4408.02 |
| 1073.9 | 0.02312  | 99.4259 |   4300.43 |
| 1074   | 0.023701 | 99.4292 |   4195.15 |



label: D=C/B
labeled_formulas: D=C/B
output: {"Arithmetic-Relationship": ["D=C/B"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_396584___xlsx_f0ab3897ceb8292f29dd6e83e00f4e31c7fb37b9.xlsx___line_587