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 |
|----:|------:|--------:|----------:|--------:|-----------------:|
|   1 | 43831 | 9485.17 | 8125      | 1360.17 | 998640           |
|   2 | 43862 | 9485.17 | 8113.95   | 1371.22 | 997269           |
|   3 | 43891 | 9485.17 | 8102.81   | 1382.36 | 995886           |
|   4 | 43922 | 9485.17 | 8091.58   | 1393.59 | 994493           |
|   5 | 43952 | 9485.17 | 8080.25   | 1404.92 | 993088           |
|   6 | 43983 | 9485.17 | 8068.84   | 1416.33 | 991671           |
|   7 | 44013 | 9485.17 | 8057.33   | 1427.84 | 990244           |
|   8 | 44044 | 9485.17 | 8045.73   | 1439.44 | 988804           |
|   9 | 44075 | 9485.17 | 8034.03   | 1451.13 | 987353           |
|  10 | 44105 | 9485.17 | 8022.24   | 1462.93 | 985890           |
|  11 | 44136 | 9485.17 | 8010.36   | 1474.81 | 984415           |
|  12 | 44166 | 9485.17 | 7998.37   | 1486.79 | 982928           |
|  13 | 44197 | 9485.17 | 7986.29   | 1498.87 | 981430           |
|  14 | 44228 | 9485.17 | 7974.12   | 1511.05 | 979919           |
|  15 | 44256 | 9485.17 | 7961.84   | 1523.33 | 978395           |
|  16 | 44287 | 9485.17 | 7949.46   | 1535.71 | 976860           |
|  17 | 44317 | 9485.17 | 7936.98   | 1548.19 | 975311           |
|  18 | 44348 | 9485.17 | 7924.4    | 1560.76 | 973751           |
|  19 | 44378 | 9485.17 | 7911.72   | 1573.45 | 972177           |
|  20 | 44409 | 9485.17 | 7898.94   | 1586.23 | 970591           |
|  21 | 44440 | 9485.17 | 7886.05   | 1599.12 | 968992           |
|  22 | 44470 | 9485.17 | 7873.06   | 1612.11 | 967380           |
|  23 | 44501 | 9485.17 | 7859.96   | 1625.21 | 965754           |
|  24 | 44531 | 9485.17 | 7846.75   | 1638.41 | 964116           |
|  25 | 44562 | 9485.17 | 7833.44   | 1651.73 | 962464           |
|  26 | 44593 | 9485.17 | 7820.02   | 1665.15 | 960799           |
|  27 | 44621 | 9485.17 | 7806.49   | 1678.68 | 959120           |
|  28 | 44652 | 9485.17 | 7792.85   | 1692.31 | 957428           |
|  29 | 44682 | 9485.17 | 7779.1    | 1706.06 | 955722           |
|  30 | 44713 | 9485.17 | 7765.24   | 1719.93 | 954002           |
|  31 | 44743 | 9485.17 | 7751.27   | 1733.9  | 952268           |
|  32 | 44774 | 9485.17 | 7737.18   | 1747.99 | 950520           |
|  33 | 44805 | 9485.17 | 7722.98   | 1762.19 | 948758           |
|  34 | 44835 | 9485.17 | 7708.66   | 1776.51 | 946982           |
|  35 | 44866 | 9485.17 | 7694.23   | 1790.94 | 945191           |
|  36 | 44896 | 9485.17 | 7679.67   | 1805.49 | 943385           |
|  37 | 44927 | 9485.17 | 7665      | 1820.16 | 941565           |
|  38 | 44958 | 9485.17 | 7650.22   | 1834.95 | 939730           |
|  39 | 44986 | 9485.17 | 7635.31   | 1849.86 | 937880           |
|  40 | 45017 | 9485.17 | 7620.28   | 1864.89 | 936015           |
|  41 | 45047 | 9485.17 | 7605.12   | 1880.04 | 934135           |
|  42 | 45078 | 9485.17 | 7589.85   | 1895.32 | 932240           |
|  43 | 45108 | 9485.17 | 7574.45   | 1910.72 | 930329           |
|  44 | 45139 | 9485.17 | 7558.92   | 1926.24 | 928403           |
|  45 | 45170 | 9485.17 | 7543.27   | 1941.89 | 926461           |
|  46 | 45200 | 9485.17 | 7527.5    | 1957.67 | 924503           |
|  47 | 45231 | 9485.17 | 7511.59   | 1973.58 | 922530           |
|  48 | 45261 | 9485.17 | 7495.55   | 1989.61 | 920540           |
|  49 | 45292 | 9485.17 | 7479.39   | 2005.78 | 918534           |
|  50 | 45323 | 9485.17 | 7463.09   | 2022.08 | 916512           |
|  51 | 45352 | 9485.17 | 7446.66   | 2038.51 | 914474           |
|  52 | 45383 | 9485.17 | 7430.1    | 2055.07 | 912419           |
|  53 | 45413 | 9485.17 | 7413.4    | 2071.77 | 910347           |
|  54 | 45444 | 9485.17 | 7396.57   | 2088.6  | 908258           |
|  55 | 45474 | 9485.17 | 7379.6    | 2105.57 | 906153           |
|  56 | 45505 | 9485.17 | 7362.49   | 2122.68 | 904030           |
|  57 | 45536 | 9485.17 | 7345.24   | 2139.92 | 901890           |
|  58 | 45566 | 9485.17 | 7327.86   | 2157.31 | 899733           |
|  59 | 45597 | 9485.17 | 7310.33   | 2174.84 | 897558           |
|  60 | 45627 | 9485.17 | 7292.66   | 2192.51 | 895366           |
|  61 | 45658 | 9485.17 | 7274.85   | 2210.32 | 893155           |
|  62 | 45689 | 9485.17 | 7256.89   | 2228.28 | 890927           |
|  63 | 45717 | 9485.17 | 7238.78   | 2246.39 | 888681           |
|  64 | 45748 | 9485.17 | 7220.53   | 2264.64 | 886416           |
|  65 | 45778 | 9485.17 | 7202.13   | 2283.04 | 884133           |
|  66 | 45809 | 9485.17 | 7183.58   | 2301.59 | 881831           |
|  67 | 45839 | 9485.17 | 7164.88   | 2320.29 | 879511           |
|  68 | 45870 | 9485.17 | 7146.03   | 2339.14 | 877172           |
|  69 | 45901 | 9485.17 | 7127.02   | 2358.15 | 874814           |
|  70 | 45931 | 9485.17 | 7107.86   | 2377.31 | 872436           |
|  71 | 45962 | 9485.17 | 7088.55   | 2396.62 | 870040           |
|  72 | 45992 | 9485.17 | 7069.07   | 2416.1  | 867624           |
|  73 | 46023 | 9485.17 | 7049.44   | 2435.73 | 865188           |
|  74 | 46054 | 9485.17 | 7029.65   | 2455.52 | 862732           |
|  75 | 46082 | 9485.17 | 7009.7    | 2475.47 | 860257           |
|  76 | 46113 | 9485.17 | 6989.59   | 2495.58 | 857761           |
|  77 | 46143 | 9485.17 | 6969.31   | 2515.86 | 855246           |
|  78 | 46174 | 9485.17 | 6948.87   | 2536.3  | 852709           |
|  79 | 46204 | 9485.17 | 6928.26   | 2556.91 | 850152           |
|  80 | 46235 | 9485.17 | 6907.49   | 2577.68 | 847575           |
|  81 | 46266 | 9485.17 | 6886.54   | 2598.62 | 844976           |
|  82 | 46296 | 9485.17 | 6865.43   | 2619.74 | 842356           |
|  83 | 46327 | 9485.17 | 6844.15   | 2641.02 | 839715           |
|  84 | 46357 | 9485.17 | 6822.69   | 2662.48 | 837053           |
|  85 | 46388 | 9485.17 | 6801.05   | 2684.11 | 834369           |
|  86 | 46419 | 9485.17 | 6779.25   | 2705.92 | 831663           |
|  87 | 46447 | 9485.17 | 6757.26   | 2727.91 | 828935           |
|  88 | 46478 | 9485.17 | 6735.1    | 2750.07 | 826185           |
|  89 | 46508 | 9485.17 | 6712.75   | 2772.42 | 823412           |
|  90 | 46539 | 9485.17 | 6690.23   | 2794.94 | 820617           |
|  91 | 46569 | 9485.17 | 6667.52   | 2817.65 | 817800           |
|  92 | 46600 | 9485.17 | 6644.62   | 2840.55 | 814959           |
|  93 | 46631 | 9485.17 | 6621.54   | 2863.62 | 812096           |
|  94 | 46661 | 9485.17 | 6598.28   | 2886.89 | 809209           |
|  95 | 46692 | 9485.17 | 6574.82   | 2910.35 | 806298           |
|  96 | 46722 | 9485.17 | 6551.17   | 2933.99 | 803364           |
|  97 | 46753 | 9485.17 | 6527.34   | 2957.83 | 800407           |
|  98 | 46784 | 9485.17 | 6503.3    | 2981.87 | 797425           |
|  99 | 46813 | 9485.17 | 6479.08   | 3006.09 | 794419           |
| 100 | 46844 | 9485.17 | 6454.65   | 3030.52 | 791388           |
| 101 | 46874 | 9485.17 | 6430.03   | 3055.14 | 788333           |
| 102 | 46905 | 9485.17 | 6405.2    | 3079.96 | 785253           |
| 103 | 46935 | 9485.17 | 6380.18   | 3104.99 | 782148           |
| 104 | 46966 | 9485.17 | 6354.95   | 3130.22 | 779018           |
| 105 | 46997 | 9485.17 | 6329.52   | 3155.65 | 775862           |
| 106 | 47027 | 9485.17 | 6303.88   | 3181.29 | 772681           |
| 107 | 47058 | 9485.17 | 6278.03   | 3207.14 | 769474           |
| 108 | 47088 | 9485.17 | 6251.97   | 3233.19 | 766240           |
| 109 | 47119 | 9485.17 | 6225.7    | 3259.46 | 762981           |
| 110 | 47150 | 9485.17 | 6199.22   | 3285.95 | 759695           |
| 111 | 47178 | 9485.17 | 6172.52   | 3312.65 | 756382           |
| 112 | 47209 | 9485.17 | 6145.61   | 3339.56 | 753043           |
| 113 | 47239 | 9485.17 | 6118.47   | 3366.7  | 749676           |
| 114 | 47270 | 9485.17 | 6091.12   | 3394.05 | 746282           |
| 115 | 47300 | 9485.17 | 6063.54   | 3421.63 | 742860           |
| 116 | 47331 | 9485.17 | 6035.74   | 3449.43 | 739411           |
| 117 | 47362 | 9485.17 | 6007.71   | 3477.45 | 735934           |
| 118 | 47392 | 9485.17 | 5979.46   | 3505.71 | 732428           |
| 119 | 47423 | 9485.17 | 5950.98   | 3534.19 | 728894           |
| 120 | 47453 | 9485.17 | 5922.26   | 3562.91 | 725331           |
| 121 | 47484 | 9485.17 | 5893.31   | 3591.86 | 721739           |
| 122 | 47515 | 9485.17 | 5864.13   | 3621.04 | 718118           |
| 123 | 47543 | 9485.17 | 5834.71   | 3650.46 | 714467           |
| 124 | 47574 | 9485.17 | 5805.05   | 3680.12 | 710787           |
| 125 | 47604 | 9485.17 | 5775.15   | 3710.02 | 707077           |
| 126 | 47635 | 9485.17 | 5745      | 3740.17 | 703337           |
| 127 | 47665 | 9485.17 | 5714.61   | 3770.55 | 699567           |
| 128 | 47696 | 9485.17 | 5683.98   | 3801.19 | 695765           |
| 129 | 47727 | 9485.17 | 5653.09   | 3832.07 | 691933           |
| 130 | 47757 | 9485.17 | 5621.96   | 3863.21 | 688070           |
| 131 | 47788 | 9485.17 | 5590.57   | 3894.6  | 684176           |
| 132 | 47818 | 9485.17 | 5558.93   | 3926.24 | 680249           |
| 133 | 47849 | 9485.17 | 5527.03   | 3958.14 | 676291           |
| 134 | 47880 | 9485.17 | 5494.87   | 3990.3  | 672301           |
| 135 | 47908 | 9485.17 | 5462.44   | 4022.72 | 668278           |
| 136 | 47939 | 9485.17 | 5429.76   | 4055.41 | 664223           |
| 137 | 47969 | 9485.17 | 5396.81   | 4088.36 | 660134           |
| 138 | 48000 | 9485.17 | 5363.59   | 4121.58 | 656013           |
| 139 | 48030 | 9485.17 | 5330.1    | 4155.06 | 651858           |
| 140 | 48061 | 9485.17 | 5296.34   | 4188.82 | 647669           |
| 141 | 48092 | 9485.17 | 5262.31   | 4222.86 | 643446           |
| 142 | 48122 | 9485.17 | 5228      | 4257.17 | 639189           |
| 143 | 48153 | 9485.17 | 5193.41   | 4291.76 | 634897           |
| 144 | 48183 | 9485.17 | 5158.54   | 4326.63 | 630570           |
| 145 | 48214 | 9485.17 | 5123.38   | 4361.78 | 626209           |
| 146 | 48245 | 9485.17 | 5087.95   | 4397.22 | 621811           |
| 147 | 48274 | 9485.17 | 5052.22   | 4432.95 | 617378           |
| 148 | 48305 | 9485.17 | 5016.2    | 4468.97 | 612910           |
| 149 | 48335 | 9485.17 | 4979.89   | 4505.28 | 608404           |
| 150 | 48366 | 9485.17 | 4943.28   | 4541.88 | 603862           |
| 151 | 48396 | 9485.17 | 4906.38   | 4578.79 | 599284           |
| 152 | 48427 | 9485.17 | 4869.18   | 4615.99 | 594668           |
| 153 | 48458 | 9485.17 | 4831.67   | 4653.49 | 590014           |
| 154 | 48488 | 9485.17 | 4793.86   | 4691.3  | 585323           |
| 155 | 48519 | 9485.17 | 4755.75   | 4729.42 | 580593           |
| 156 | 48549 | 9485.17 | 4717.32   | 4767.85 | 575826           |
| 157 | 48580 | 9485.17 | 4678.58   | 4806.59 | 571019           |
| 158 | 48611 | 9485.17 | 4639.53   | 4845.64 | 566173           |
| 159 | 48639 | 9485.17 | 4600.16   | 4885.01 | 561288           |
| 160 | 48670 | 9485.17 | 4560.47   | 4924.7  | 556364           |
| 161 | 48700 | 9485.17 | 4520.45   | 4964.71 | 551399           |
| 162 | 48731 | 9485.17 | 4480.12   | 5005.05 | 546394           |
| 163 | 48761 | 9485.17 | 4439.45   | 5045.72 | 541348           |
| 164 | 48792 | 9485.17 | 4398.45   | 5086.72 | 536261           |
| 165 | 48823 | 9485.17 | 4357.12   | 5128.04 | 531133           |
| 166 | 48853 | 9485.17 | 4315.46   | 5169.71 | 525964           |
| 167 | 48884 | 9485.17 | 4273.45   | 5211.71 | 520752           |
| 168 | 48914 | 9485.17 | 4231.11   | 5254.06 | 515498           |
| 169 | 48945 | 9485.17 | 4188.42   | 5296.75 | 510201           |
| 170 | 48976 | 9485.17 | 4145.38   | 5339.78 | 504861           |
| 171 | 49004 | 9485.17 | 4102      | 5383.17 | 499478           |
| 172 | 49035 | 9485.17 | 4058.26   | 5426.91 | 494051           |
| 173 | 49065 | 9485.17 | 4014.17   | 5471    | 488580           |
| 174 | 49096 | 9485.17 | 3969.71   | 5515.45 | 483065           |
| 175 | 49126 | 9485.17 | 3924.9    | 5560.27 | 477505           |
| 176 | 49157 | 9485.17 | 3879.72   | 5605.44 | 471899           |
| 177 | 49188 | 9485.17 | 3834.18   | 5650.99 | 466248           |
| 178 | 49218 | 9485.17 | 3788.27   | 5696.9  | 460551           |
| 179 | 49249 | 9485.17 | 3741.98   | 5743.19 | 454808           |
| 180 | 49279 | 9485.17 | 3695.31   | 5789.85 | 449018           |
| 181 | 49310 | 9485.17 | 3648.27   | 5836.9  | 443181           |
| 182 | 49341 | 9485.17 | 3600.85   | 5884.32 | 437297           |
| 183 | 49369 | 9485.17 | 3553.04   | 5932.13 | 431365           |
| 184 | 49400 | 9485.17 | 3504.84   | 5980.33 | 425384           |
| 185 | 49430 | 9485.17 | 3456.25   | 6028.92 | 419356           |
| 186 | 49461 | 9485.17 | 3407.26   | 6077.9  | 413278           |
| 187 | 49491 | 9485.17 | 3357.88   | 6127.29 | 407150           |
| 188 | 49522 | 9485.17 | 3308.1    | 6177.07 | 400973           |
| 189 | 49553 | 9485.17 | 3257.91   | 6227.26 | 394746           |
| 190 | 49583 | 9485.17 | 3207.31   | 6277.86 | 388468           |
| 191 | 49614 | 9485.17 | 3156.3    | 6328.86 | 382139           |
| 192 | 49644 | 9485.17 | 3104.88   | 6380.29 | 375759           |
| 193 | 49675 | 9485.17 | 3053.04   | 6432.13 | 369327           |
| 194 | 49706 | 9485.17 | 3000.78   | 6484.39 | 362842           |
| 195 | 49735 | 9485.17 | 2948.1    | 6537.07 | 356305           |
| 196 | 49766 | 9485.17 | 2894.98   | 6590.19 | 349715           |
| 197 | 49796 | 9485.17 | 2841.44   | 6643.73 | 343071           |
| 198 | 49827 | 9485.17 | 2787.46   | 6697.71 | 336374           |
| 199 | 49857 | 9485.17 | 2733.04   | 6752.13 | 329622           |
| 200 | 49888 | 9485.17 | 2678.18   | 6806.99 | 322815           |
| 201 | 49919 | 9485.17 | 2622.87   | 6862.3  | 315952           |
| 202 | 49949 | 9485.17 | 2567.11   | 6918.06 | 309034           |
| 203 | 49980 | 9485.17 | 2510.9    | 6974.26 | 302060           |
| 204 | 50010 | 9485.17 | 2454.24   | 7030.93 | 295029           |
| 205 | 50041 | 9485.17 | 2397.11   | 7088.06 | 287941           |
| 206 | 50072 | 9485.17 | 2339.52   | 7145.65 | 280795           |
| 207 | 50100 | 9485.17 | 2281.46   | 7203.71 | 273592           |
| 208 | 50131 | 9485.17 | 2222.93   | 7262.24 | 266329           |
| 209 | 50161 | 9485.17 | 2163.93   | 7321.24 | 259008           |
| 210 | 50192 | 9485.17 | 2104.44   | 7380.73 | 251627           |
| 211 | 50222 | 9485.17 | 2044.47   | 7440.7  | 244187           |
| 212 | 50253 | 9485.17 | 1984.02   | 7501.15 | 236686           |
| 213 | 50284 | 9485.17 | 1923.07   | 7562.1  | 229124           |
| 214 | 50314 | 9485.17 | 1861.63   | 7623.54 | 221500           |
| 215 | 50345 | 9485.17 | 1799.69   | 7685.48 | 213815           |
| 216 | 50375 | 9485.17 | 1737.24   | 7747.93 | 206067           |
| 217 | 50406 | 9485.17 | 1674.29   | 7810.88 | 198256           |
| 218 | 50437 | 9485.17 | 1610.83   | 7874.34 | 190381           |
| 219 | 50465 | 9485.17 | 1546.85   | 7938.32 | 182443           |
| 220 | 50496 | 9485.17 | 1482.35   | 8002.82 | 174440           |
| 221 | 50526 | 9485.17 | 1417.33   | 8067.84 | 166372           |
| 222 | 50557 | 9485.17 | 1351.78   | 8133.39 | 158239           |
| 223 | 50587 | 9485.17 | 1285.69   | 8199.48 | 150040           |
| 224 | 50618 | 9485.17 | 1219.07   | 8266.1  | 141773           |
| 225 | 50649 | 9485.17 | 1151.91   | 8333.26 | 133440           |
| 226 | 50679 | 9485.17 | 1084.2    | 8400.97 | 125039           |
| 227 | 50710 | 9485.17 | 1015.94   | 8469.22 | 116570           |
| 228 | 50740 | 9485.17 |  947.131  | 8538.04 | 108032           |
| 229 | 50771 | 9485.17 |  877.76   | 8607.41 |  99424.5         |
| 230 | 50802 | 9485.17 |  807.824  | 8677.34 |  90747.2         |
| 231 | 50830 | 9485.17 |  737.321  | 8747.85 |  81999.4         |
| 232 | 50861 | 9485.17 |  666.245  | 8818.92 |  73180.4         |
| 233 | 50891 | 9485.17 |  594.591  | 8890.58 |  64289.9         |
| 234 | 50922 | 9485.17 |  522.355  | 8962.81 |  55327           |
| 235 | 50952 | 9485.17 |  449.532  | 9035.64 |  46291.4         |
| 236 | 50983 | 9485.17 |  376.118  | 9109.05 |  37182.4         |
| 237 | 51014 | 9485.17 |  302.107  | 9183.06 |  27999.3         |
| 238 | 51044 | 9485.17 |  227.494  | 9257.67 |  18741.6         |
| 239 | 51075 | 9485.17 |  152.276  | 9332.89 |   9408.72        |
| 240 | 51105 | 9485.17 |   76.4459 | 9408.72 |     -7.71252e-10 |



label: E=C-D
labeled_formulas: E=C-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_242902___xlsx_9bfd95275b679db7043c95c62f494a6278a5d4c8.xlsx___line_439