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:
|   H |        I |        J |        K |        L |   M |   N |   O |   P |   Q |   R |   S |
|----:|---------:|---------:|---------:|---------:|----:|----:|----:|----:|----:|----:|----:|
|  25 | 1        | 1        | 1        | 1        | 1   | 1   | 1   |  25 | 1   | 1   | 1   |
|  26 | 0.96591  | 1        | 1        | 1        | 1   | 1   | 1   |  26 | 1   | 1   | 1   |
|  27 | 0.93182  | 1        | 1        | 1        | 1   | 1   | 1   |  27 | 1   | 1   | 1   |
|  28 | 0.89773  | 1        | 1        | 1        | 1   | 1   | 1   |  28 | 1   | 1   | 1   |
|  29 | 0.86364  | 1        | 1        | 1        | 1   | 1   | 1   |  29 | 1   | 1   | 1   |
|  30 | 0.82955  | 1        | 1        | 1        | 1   | 1   | 1   |  30 | 1   | 1   | 1   |
|  31 | 0.801996 | 1        | 1        | 1        | 1   | 1   | 1   |  31 | 1   | 1   | 1   |
|  32 | 0.774442 | 1        | 1        | 1        | 1   | 1   | 1   |  32 | 1   | 1   | 1   |
|  33 | 0.746888 | 1        | 1        | 1        | 1   | 1   | 1   |  33 | 1   | 1   | 1   |
|  34 | 0.719334 | 1        | 1        | 1        | 1   | 1   | 1   |  34 | 1   | 1   | 1   |
|  35 | 0.69178  | 1        | 1        | 1        | 1   | 1   | 1   |  35 | 1   | 1   | 1   |
|  36 | 0.669386 | 1        | 1        | 1        | 1   | 1   | 1   |  36 | 1   | 1   | 1   |
|  37 | 0.646992 | 1        | 1        | 1        | 1   | 1   | 1   |  37 | 1   | 1   | 1   |
|  38 | 0.624598 | 1        | 1        | 1        | 1   | 1   | 1   |  38 | 1   | 1   | 1   |
|  39 | 0.602204 | 1        | 1        | 1        | 1   | 1   | 1   |  39 | 1   | 1   | 1   |
|  40 | 0.57981  | 1        | 1        | 1        | 1   | 1   | 1   |  40 | 1   | 1   | 1   |
|  41 | 0.561516 | 1        | 1        | 1        | 1   | 1   | 1   |  41 | 1   | 1   | 1   |
|  42 | 0.543222 | 1        | 1        | 1        | 1   | 1   | 1   |  42 | 1   | 1   | 1   |
|  43 | 0.524928 | 1        | 1        | 1        | 1   | 1   | 1   |  43 | 1   | 1   | 1   |
|  44 | 0.506634 | 1        | 1        | 1        | 1   | 1   | 1   |  44 | 1   | 1   | 1   |
|  45 | 0.48834  | 1        | 1        | 1        | 1   | 1   | 1   |  45 | 1   | 1   | 1   |
|  46 | 0.473316 | 1        | 1        | 1        | 1   | 1   | 1   |  46 | 1   | 1   | 1   |
|  47 | 0.458292 | 1        | 1        | 1        | 1   | 1   | 1   |  47 | 1   | 1   | 1   |
|  48 | 0.443268 | 1        | 1        | 1        | 1   | 1   | 1   |  48 | 1   | 1   | 1   |
|  49 | 0.428244 | 1        | 1        | 1        | 1   | 1   | 1   |  49 | 1   | 1   | 1   |
|  50 | 0.41322  | 1        | 1        | 1        | 1   | 1   | 1   |  50 | 1   | 1   | 1   |
|  51 | 0.400824 | 1        | 1        | 1        | 1   | 1   | 1   |  51 | 1   | 1   | 1   |
|  52 | 0.388428 | 1        | 1        | 1        | 1   | 1   | 1   |  52 | 1   | 1   | 1   |
|  53 | 0.376032 | 1        | 1        | 1        | 1   | 1   | 1   |  53 | 1   | 1   | 1   |
|  54 | 0.363636 | 1        | 1        | 1        | 1   | 1   | 1   |  54 | 1   | 1   | 1   |
|  55 | 0.35124  | 1        | 1        | 1        | 1   | 1   | 1   |  55 | 1   | 1   | 1   |
|  56 | 0.34096  | 1        | 1        | 1        | 1   | 1   | 1   |  56 | 1   | 1   | 1   |
|  57 | 0.33068  | 1        | 1        | 1        | 1   | 1   | 1   |  57 | 1   | 1   | 1   |
|  58 | 0.3204   | 1        | 1        | 1        | 1   | 1   | 1   |  58 | 1   | 1   | 1   |
|  59 | 0.31012  | 1        | 1        | 1        | 1   | 1   | 1   |  59 | 1   | 1   | 1   |
|  60 | 0.29984  | 1        | 1        | 1        | 1   | 1   | 1   |  60 | 1   | 1   | 1   |
|  61 | 0.29128  | 1        | 1        | 1        | 1   | 1   | 1   |  61 | 1   | 1   | 1   |
|  62 | 0.28272  | 1        | 1        | 1        | 1   | 1   | 1   |  62 | 1   | 1   | 1   |
|  63 | 0.27416  | 1        | 1        | 1        | 1   | 1   | 1   |  63 | 1   | 1   | 1   |
|  64 | 0.2656   | 1        | 1        | 1        | 1   | 1   | 1   |  64 | 1   | 1   | 1   |
|  65 | 0.25704  | 1        | 1        | 1        | 1   | 1   | 1   |  65 | 1   | 1   | 1   |
|  66 | 0.249878 | 1        | 1        | 1        | 1   | 1   | 1   |  66 | 1   | 1   | 1   |
|  67 | 0.242716 | 1        | 1        | 1        | 1   | 1   | 1   |  67 | 1   | 1   | 1   |
|  68 | 0.235554 | 1        | 1        | 1        | 1   | 1   | 1   |  68 | 1   | 1   | 1   |
|  69 | 0.228392 | 1        | 1        | 1        | 1   | 1   | 1   |  69 | 1   | 1   | 1   |
|  70 | 0.22123  | 1        | 1        | 1        | 1   | 1   | 1   |  70 | 1   | 1   | 1   |
|  71 | 0.215212 | 1        | 1        | 1        | 1   | 1   | 1   |  71 | 1   | 1   | 1   |
|  72 | 0.209194 | 1        | 1        | 1        | 1   | 1   | 1   |  72 | 1   | 1   | 1   |
|  73 | 0.203176 | 1        | 1        | 1        | 1   | 1   | 1   |  73 | 1   | 1   | 1   |
|  74 | 0.197158 | 1        | 1        | 1        | 1   | 1   | 1   |  74 | 1   | 1   | 1   |
|  75 | 0.19114  | 1        | 1        | 1        | 1   | 1   | 1   |  75 | 1   | 1   | 1   |
|  76 | 0.186066 | 1        | 1        | 1        | 1   | 1   | 1   |  76 | 1   | 1   | 1   |
|  77 | 0.180992 | 1        | 1        | 1        | 1   | 1   | 1   |  77 | 1   | 1   | 1   |
|  78 | 0.175918 | 1        | 1        | 1        | 1   | 1   | 1   |  78 | 1   | 1   | 1   |
|  79 | 0.170844 | 1        | 1        | 1        | 1   | 1   | 1   |  79 | 1   | 1   | 1   |
|  80 | 0.16577  | 1        | 1        | 1        | 1   | 1   | 1   |  80 | 1   | 1   | 1   |
|  81 | 0.16147  | 1        | 1        | 1        | 1   | 1   | 1   |  81 | 1   | 1   | 1   |
|  82 | 0.15717  | 1        | 1        | 1        | 1   | 1   | 1   |  82 | 1   | 1   | 1   |
|  83 | 0.15287  | 1        | 1        | 1        | 1   | 1   | 1   |  83 | 1   | 1   | 1   |
|  84 | 0.14857  | 1        | 1        | 1        | 1   | 1   | 1   |  84 | 1   | 1   | 1   |
|  85 | 0.14427  | 1        | 1        | 1        | 1   | 1   | 1   |  85 | 1   | 1   | 1   |
|  86 | 0.140616 | 1        | 1        | 1        | 1   | 1   | 1   |  86 | 1   | 1   | 1   |
|  87 | 0.136962 | 1        | 1        | 1        | 1   | 1   | 1   |  87 | 1   | 1   | 1   |
|  88 | 0.133308 | 1        | 1        | 1        | 1   | 1   | 1   |  88 | 1   | 1   | 1   |
|  89 | 0.129654 | 1        | 1        | 1        | 1   | 1   | 1   |  89 | 1   | 1   | 1   |
|  90 | 0.126    | 1        | 1        | 1        | 1   | 1   | 1   |  90 | 1   | 1   | 1   |
|  91 | 0.122882 | 1        | 1        | 1        | 1   | 1   | 1   |  91 | 1   | 1   | 1   |
|  92 | 0.119764 | 1        | 1        | 1        | 1   | 1   | 1   |  92 | 1   | 1   | 1   |
|  93 | 0.116646 | 1        | 1        | 1        | 1   | 1   | 1   |  93 | 1   | 1   | 1   |
|  94 | 0.113528 | 1        | 1        | 1        | 1   | 1   | 1   |  94 | 1   | 1   | 1   |
|  95 | 0.11041  | 1        | 1        | 1        | 1   | 1   | 1   |  95 | 1   | 1   | 1   |
|  96 | 0.107741 | 1        | 1        | 1        | 1   | 1   | 1   |  96 | 1   | 1   | 1   |
|  97 | 0.105072 | 1        | 1        | 1        | 1   | 1   | 1   |  97 | 1   | 1   | 1   |
| 124 | 0.054576 | 0.596608 | 0.633896 | 0.671184 | 0.5 | 0.5 | 0.5 | 124 | 0.5 | 0.5 | 0.5 |
| 125 | 0.053285 | 0.58628  | 0.622923 | 0.659565 | 0.5 | 0.5 | 0.5 | 125 | 0.5 | 0.5 | 0.5 |
| 126 | 0.052168 | 0.577344 | 0.613428 | 0.649512 | 0.5 | 0.5 | 0.5 | 126 | 0.5 | 0.5 | 0.5 |
| 127 | 0.051051 | 0.568408 | 0.603934 | 0.639459 | 0.5 | 0.5 | 0.5 | 127 | 0.5 | 0.5 | 0.5 |
| 128 | 0.049934 | 0.559472 | 0.594439 | 0.629406 | 0.5 | 0.5 | 0.5 | 128 | 0.5 | 0.5 | 0.5 |
| 129 | 0.048817 | 0.550536 | 0.584944 | 0.619353 | 0.5 | 0.5 | 0.5 | 129 | 0.5 | 0.5 | 0.5 |
| 130 | 0.0477   | 0.5416   | 0.57545  | 0.6093   | 0.5 | 0.5 | 0.5 | 130 | 0.5 | 0.5 | 0.5 |
| 131 | 0.0467   | 0.5336   | 0.56695  | 0.6003   | 0.5 | 0.5 | 0.5 | 131 | 0.5 | 0.5 | 0.5 |
| 132 | 0.0457   | 0.5256   | 0.55845  | 0.5913   | 0.5 | 0.5 | 0.5 | 132 | 0.5 | 0.5 | 0.5 |
| 133 | 0.0447   | 0.5176   | 0.54995  | 0.5823   | 0.5 | 0.5 | 0.5 | 133 | 0.5 | 0.5 | 0.5 |
| 134 | 0.0437   | 0.5096   | 0.54145  | 0.5733   | 0.5 | 0.5 | 0.5 | 134 | 0.5 | 0.5 | 0.5 |
| 135 | 0.0427   | 0.5016   | 0.53295  | 0.5643   | 0.5 | 0.5 | 0.5 | 135 | 0.5 | 0.5 | 0.5 |



labeled_formulas: P=(H+M)-N
Q=(H+M)-P
P=(H+N)-O
R=(H+N)-P
S=(H+O)-P
R=(M-N)+O
R=(M-N)+S
Q=(M-O)+S
Q=(N-O)+R
S=(N-Q)+R
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_22584___xlsx_9b8cb53d396681bd2c73684b75387ba33b58edd5.xlsx___line_683