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 |
|----:|-----:|----:|----:|----------:|----------:|------------:|------------:|------------:|----------:|------------:|------------:|------------:|
|   0 | 2018 |  70 |  75 | 0.0203928 | 0.0323545 | 1           | 1           | 1           | 1         | 1           | 1           | 1           |
|   1 | 2019 |  71 |  76 | 0.0216334 | 0.0352265 | 0.979607    | 0.967645    | 0.947912    | 0.980392  | 0.960399    | 0.948672    | 0.929326    |
|   2 | 2020 |  72 |  77 | 0.022985  | 0.0384235 | 0.958415    | 0.933559    | 0.894737    | 0.961169  | 0.921199    | 0.897308    | 0.859993    |
|   3 | 2021 |  73 |  78 | 0.0244906 | 0.0420024 | 0.936386    | 0.897688    | 0.840583    | 0.942322  | 0.882377    | 0.845912    | 0.7921      |
|   4 | 2022 |  74 |  79 | 0.0262651 | 0.0459998 | 0.913453    | 0.859983    | 0.785554    | 0.923845  | 0.84389     | 0.794491    | 0.725731    |
|   5 | 2023 |  75 |  80 | 0.0284327 | 0.0507533 | 0.889461    | 0.820424    | 0.729735    | 0.905731  | 0.805612    | 0.743083    | 0.660944    |
|   6 | 2024 |  76 |  81 | 0.0310196 | 0.0563264 | 0.864171    | 0.778785    | 0.673004    | 0.887971  | 0.767359    | 0.691539    | 0.597608    |
|   7 | 2025 |  77 |  82 | 0.0339276 | 0.0629262 | 0.837365    | 0.734919    | 0.615395    | 0.87056   | 0.728977    | 0.639791    | 0.535739    |
|   8 | 2026 |  78 |  83 | 0.0372129 | 0.0705986 | 0.808955    | 0.688673    | 0.557106    | 0.85349   | 0.690436    | 0.587776    | 0.475484    |
|   9 | 2027 |  79 |  84 | 0.0409164 | 0.0796398 | 0.778852    | 0.640054    | 0.498507    | 0.836755  | 0.651708    | 0.535568    | 0.417128    |
|  10 | 2028 |  80 |  85 | 0.0453545 | 0.0898872 | 0.746984    | 0.58908     | 0.440033    | 0.820348  | 0.612787    | 0.483251    | 0.360981    |
|  11 | 2029 |  81 |  86 | 0.0506068 | 0.101123  | 0.713105    | 0.536129    | 0.382316    | 0.804263  | 0.573524    | 0.431189    | 0.307483    |
|  12 | 2030 |  82 |  87 | 0.0568855 | 0.113218  | 0.677017    | 0.481914    | 0.326264    | 0.788493  | 0.533823    | 0.379986    | 0.257257    |
|  13 | 2031 |  83 |  88 | 0.0642564 | 0.126423  | 0.638505    | 0.427353    | 0.272867    | 0.773033  | 0.493585    | 0.330358    | 0.210935    |
|  14 | 2032 |  84 |  89 | 0.0730093 | 0.141692  | 0.597477    | 0.373326    | 0.223053    | 0.757875  | 0.452813    | 0.282934    | 0.169047    |
|  15 | 2033 |  85 |  90 | 0.0830069 | 0.15909   | 0.553855    | 0.320428    | 0.177471    | 0.743015  | 0.411523    | 0.238083    | 0.131864    |
|  16 | 2034 |  86 |  91 | 0.0940523 | 0.179466  | 0.507881    | 0.269451    | 0.136849    | 0.728446  | 0.369964    | 0.196281    | 0.0996873   |
|  17 | 2035 |  87 |  92 | 0.106035  | 0.200341  | 0.460114    | 0.221094    | 0.101728    | 0.714163  | 0.328596    | 0.157897    | 0.0726506   |
|  18 | 2036 |  88 |  93 | 0.119214  | 0.221912  | 0.411326    | 0.1768      | 0.0727223   | 0.700159  | 0.287994    | 0.123788    | 0.0509172   |
|  19 | 2037 |  89 |  94 | 0.134533  | 0.242088  | 0.36229     | 0.137566    | 0.0498387   | 0.686431  | 0.248687    | 0.0944294   | 0.0342108   |
|  20 | 2038 |  90 |  95 | 0.152096  | 0.260661  | 0.31355     | 0.104263    | 0.0326916   | 0.672971  | 0.21101     | 0.0701659   | 0.0220005   |
|  21 | 2039 |  91 |  96 | 0.172719  | 0.284509  | 0.26586     | 0.0770856   | 0.020494    | 0.659776  | 0.175408    | 0.0508592   | 0.0135214   |
|  22 | 2040 |  92 |  97 | 0.193872  | 0.309639  | 0.219941    | 0.055154    | 0.0121306   | 0.646839  | 0.142267    | 0.0356758   | 0.00784657  |
|  23 | 2041 |  93 |  98 | 0.2157    | 0.336004  | 0.177301    | 0.0380762   | 0.00675093  | 0.634156  | 0.112436    | 0.0241462   | 0.00428114  |
|  24 | 2042 |  94 |  99 | 0.237284  | 0.364401  | 0.139057    | 0.0252824   | 0.0035157   | 0.621721  | 0.0864547   | 0.0157186   | 0.00218578  |
|  25 | 2043 |  95 | 100 | 0.257114  | 0.393732  | 0.106061    | 0.0160695   | 0.00170434  | 0.609531  | 0.0646474   | 0.00979484  | 0.00103885  |
|  26 | 2044 |  96 | 101 | 0.282296  | 0.423917  | 0.0787912   | 0.00974241  | 0.000767616 | 0.597579  | 0.047084    | 0.00582186  | 0.000458711 |
|  27 | 2045 |  97 | 102 | 0.308613  | 0.454873  | 0.0565488   | 0.00561244  | 0.000317376 | 0.585862  | 0.0331298   | 0.00328812  | 0.000185939 |
|  28 | 2046 |  98 | 103 | 0.336004  | 0.486512  | 0.0390971   | 0.00305949  | 0.000119617 | 0.574375  | 0.0224564   | 0.00175729  | 6.8705e-05  |
|  29 | 2047 |  99 | 104 | 0.364401  | 0.51874   | 0.0259603   | 0.00157101  | 4.07839e-05 | 0.563112  | 0.0146186   | 0.000884656 | 2.29659e-05 |
|  30 | 2048 | 100 | 105 | 0.393732  | 0.551456  | 0.0165003   | 0.000756065 | 1.24753e-05 | 0.552071  | 0.00910934  | 0.000417402 | 6.88726e-06 |
|  31 | 2049 | 101 | 106 | 0.423917  | 0.584554  | 0.0100036   | 0.000339128 | 3.39251e-06 | 0.541246  | 0.00541442  | 0.000183552 | 1.83618e-06 |
|  32 | 2050 | 102 | 107 | 0.454873  | 0.61792   | 0.00576292  | 0.000140889 | 8.11934e-07 | 0.530633  | 0.00305799  | 7.47606e-05 | 4.30839e-07 |
|  33 | 2051 | 103 | 108 | 0.486512  | 0.651429  | 0.00314152  | 5.3831e-05  | 1.69111e-07 | 0.520229  | 0.00163431  | 2.80044e-05 | 8.79765e-08 |
|  34 | 2052 | 104 | 109 | 0.51874   | 0.684946  | 0.00161313  | 1.87639e-05 | 3.02687e-08 | 0.510028  | 0.000822743 | 9.57014e-06 | 1.54379e-08 |
|  35 | 2053 | 105 | 110 | 0.551456  | 0.718321  | 0.000776336 | 5.91166e-06 | 4.58944e-09 | 0.500028  | 0.00038819  | 2.956e-06   | 2.29485e-09 |
|  36 | 2054 | 106 | 111 | 0.584554  | 0.751391  | 0.000348221 | 1.66519e-06 | 5.79854e-10 | 0.490223  | 0.000170706 | 8.16314e-07 | 2.84258e-10 |
|  37 | 2055 | 107 | 112 | 0.61792   | 0.783968  | 0.000144667 | 4.13981e-07 | 5.98894e-11 | 0.480611  | 6.95284e-05 | 1.98964e-07 | 2.87835e-11 |
|  38 | 2056 | 108 | 113 | 0.651429  | 0.815842  | 5.52743e-05 | 8.94332e-08 | 4.94336e-12 | 0.471187  | 2.60445e-05 | 4.21398e-08 | 2.32925e-12 |
|  39 | 2057 | 109 | 114 | 0.684946  | 0.846771  | 1.9267e-05  | 1.64698e-08 | 3.17325e-13 | 0.461948  | 8.90037e-06 | 7.60821e-09 | 1.46588e-13 |
|  40 | 2058 | 110 | 115 | 0.718321  | 0.876471  | 6.07016e-06 | 2.52366e-09 | 1.5319e-14  | 0.45289   | 2.74912e-06 | 1.14294e-09 | 6.93784e-15 |
|  41 | 2059 | 111 | 116 | 0.751391  | 0.904608  | 1.70984e-06 | 3.11744e-10 | 5.33031e-16 | 0.44401   | 7.59184e-07 | 1.38418e-10 | 2.36671e-16 |
|  42 | 2060 | 112 | 117 | 0.783968  | 0.93077   | 4.25081e-07 | 2.9738e-11  | 1.26411e-17 | 0.435304  | 1.85039e-07 | 1.29451e-11 | 5.50271e-18 |
|  43 | 2061 | 113 | 118 | 0.815842  | 0.954436  | 9.1831e-08  | 2.05877e-12 | 1.89059e-19 | 0.426769  | 3.91906e-08 | 8.7862e-13  | 8.06846e-20 |
|  44 | 2062 | 114 | 119 | 0.846771  | 0.974893  | 1.69114e-08 | 9.38069e-14 | 1.58641e-21 | 0.418401  | 7.07574e-09 | 3.92489e-14 | 6.63753e-22 |
|  45 | 2063 | 115 | 120 | 0.876471  | 1         | 2.59132e-09 | 2.35525e-15 | 6.1032e-24  | 0.410197  | 1.06295e-09 | 9.66115e-16 | 2.50351e-24 |
|  46 | 2064 | 116 | 121 | 0.904608  | 0         | 3.20103e-10 | 0           | 0           | 0.402154  | 1.2873e-10  | 0           | 0           |
|  47 | 2065 | 117 | 122 | 0.93077   | 0         | 3.05353e-11 | 0           | 0           | 0.394268  | 1.20391e-11 | 0           | 0           |
|  48 | 2066 | 118 | 123 | 0.954436  | 0         | 2.11397e-12 | 0           | 0           | 0.386538  | 8.1713e-13  | 0           | 0           |
|  49 | 2067 | 119 | 124 | 0.974893  | 0         | 9.63219e-14 | 0           | 0           | 0.378958  | 3.6502e-14  | 0           | 0           |
|  50 | 2068 | 120 | 125 | 1         | 0         | 2.41839e-15 | 0           | 0           | 0.371528  | 8.98501e-16 | 0           | 0           |
|  51 | 2069 | 121 | 126 | 0         | 0         | 0           | 0           | 0           | 0.364243  | 0           | 0           | 0           |
|  52 | 2070 | 122 | 127 | 0         | 0         | 0           | 0           | 0           | 0.357101  | 0           | 0           | 0           |
|  53 | 2071 | 123 | 128 | 0         | 0         | 0           | 0           | 0           | 0.350099  | 0           | 0           | 0           |
|  54 | 2072 | 124 | 129 | 0         | 0         | 0           | 0           | 0           | 0.343234  | 0           | 0           | 0           |
|  55 | 2073 | 125 | 130 | 0         | 0         | 0           | 0           | 0           | 0.336504  | 0           | 0           | 0           |
|  56 | 2074 | 126 | 131 | 0         | 0         | 0           | 0           | 0           | 0.329906  | 0           | 0           | 0           |
|  57 | 2075 | 127 | 132 | 0         | 0         | 0           | 0           | 0           | 0.323437  | 0           | 0           | 0           |
|  58 | 2076 | 128 | 133 | 0         | 0         | 0           | 0           | 0           | 0.317095  | 0           | 0           | 0           |
|  59 | 2077 | 129 | 134 | 0         | 0         | 0           | 0           | 0           | 0.310878  | 0           | 0           | 0           |
|  60 | 2078 | 130 | 135 | 0         | 0         | 0           | 0           | 0           | 0.304782  | 0           | 0           | 0           |
|  61 | 2079 | 131 | 136 | 0         | 0         | 0           | 0           | 0           | 0.298806  | 0           | 0           | 0           |
|  62 | 2080 | 132 | 137 | 0         | 0         | 0           | 0           | 0           | 0.292947  | 0           | 0           | 0           |
|  63 | 2081 | 133 | 138 | 0         | 0         | 0           | 0           | 0           | 0.287203  | 0           | 0           | 0           |
|  64 | 2082 | 134 | 139 | 0         | 0         | 0           | 0           | 0           | 0.281572  | 0           | 0           | 0           |
|  65 | 2083 | 135 | 140 | 0         | 0         | 0           | 0           | 0           | 0.276051  | 0           | 0           | 0           |
|  66 | 2084 | 136 | 141 | 0         | 0         | 0           | 0           | 0           | 0.270638  | 0           | 0           | 0           |
|  67 | 2085 | 137 | 142 | 0         | 0         | 0           | 0           | 0           | 0.265331  | 0           | 0           | 0           |
|  68 | 2086 | 138 | 143 | 0         | 0         | 0           | 0           | 0           | 0.260129  | 0           | 0           | 0           |
|  69 | 2087 | 139 | 144 | 0         | 0         | 0           | 0           | 0           | 0.255028  | 0           | 0           | 0           |
|  70 | 2088 | 140 | 145 | 0         | 0         | 0           | 0           | 0           | 0.250028  | 0           | 0           | 0           |
|  71 | 2089 | 141 | 146 | 0         | 0         | 0           | 0           | 0           | 0.245125  | 0           | 0           | 0           |
|  72 | 2090 | 142 | 147 | 0         | 0         | 0           | 0           | 0           | 0.240319  | 0           | 0           | 0           |
|  73 | 2091 | 143 | 148 | 0         | 0         | 0           | 0           | 0           | 0.235607  | 0           | 0           | 0           |
|  74 | 2092 | 144 | 149 | 0         | 0         | 0           | 0           | 0           | 0.230987  | 0           | 0           | 0           |
|  75 | 2093 | 145 | 150 | 0         | 0         | 0           | 0           | 0           | 0.226458  | 0           | 0           | 0           |
|  76 | 2094 | 146 | 151 | 0         | 0         | 0           | 0           | 0           | 0.222017  | 0           | 0           | 0           |
|  77 | 2095 | 147 | 152 | 0         | 0         | 0           | 0           | 0           | 0.217664  | 0           | 0           | 0           |
|  78 | 2096 | 148 | 153 | 0         | 0         | 0           | 0           | 0           | 0.213396  | 0           | 0           | 0           |
|  79 | 2097 | 149 | 154 | 0         | 0         | 0           | 0           | 0           | 0.209212  | 0           | 0           | 0           |
|  80 | 2098 | 150 | 155 | 0         | 0         | 0           | 0           | 0           | 0.20511   | 0           | 0           | 0           |
|  81 | 2099 | 151 | 156 | 0         | 0         | 0           | 0           | 0           | 0.201088  | 0           | 0           | 0           |
|  82 | 2100 | 152 | 157 | 0         | 0         | 0           | 0           | 0           | 0.197145  | 0           | 0           | 0           |
|  83 | 2101 | 153 | 158 | 0         | 0         | 0           | 0           | 0           | 0.193279  | 0           | 0           | 0           |
|  84 | 2102 | 154 | 159 | 0         | 0         | 0           | 0           | 0           | 0.18949   | 0           | 0           | 0           |
|  85 | 2103 | 155 | 160 | 0         | 0         | 0           | 0           | 0           | 0.185774  | 0           | 0           | 0           |
|  86 | 2104 | 156 | 161 | 0         | 0         | 0           | 0           | 0           | 0.182132  | 0           | 0           | 0           |
|  87 | 2105 | 157 | 162 | 0         | 0         | 0           | 0           | 0           | 0.17856   | 0           | 0           | 0           |
|  88 | 2106 | 158 | 163 | 0         | 0         | 0           | 0           | 0           | 0.175059  | 0           | 0           | 0           |
|  89 | 2107 | 159 | 164 | 0         | 0         | 0           | 0           | 0           | 0.171627  | 0           | 0           | 0           |
|  90 | 2108 | 160 | 165 | 0         | 0         | 0           | 0           | 0           | 0.168261  | 0           | 0           | 0           |
|  91 | 2109 | 161 | 166 | 0         | 0         | 0           | 0           | 0           | 0.164962  | 0           | 0           | 0           |
|  92 | 2110 | 162 | 167 | 0         | 0         | 0           | 0           | 0           | 0.161728  | 0           | 0           | 0           |
|  93 | 2111 | 163 | 168 | 0         | 0         | 0           | 0           | 0           | 0.158556  | 0           | 0           | 0           |
|  94 | 2112 | 164 | 169 | 0         | 0         | 0           | 0           | 0           | 0.155448  | 0           | 0           | 0           |
|  95 | 2113 | 165 | 170 | 0         | 0         | 0           | 0           | 0           | 0.1524    | 0           | 0           | 0           |
|  96 | 2114 | 166 | 171 | 0         | 0         | 0           | 0           | 0           | 0.149411  | 0           | 0           | 0           |
|  97 | 2115 | 167 | 172 | 0         | 0         | 0           | 0           | 0           | 0.146482  | 0           | 0           | 0           |
|  98 | 2116 | 168 | 173 | 0         | 0         | 0           | 0           | 0           | 0.143609  | 0           | 0           | 0           |
|  99 | 2117 | 169 | 174 | 0         | 0         | 0           | 0           | 0           | 0.140794  | 0           | 0           | 0           |
| 100 | 2118 | 170 | 175 | 0         | 0         | 0           | 0           | 0           | 0.138033  | 0           | 0           | 0           |
| 101 | 2119 | 171 | 176 | 0         | 0         | 0           | 0           | 0           | 0.135326  | 0           | 0           | 0           |
| 102 | 2120 | 172 | 177 | 0         | 0         | 0           | 0           | 0           | 0.132673  | 0           | 0           | 0           |
| 103 | 2121 | 173 | 178 | 0         | 0         | 0           | 0           | 0           | 0.130072  | 0           | 0           | 0           |
| 104 | 2122 | 174 | 179 | 0         | 0         | 0           | 0           | 0           | 0.127521  | 0           | 0           | 0           |
| 105 | 2123 | 175 | 180 | 0         | 0         | 0           | 0           | 0           | 0.125021  | 0           | 0           | 0           |
| 106 | 2124 | 176 | 181 | 0         | 0         | 0           | 0           | 0           | 0.122569  | 0           | 0           | 0           |
| 107 | 2125 | 177 | 182 | 0         | 0         | 0           | 0           | 0           | 0.120166  | 0           | 0           | 0           |
| 108 | 2126 | 178 | 183 | 0         | 0         | 0           | 0           | 0           | 0.11781   | 0           | 0           | 0           |
| 109 | 2127 | 179 | 184 | 0         | 0         | 0           | 0           | 0           | 0.1155    | 0           | 0           | 0           |
| 110 | 2128 | 180 | 185 | 0         | 0         | 0           | 0           | 0           | 0.113235  | 0           | 0           | 0           |
| 111 | 2129 | 181 | 186 | 0         | 0         | 0           | 0           | 0           | 0.111015  | 0           | 0           | 0           |
| 112 | 2130 | 182 | 187 | 0         | 0         | 0           | 0           | 0           | 0.108838  | 0           | 0           | 0           |
| 113 | 2131 | 183 | 188 | 0         | 0         | 0           | 0           | 0           | 0.106704  | 0           | 0           | 0           |
| 114 | 2132 | 184 | 189 | 0         | 0         | 0           | 0           | 0           | 0.104612  | 0           | 0           | 0           |
| 115 | 2133 | 185 | 190 | 0         | 0         | 0           | 0           | 0           | 0.102561  | 0           | 0           | 0           |
| 116 | 2134 | 186 | 191 | 0         | 0         | 0           | 0           | 0           | 0.10055   | 0           | 0           | 0           |
| 117 | 2135 | 187 | 192 | 0         | 0         | 0           | 0           | 0           | 0.098578  | 0           | 0           | 0           |
| 118 | 2136 | 188 | 193 | 0         | 0         | 0           | 0           | 0           | 0.0966451 | 0           | 0           | 0           |
| 119 | 2137 | 189 | 194 | 0         | 0         | 0           | 0           | 0           | 0.0947501 | 0           | 0           | 0           |
| 120 | 2138 | 190 | 195 | 0         | 0         | 0           | 0           | 0           | 0.0928922 | 0           | 0           | 0           |



label: I=G*H
K=G*J
L=H*J
M=I*J
labeled_formulas: I=G*H
K=G*J
L=H*J
M=I*J
output: {"Arithmetic-Relationship": ["I=G*H", "K=G*J", "L=H*J", "M=I*J"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_53270___xlsx_ad0d08712cb4372098330c1129b28d8c0d2b7dd0.xlsx___line_617