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 |
|:------------|------:|------:|---------:|---------:|--------:|--------:|--------:|---------:|-------:|------:|-------:|------:|-------:|-------:|-------:|------:|
| Longmac1-72 | 16.01 | 20.61 | 0.776807 |  0.10978 | 0.00378 | 0.01603 | 0.0002  | 0.36235  |  102.5 |  1.25 |  105.8 |  3.46 |  179.3 |  80.63 |  102.5 |  1.25 |
| Longmac1-10 |  2.52 |  3.07 | 0.820847 |  0.10761 | 0.00639 | 0.01606 | 0.00025 | 0.262148 |  102.7 |  1.57 |  103.8 |  5.86 |  129.5 | 137.08 |  102.7 |  1.57 |
| Longmac1-7  |  5.45 | 11.2  | 0.486607 |  0.114   | 0.00556 | 0.01631 | 0.00024 | 0.301708 |  104.3 |  1.55 |  109.6 |  5.07 |  227.3 | 111.31 |  104.3 |  1.55 |
| Longmac1-34 |  8.81 |  8.69 | 1.01381  |  0.11208 | 0.00378 | 0.01632 | 0.00019 | 0.345199 |  104.3 |  1.23 |  107.9 |  3.46 |  186.7 |  78.78 |  104.3 |  1.23 |
| Longmac1-19 | 17.57 | 16.07 | 1.09334  |  0.11215 | 0.00413 | 0.01636 | 0.00019 | 0.315369 |  104.6 |  1.23 |  107.9 |  3.77 |  182.3 |  86.14 |  104.6 |  1.23 |
| Longmac1-51 | 20.21 | 40.57 | 0.498151 |  0.10788 | 0.0019  | 0.01656 | 0.00016 | 0.548589 |  105.9 |  1.02 |  104   |  1.74 |   61.9 |  43.77 |  105.9 |  1.02 |
| Longmac1-50 |  4.69 |  6.18 | 0.7589   |  0.10935 | 0.00413 | 0.01664 | 0.0002  | 0.318233 |  106.4 |  1.26 |  105.4 |  3.78 |   81.7 |  90.34 |  106.4 |  1.26 |
| Longmac1-8  |  6.89 | 11.39 | 0.604917 |  0.10767 | 0.00317 | 0.01666 | 0.00019 | 0.387359 |  106.5 |  1.23 |  103.8 |  2.9  |   42.9 |  70.58 |  106.5 |  1.23 |
| Longmac1-18 | 15.29 | 17.88 | 0.855145 |  0.11175 | 0.00271 | 0.01682 | 0.00018 | 0.441291 |  107.5 |  1.14 |  107.6 |  2.48 |  108.6 |  57.95 |  107.5 |  1.14 |
| Longmac1-64 |  7.01 | 18.19 | 0.385377 |  0.1119  | 0.00247 | 0.01693 | 0.00017 | 0.45491  |  108.2 |  1.1  |  107.7 |  2.25 |   94.9 |  54.48 |  108.2 |  1.1  |
| Longmac1-47 | 12.93 | 13.12 | 0.985518 |  0.11509 | 0.00306 | 0.01694 | 0.00019 | 0.421848 |  108.3 |  1.18 |  110.6 |  2.78 |  160.5 |  62.73 |  108.3 |  1.18 |
| Longmac1-40 |  4.18 |  5.53 | 0.755877 |  0.11271 | 0.00623 | 0.01719 | 0.00026 | 0.273635 |  109.9 |  1.67 |  108.4 |  5.68 |   76.8 | 129.76 |  109.9 |  1.67 |
| Longmac1-3  | 15.61 | 26.26 | 0.59444  |  0.11545 | 0.00427 | 0.01735 | 0.00021 | 0.327255 |  110.9 |  1.35 |  110.9 |  3.88 |  113   |  87.03 |  110.9 |  1.35 |
| Longmac1-42 |  3.64 |  4.94 | 0.736842 |  0.11556 | 0.00697 | 0.01737 | 0.00028 | 0.267259 |  111   |  1.75 |  111   |  6.34 |  112.2 | 139.84 |  111   |  1.75 |
| Longmac1-44 |  4.71 |  4.35 | 1.08276  |  0.11946 | 0.00493 | 0.01754 | 0.00022 | 0.303927 |  112.1 |  1.41 |  114.6 |  4.47 |  167.6 |  96.14 |  112.1 |  1.41 |
| Longmac1-26 |  8.81 | 10.91 | 0.807516 |  0.12513 | 0.00368 | 0.01842 | 0.00021 | 0.387653 |  117.7 |  1.32 |  119.7 |  3.32 |  160.3 |  69.15 |  117.7 |  1.32 |
| Longmac1-33 |  3.74 |  8.84 | 0.423077 |  0.12967 | 0.00504 | 0.01843 | 0.00023 | 0.321079 |  117.7 |  1.47 |  123.8 |  4.53 |  242.2 |  89.46 |  117.7 |  1.47 |
| Longmac1-21 | 23.46 | 16.64 | 1.40986  |  0.12821 | 0.00562 | 0.01883 | 0.00025 | 0.302883 |  120.3 |  1.61 |  122.5 |  5.06 |  165.7 | 101.78 |  120.3 |  1.61 |
| Longmac1-16 |  4.43 |  7.59 | 0.583663 |  0.12221 | 0.00548 | 0.01891 | 0.00024 | 0.283039 |  120.8 |  1.54 |  117.1 |  4.96 |   42.9 | 106.88 |  120.8 |  1.54 |
| Longmac1-24 |  8.34 | 16.02 | 0.520599 |  0.1271  | 0.00418 | 0.01914 | 0.00022 | 0.349502 |  122.2 |  1.42 |  121.5 |  3.76 |  107.8 |  77.77 |  122.2 |  1.42 |
| Longmac1-1  | 18.62 | 34.58 | 0.538462 |  0.14766 | 0.0035  | 0.02188 | 0.00024 | 0.462763 |  139.5 |  1.53 |  139.8 |  3.1  |  145.2 |  55.79 |  139.5 |  1.53 |
| Longmac1-60 |  2.71 |  5.43 | 0.499079 |  0.15844 | 0.00512 | 0.02222 | 0.00025 | 0.34817  |  141.6 |  1.61 |  149.3 |  4.49 |  273.5 |  74.6  |  141.6 |  1.61 |
| Longmac1-54 | 11.75 | 14.3  | 0.821678 |  0.17914 | 0.00486 | 0.02278 | 0.00026 | 0.420703 |  145.2 |  1.62 |  167.3 |  4.18 |  493   |  61.14 |  145.2 |  1.62 |
| Longmac1-37 | 26.7  | 29.84 | 0.894772 |  0.15871 | 0.00303 | 0.02347 | 0.00024 | 0.535624 |  149.6 |  1.5  |  149.6 |  2.65 |  149.8 |  45.62 |  149.6 |  1.5  |
| Longmac1-55 | 20.49 | 44.13 | 0.46431  |  0.17775 | 0.00289 | 0.02636 | 0.00025 | 0.583319 |  167.7 |  1.59 |  166.1 |  2.49 |  144   |  39.74 |  167.7 |  1.59 |
| Longmac1-13 |  2.11 |  3.84 | 0.549479 |  0.19829 | 0.01061 | 0.02834 | 0.00044 | 0.29016  |  180.2 |  2.79 |  183.7 |  8.99 |  229.2 | 121.55 |  180.2 |  2.79 |
| Longmac1-31 | 21.11 | 11.79 | 1.7905   |  0.21027 | 0.00952 | 0.02939 | 0.0004  | 0.300608 |  186.8 |  2.52 |  193.8 |  7.99 |  280.3 | 103.19 |  186.8 |  2.52 |
| Longmac1-12 |  5.62 |  9.62 | 0.5842   |  0.21885 | 0.00615 | 0.0302  | 0.00035 | 0.412413 |  191.8 |  2.19 |  200.9 |  5.12 |  310   |  64.07 |  191.8 |  2.19 |
| Longmac1-20 |  6.34 |  7.05 | 0.899291 |  0.24772 | 0.00562 | 0.03022 | 0.00032 | 0.466746 |  191.9 |  2.03 |  224.7 |  4.57 |  583.7 |  50.03 |  191.9 |  2.03 |
| Longmac1-14 | 14.53 | 23.16 | 0.627375 |  0.2071  | 0.00377 | 0.03032 | 0.00031 | 0.561657 |  192.5 |  1.91 |  191.1 |  3.17 |  174   |  43.35 |  192.5 |  1.91 |
| Longmac1-25 |  8.57 |  9.74 | 0.879877 |  0.20734 | 0.00484 | 0.03056 | 0.00032 | 0.448574 |  194   |  2    |  191.3 |  4.07 |  158.4 |  55.48 |  194   |  2    |
| Longmac1-53 |  6.13 | 11.73 | 0.522592 |  0.2163  | 0.00679 | 0.03132 | 0.00037 | 0.376328 |  198.8 |  2.33 |  198.8 |  5.67 |  199.5 |  73.14 |  198.8 |  2.33 |
| Longmac1-5  | 16.87 | 23.97 | 0.703796 |  0.21314 | 0.00362 | 0.03136 | 0.00031 | 0.582026 |  199.1 |  1.94 |  196.2 |  3.03 |  161.9 |  40.65 |  199.1 |  1.94 |
| Longmac1-46 |  9.66 | 18.39 | 0.525285 |  0.22042 | 0.00394 | 0.03197 | 0.00032 | 0.559967 |  202.9 |  1.98 |  202.3 |  3.28 |  195.4 |  42.72 |  202.9 |  1.98 |
| Longmac1-28 |  5.65 |  4.56 | 1.23904  |  0.22089 | 0.01006 | 0.03241 | 0.00044 | 0.298093 |  205.6 |  2.73 |  202.6 |  8.37 |  168.5 | 105.81 |  205.6 |  2.73 |
| Longmac1-23 | 15    | 20.51 | 0.731351 |  0.22418 | 0.004   | 0.03283 | 0.00032 | 0.546281 |  208.2 |  2.03 |  205.4 |  3.32 |  173.1 |  42.71 |  208.2 |  2.03 |
| Longmac1-2  | 14.97 | 13.77 | 1.08715  |  0.25524 | 0.00803 | 0.0365  | 0.00046 | 0.400588 |  231.1 |  2.86 |  230.8 |  6.5  |  228.2 |  72.18 |  231.1 |  2.86 |
| Longmac1-35 |  4.16 |  5.9  | 0.705085 |  0.27318 | 0.00824 | 0.03737 | 0.00044 | 0.390347 |  236.5 |  2.72 |  245.2 |  6.57 |  329.9 |  68.89 |  236.5 |  2.72 |
| Longmac1-45 | 14.02 | 15.78 | 0.888466 |  0.25683 | 0.00573 | 0.03769 | 0.0004  | 0.475691 |  238.5 |  2.5  |  232.1 |  4.63 |  167.8 |  52.82 |  238.5 |  2.5  |
| Longmac1-65 | 22.06 | 27.33 | 0.807172 |  0.27105 | 0.00446 | 0.03903 | 0.00038 | 0.591697 |  246.8 |  2.34 |  243.5 |  3.56 |  212.2 |  39.67 |  246.8 |  2.34 |
| Longmac1-62 | 28.87 | 26.83 | 1.07603  |  0.28983 | 0.00572 | 0.041   | 0.00044 | 0.543771 |  259.1 |  2.7  |  258.4 |  4.5  |  252.7 |  46.02 |  259.1 |  2.7  |
| Longmac1-43 | 12.51 | 21.15 | 0.591489 |  0.29262 | 0.00668 | 0.04181 | 0.00044 | 0.460999 |  264   |  2.74 |  260.6 |  5.25 |  230.2 |  53.67 |  264   |  2.74 |
| Longmac1-48 | 18.33 | 31.16 | 0.588254 |  0.29355 | 0.00477 | 0.04183 | 0.00041 | 0.603198 |  264.1 |  2.53 |  261.3 |  3.74 |  236.6 |  38.76 |  264.1 |  2.53 |
| Longmac1-27 |  5.45 | 14.72 | 0.370245 |  0.32357 | 0.00743 | 0.04569 | 0.00051 | 0.486103 |  288   |  3.16 |  284.6 |  5.7  |  257.5 |  52.83 |  288   |  3.16 |
| Longmac1-22 |  4.9  | 12.53 | 0.391061 |  0.33008 | 0.01266 | 0.0463  | 0.00064 | 0.3604   |  291.8 |  3.97 |  289.6 |  9.66 |  272.6 |  86.88 |  291.8 |  3.97 |
| Longmac1-49 | 12.42 | 22.28 | 0.557451 |  0.40177 | 0.0062  | 0.05475 | 0.00052 | 0.615467 |  343.6 |  3.19 |  342.9 |  4.49 |  338.6 |  36.38 |  343.6 |  3.19 |
| Longmac1-41 |  1.66 |  3.68 | 0.451087 |  0.44955 | 0.0159  | 0.0603  | 0.00078 | 0.365728 |  377.5 |  4.72 |  377   | 11.14 |  373.9 |  79.34 |  377.5 |  4.72 |
| Longmac1-9  |  5.66 |  9.14 | 0.619256 |  0.51472 | 0.00875 | 0.06918 | 0.00068 | 0.578218 |  431.2 |  4.13 |  421.6 |  5.86 |  369.9 |  39.41 |  431.2 |  4.13 |
| Longmac1-15 | 15.31 | 20.15 | 0.759801 |  0.59548 | 0.01165 | 0.07635 | 0.00082 | 0.548967 |  474.3 |  4.93 |  474.4 |  7.41 |  474.3 |  43.98 |  474.3 |  4.93 |
| Longmac1-61 |  2.87 | 13.83 | 0.20752  |  0.60194 | 0.01527 | 0.07681 | 0.00082 | 0.420833 |  477   |  4.93 |  478.5 |  9.68 |  484.6 |  58.25 |  477   |  4.93 |
| Longmac1-73 |  5.57 | 11.98 | 0.464942 |  0.66222 | 0.01142 | 0.08155 | 0.00079 | 0.561745 |  505.4 |  4.73 |  516   |  6.98 |  563.4 |  39.23 |  505.4 |  4.73 |
| Longmac1-36 | 15.07 | 17.74 | 0.849493 |  0.66108 | 0.01232 | 0.08246 | 0.00078 | 0.507568 |  510.8 |  4.67 |  515.3 |  7.53 |  535   |  43.18 |  510.8 |  4.67 |
| Longmac1-11 |  7.85 | 13.82 | 0.568017 |  0.65604 | 0.01061 | 0.08253 | 0.0008  | 0.599367 |  511.2 |  4.77 |  512.2 |  6.51 |  516.6 |  37.04 |  511.2 |  4.77 |
| Longmac1-69 | 10.2  | 29.81 | 0.342167 |  0.659   | 0.01058 | 0.0834  | 0.00083 | 0.619886 |  516.4 |  4.93 |  514   |  6.48 |  503.2 |  36.49 |  516.4 |  4.93 |
| Longmac1-71 |  2.05 |  2.71 | 0.756458 |  0.71726 | 0.02466 | 0.0884  | 0.00107 | 0.352059 |  546.1 |  6.35 |  549   | 14.58 |  561.5 |  75.97 |  546.1 |  6.35 |
| Longmac1-32 | 11.02 | 14.62 | 0.753762 |  0.71607 | 0.01106 | 0.0908  | 0.00085 | 0.606085 |  560.3 |  5.04 |  548.3 |  6.55 |  498.8 |  35.74 |  560.3 |  5.04 |
| Longmac1-38 |  8.99 | 26.69 | 0.33683  |  0.74932 | 0.0114  | 0.09196 | 0.00091 | 0.650436 |  567.1 |  5.39 |  567.8 |  6.62 |  570.9 |  34.06 |  567.1 |  5.39 |
| Longmac1-17 |  4.04 | 10.78 | 0.374768 |  0.84923 | 0.02096 | 0.10263 | 0.00122 | 0.481637 |  629.8 |  7.15 |  624.2 | 11.51 |  604.3 |  53.2  |  629.8 |  7.15 |
| Longmac1-68 |  6.32 | 12.26 | 0.515498 |  0.85527 | 0.01361 | 0.10454 | 0.00098 | 0.5891   |  641   |  5.73 |  627.5 |  7.45 |  579.7 |  36.59 |  641   |  5.73 |
| Longmac1-56 |  2.93 |  6.41 | 0.457098 |  1.05249 | 0.0425  | 0.11925 | 0.00165 | 0.342653 |  726.3 |  9.5  |  730.1 | 21.02 |  742   |  86.15 |  726.3 |  9.5  |
| Longmac1-4  |  1.38 |  3.97 | 0.347607 |  1.45715 | 0.02689 | 0.14727 | 0.0016  | 0.588734 |  885.6 |  8.97 |  912.8 | 11.11 |  979.7 |  37.92 |  885.6 |  8.97 |
| Longmac1-39 | 21.35 | 16.09 | 1.32691  |  1.90565 | 0.03383 | 0.18671 | 0.00196 | 0.59133  | 1103.6 | 10.64 | 1083.1 | 11.82 | 1042.4 |  36.46 | 1042.4 | 36.46 |
| Longmac1-70 |  1.47 |  5.83 | 0.252144 |  2.15373 | 0.03473 | 0.20508 | 0.00193 | 0.583607 | 1202.6 | 10.35 | 1166.3 | 11.18 | 1099.6 |  34.36 | 1099.6 | 34.36 |
| Longmac1-63 |  5.04 |  3.66 | 1.37705  |  2.45238 | 0.04178 | 0.22096 | 0.00215 | 0.571142 | 1287   | 11.33 | 1258.1 | 12.29 | 1209.4 |  35.32 | 1209.4 | 35.32 |
| Longmac1-52 | 23.97 | 31.02 | 0.772727 |  2.8059  | 0.04122 | 0.22518 | 0.00218 | 0.659008 | 1309.2 | 11.45 | 1357.1 | 11    | 1433.6 |  29.35 | 1433.6 | 29.35 |
| Longmac1-58 |  6.15 | 13.4  | 0.458955 |  7.94088 | 0.10951 | 0.404   | 0.00392 | 0.70359  | 2187.4 | 18.01 | 2224.3 | 12.44 | 2258.6 |  24.93 | 2258.6 | 24.93 |
| Longmac1-29 | 16.46 | 19.07 | 0.863136 | 12.9743  | 0.25572 | 0.50336 | 0.00483 | 0.486842 | 2628.2 | 20.69 | 2677.8 | 18.58 | 2715.7 |  34.08 | 2715.7 | 34.08 |
| Longmac1-59 |  8.13 | 12.2  | 0.666393 | 12.9186  | 0.16432 | 0.51961 | 0.00485 | 0.733818 | 2697.5 | 20.57 | 2673.7 | 11.99 | 2656   |  22.52 | 2656   | 22.52 |
| Longmac1-6  |  9.28 | 12.69 | 0.731284 | 19.9322  | 0.23746 | 0.62658 | 0.00617 | 0.826558 | 3136   | 24.47 | 3088.1 | 11.52 | 3057.3 |  19.5  | 3057.3 | 19.5  |



label: D=B/C
labeled_formulas: D=B/C
output: {"Arithmetic-Relationship": ["D=B/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_107260___xlsx_bcf20ee4fc2756512b982e02837f5980f282b2a1.xlsx___line_595