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 |      N |      O |      P |     Q |
|:--------|-------:|-------:|---------:|---------:|--------:|--------:|--------:|---------:|-------:|------:|-------:|------:|-------:|-------:|-------:|------:|
| ISIS-43 | 210.58 | 131.66 | 1.59942  |  0.1052  | 0.00333 | 0.01572 | 0.00018 | 0.361736 |  100.5 |  1.14 |  101.6 |  3.06 |  125.9 |  74.85 |  100.5 |  1.14 |
| ISIS-5  |  60.12 | 115.53 | 0.520384 |  0.10857 | 0.00432 | 0.01598 | 0.00021 | 0.33027  |  102.2 |  1.33 |  104.7 |  3.96 |  161.5 |  92.27 |  102.2 |  1.33 |
| ISIS-44 | 251.26 | 151.51 | 1.65837  |  0.10939 | 0.00301 | 0.01597 | 0.00017 | 0.386861 |  102.2 |  1.1  |  105.4 |  2.76 |  179.7 |  64.87 |  102.2 |  1.1  |
| ISIS-25 | 124.64 | 180.39 | 0.690947 |  0.10627 | 0.003   | 0.016   | 0.00018 | 0.398512 |  102.3 |  1.13 |  102.5 |  2.75 |  108.3 |  67.32 |  102.3 |  1.13 |
| ISIS-50 |  28.08 |  29.76 | 0.943548 |  0.10954 | 0.00838 | 0.01618 | 0.00031 | 0.250445 |  103.5 |  1.96 |  105.5 |  7.67 |  153.3 | 173.53 |  103.5 |  1.96 |
| ISIS-10 | 113    | 166.62 | 0.67819  |  0.10566 | 0.00318 | 0.01627 | 0.00018 | 0.367594 |  104.1 |  1.15 |  102   |  2.92 |   53.7 |  72.77 |  104.1 |  1.15 |
| ISIS-2  |  61.98 | 118.78 | 0.521805 |  0.12203 | 0.00471 | 0.01639 | 0.00021 | 0.33196  |  104.8 |  1.35 |  116.9 |  4.26 |  371   |  86.59 |  104.8 |  1.35 |
| ISIS-40 | 561.9  | 135.48 | 4.14748  |  0.11055 | 0.00381 | 0.01639 | 0.00021 | 0.37177  |  104.8 |  1.31 |  106.5 |  3.49 |  143.5 |  80.53 |  104.8 |  1.31 |
| ISIS-69 | 518.98 | 195.25 | 2.65803  |  0.11028 | 0.00421 | 0.01654 | 0.00022 | 0.348419 |  105.7 |  1.38 |  106.2 |  3.85 |  117.7 |  90.48 |  105.7 |  1.38 |
| ISIS-51 | 203.98 | 152.4  | 1.33845  |  0.11128 | 0.00329 | 0.0167  | 0.00019 | 0.384821 |  106.8 |  1.18 |  107.1 |  3.01 |  116.1 |  70.47 |  106.8 |  1.18 |
| ISIS-64 | 115.7  |  62.73 | 1.84441  |  0.11236 | 0.00508 | 0.01675 | 0.00023 | 0.303711 |  107.1 |  1.46 |  108.1 |  4.63 |  132.1 | 105.99 |  107.1 |  1.46 |
| ISIS-28 | 174.78 | 338.91 | 0.515712 |  0.11183 | 0.00287 | 0.01683 | 0.00018 | 0.41674  |  107.6 |  1.12 |  107.6 |  2.62 |  109.2 |  62.01 |  107.6 |  1.12 |
| ISIS-59 | 276.87 | 178.79 | 1.54858  |  0.11801 | 0.00372 | 0.01692 | 0.00019 | 0.356229 |  108.1 |  1.24 |  113.3 |  3.38 |  222.9 |  73.75 |  108.1 |  1.24 |
| ISIS-20 |  92.38 | 112.97 | 0.817739 |  0.11607 | 0.00334 | 0.01706 | 0.00018 | 0.366663 |  109.1 |  1.15 |  111.5 |  3.04 |  164.4 |  68.09 |  109.1 |  1.15 |
| ISIS-30 |  88.89 | 162.66 | 0.546477 |  0.11387 | 0.0033  | 0.01725 | 0.00018 | 0.360063 |  110.2 |  1.12 |  109.5 |  3.01 |   92.8 |  71.3  |  110.2 |  1.12 |
| ISIS-65 | 288.81 | 126.99 | 2.27427  |  0.11783 | 0.00344 | 0.01725 | 0.00019 | 0.377278 |  110.3 |  1.21 |  113.1 |  3.12 |  173.6 |  69.33 |  110.3 |  1.21 |
| ISIS-42 | 141.69 | 136.97 | 1.03446  |  0.11857 | 0.00441 | 0.01757 | 0.00022 | 0.336657 |  112.3 |  1.37 |  113.8 |  4    |  146   |  87.02 |  112.3 |  1.37 |
| ISIS-26 |  29.41 |  53.16 | 0.553236 |  0.12093 | 0.00457 | 0.01765 | 0.00021 | 0.314842 |  112.8 |  1.31 |  115.9 |  4.14 |  181.5 |  88.14 |  112.8 |  1.31 |
| ISIS-54 | 136.24 |  92.18 | 1.47798  |  0.13314 | 0.00744 | 0.01861 | 0.00029 | 0.278861 |  118.9 |  1.85 |  126.9 |  6.66 |  281.3 | 126.26 |  118.9 |  1.85 |
| ISIS-24 |  63.82 |  68.56 | 0.930863 |  0.12592 | 0.00484 | 0.01888 | 0.00022 | 0.303159 |  120.6 |  1.41 |  120.4 |  4.36 |  117.8 |  91.1  |  120.6 |  1.41 |
| ISIS-4  | 176.35 | 349.31 | 0.504852 |  0.12837 | 0.00223 | 0.01935 | 0.00019 | 0.565238 |  123.5 |  1.19 |  122.6 |  2    |  105.3 |  42.21 |  123.5 |  1.19 |
| ISIS-48 | 165.95 | 126.2  | 1.31498  |  0.1294  | 0.0055  | 0.01934 | 0.00026 | 0.316292 |  123.5 |  1.66 |  123.6 |  4.94 |  125.4 |  99.27 |  123.5 |  1.66 |
| ISIS-62 | 252.19 | 149.84 | 1.68306  |  0.13637 | 0.00432 | 0.01958 | 0.00022 | 0.354687 |  125   |  1.41 |  129.8 |  3.86 |  218.7 |  74.43 |  125   |  1.41 |
| ISIS-57 | 315.62 | 159.39 | 1.98017  |  0.13429 | 0.00381 | 0.01967 | 0.00021 | 0.376299 |  125.6 |  1.36 |  127.9 |  3.41 |  172.8 |  67.32 |  125.6 |  1.36 |
| ISIS-41 |  97.06 |  59.21 | 1.63925  |  0.17399 | 0.00755 | 0.02436 | 0.00033 | 0.312186 |  155.2 |  2.07 |  162.9 |  6.53 |  276.7 |  98.41 |  155.2 |  2.07 |
| ISIS-17 |  34.12 |  44.99 | 0.758391 |  0.18203 | 0.00861 | 0.02547 | 0.00036 | 0.298823 |  162.1 |  2.29 |  169.8 |  7.39 |  278.4 | 107.07 |  162.1 |  2.29 |
| ISIS-70 | 231.03 | 152.27 | 1.51724  |  0.17644 | 0.0051  | 0.02581 | 0.00029 | 0.38872  |  164.3 |  1.79 |  165   |  4.4  |  175.5 |  68.96 |  164.3 |  1.79 |
| ISIS-23 | 102.57 |  72.6  | 1.41281  |  0.22162 | 0.00654 | 0.03135 | 0.00032 | 0.345894 |  199   |  2.02 |  203.3 |  5.44 |  253.1 |  69.75 |  199   |  2.02 |
| ISIS-39 | 165.86 |  91.83 | 1.80616  |  0.21785 | 0.00886 | 0.03164 | 0.00043 | 0.334161 |  200.8 |  2.68 |  200.1 |  7.38 |  192.5 |  93.75 |  200.8 |  2.68 |
| ISIS-3  | 206.29 | 258.95 | 0.79664  |  0.22565 | 0.00376 | 0.03175 | 0.00032 | 0.604858 |  201.5 |  1.98 |  206.6 |  3.11 |  265.8 |  39.11 |  201.5 |  1.98 |
| ISIS-12 |  65.82 |  78.09 | 0.842874 |  0.23348 | 0.00743 | 0.03315 | 0.00036 | 0.341256 |  210.2 |  2.26 |  213.1 |  6.11 |  245.1 |  74.23 |  210.2 |  2.26 |
| ISIS-61 | 305.97 | 218.59 | 1.39974  |  0.24164 | 0.01159 | 0.03474 | 0.00051 | 0.306074 |  220.2 |  3.18 |  219.8 |  9.48 |  216.3 | 110.85 |  220.2 |  3.18 |
| ISIS-14 |  80.05 | 121.04 | 0.661352 |  0.25395 | 0.00727 | 0.03518 | 0.00041 | 0.407101 |  222.9 |  2.55 |  229.8 |  5.89 |  301.5 |  65.5  |  222.9 |  2.55 |
| ISIS-8  | 193.52 | 220.71 | 0.876807 |  0.25399 | 0.0062  | 0.0357  | 0.00038 | 0.436054 |  226.1 |  2.39 |  229.8 |  5.02 |  268.2 |  56.76 |  226.1 |  2.39 |
| ISIS-15 |  95.12 |  89.09 | 1.06768  |  0.25363 | 0.00607 | 0.03593 | 0.00036 | 0.418656 |  227.5 |  2.27 |  229.5 |  4.92 |  250.3 |  56.38 |  227.5 |  2.27 |
| ISIS-47 | 227.69 | 134.81 | 1.68897  |  0.25204 | 0.0075  | 0.03603 | 0.00042 | 0.391736 |  228.2 |  2.62 |  228.2 |  6.08 |  228.7 |  68.93 |  228.2 |  2.62 |
| ISIS-38 | 388.4  | 318.61 | 1.21905  |  0.24928 | 0.00804 | 0.03631 | 0.00044 | 0.375714 |  229.9 |  2.71 |  226   |  6.53 |  185.9 |  74.6  |  229.9 |  2.71 |
| ISIS-55 | 262.05 | 124.1  | 2.1116   |  0.26014 | 0.01028 | 0.03648 | 0.00049 | 0.339903 |  231   |  3.06 |  234.8 |  8.28 |  273.6 |  90.31 |  231   |  3.06 |
| ISIS-52 | 213.03 | 105.1  | 2.02693  |  0.26733 | 0.01002 | 0.0372  | 0.00047 | 0.337081 |  235.4 |  2.9  |  240.6 |  8.03 |  291.4 |  85.62 |  235.4 |  2.9  |
| ISIS-6  | 148.48 | 283.31 | 0.52409  |  0.26666 | 0.0048  | 0.03864 | 0.0004  | 0.575095 |  244.4 |  2.46 |  240   |  3.85 |  198   |  42.49 |  244.4 |  2.46 |
| ISIS-60 | 352.02 | 258.33 | 1.36268  |  0.31453 | 0.01724 | 0.04032 | 0.00068 | 0.30769  |  254.8 |  4.24 |  277.7 | 13.31 |  474.8 | 120.27 |  254.8 |  4.24 |
| ISIS-9  |  40.69 |  81.63 | 0.498469 |  0.30521 | 0.00809 | 0.04157 | 0.00045 | 0.408397 |  262.6 |  2.81 |  270.5 |  6.29 |  339.7 |  60.4  |  262.6 |  2.81 |
| ISIS-18 |  63.03 | 178.62 | 0.352872 |  0.32039 | 0.0074  | 0.04462 | 0.00051 | 0.494866 |  281.4 |  3.14 |  282.2 |  5.69 |  289.3 |  52.75 |  281.4 |  3.14 |
| ISIS-56 | 439.6  |  60.87 | 7.22195  |  0.31979 | 0.00936 | 0.0453  | 0.00053 | 0.39973  |  285.6 |  3.25 |  281.7 |  7.2  |  250.2 |  67.94 |  285.6 |  3.25 |
| ISIS-13 |  89.27 | 226.55 | 0.394041 |  0.32909 | 0.00567 | 0.04649 | 0.00043 | 0.536835 |  292.9 |  2.63 |  288.9 |  4.33 |  256.9 |  41.69 |  292.9 |  2.63 |
| ISIS-66 | 290.76 | 204.63 | 1.42091  |  0.43808 | 0.01474 | 0.05908 | 0.00069 | 0.347108 |  370   |  4.21 |  368.9 | 10.4  |  362.3 |  77.16 |  370   |  4.21 |
| ISIS-45 | 343.63 |  49.9  | 6.88637  |  0.57342 | 0.01531 | 0.07362 | 0.00083 | 0.42226  |  457.9 |  5.01 |  460.2 |  9.88 |  471.1 |  59.66 |  457.9 |  5.01 |
| ISIS-1  |  44.39 |  85.62 | 0.518454 |  0.67417 | 0.01406 | 0.08443 | 0.00092 | 0.522487 |  522.5 |  5.46 |  523.2 |  8.53 |  526.1 |  46.43 |  522.5 |  5.46 |
| ISIS-11 | 148.65 | 367.93 | 0.404017 |  0.69816 | 0.00888 | 0.08598 | 0.00079 | 0.72239  |  531.7 |  4.7  |  537.7 |  5.31 |  563.5 |  29.86 |  531.7 |  4.7  |
| ISIS-49 | 163.77 |  69.17 | 2.36764  |  0.71478 | 0.02118 | 0.08796 | 0.00098 | 0.376    |  543.4 |  5.79 |  547.6 | 12.54 |  565.2 |  65.2  |  543.4 |  5.79 |
| ISIS-21 |  37.18 |  77.86 | 0.477524 |  0.74808 | 0.01391 | 0.09108 | 0.00094 | 0.555042 |  561.9 |  5.54 |  567.1 |  8.08 |  588.3 |  41.42 |  561.9 |  5.54 |
| ISIS-34 |  40.18 | 120.47 | 0.333527 |  0.82029 | 0.01716 | 0.10022 | 0.00102 | 0.486515 |  615.7 |  5.99 |  608.2 |  9.57 |  580.4 |  47.3  |  615.7 |  5.99 |
| ISIS-72 | 205.23 |  39.62 | 5.17996  |  1.01624 | 0.04228 | 0.11778 | 0.00166 | 0.338764 |  717.8 |  9.57 |  712   | 21.29 |  694.6 |  89.52 |  717.8 |  9.57 |
| ISIS-22 |  36.76 |  83.24 | 0.441615 |  1.56343 | 0.02438 | 0.15888 | 0.00157 | 0.633688 |  950.6 |  8.71 |  955.8 |  9.66 |  968.3 |  33.27 |  950.6 |  8.71 |
| ISIS-53 | 197.74 |  59.36 | 3.3312   |  1.65352 | 0.05363 | 0.16669 | 0.00213 | 0.393978 |  993.8 | 11.76 |  990.9 | 20.52 |  984.7 |  66.17 |  993.8 | 11.76 |
| ISIS-46 | 153.54 | 102.52 | 1.49766  |  1.74533 | 0.04832 | 0.17514 | 0.00197 | 0.406286 | 1040.4 | 10.79 | 1025.4 | 17.87 |  994   |  56.71 |  994   | 56.71 |
| ISIS-32 |  77.17 | 179.83 | 0.429128 |  2.06545 | 0.04666 | 0.18653 | 0.0021  | 0.498357 | 1102.6 | 11.43 | 1137.4 | 15.45 | 1205.2 |  45.79 | 1205.2 | 45.79 |
| ISIS-58 | 157.75 | 268.52 | 0.58748  |  1.98967 | 0.04814 | 0.19054 | 0.00201 | 0.435998 | 1124.3 | 10.86 | 1112   | 16.35 | 1088.4 |  49.71 | 1088.4 | 49.71 |
| ISIS-27 |  39.4  |  89.69 | 0.439291 | 11.3967  | 0.13125 | 0.45428 | 0.00413 | 0.789417 | 2414.3 | 18.31 | 2556.2 | 10.75 | 2671   |  20.9  | 2671   | 20.9  |
| ISIS-68 | 230.71 |  64.53 | 3.57524  | 12.8449  | 0.62898 | 0.48835 | 0.00779 | 0.325761 | 2563.6 | 33.73 | 2668.3 | 46.13 | 2749.1 |  80.65 | 2749.1 | 80.65 |
| ISIS-67 |  74.33 |  31.84 | 2.33448  | 17.01    | 0.53937 | 0.57667 | 0.00678 | 0.370784 | 2935.1 | 27.7  | 2935.4 | 30.41 | 2935.9 |  52.68 | 2935.9 | 52.68 |
| ISIS-29 |  13.21 |  18.02 | 0.733074 | 22.1319  | 0.27691 | 0.61423 | 0.00596 | 0.775523 | 3086.9 | 23.82 | 3189.5 | 12.16 | 3255   |  21.14 | 3255   | 21.14 |



label: D=B/C
labeled_formulas: D=B/C
output: {"Arithmetic-Relationship": ["D=B/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_636684___xlsx_c946dbe1866e597a1a69ac7a739e04b9da6e8499.xlsx___line_527