This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
---|---|---|---|---|---|---|---|---|
24 | substitute LHS of expr 1 into expr 2 |
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LHS diff is pdg7882 - pdg8251 RHS diff is 0 |
6774684564:
8497631728: 8283354808: |
6774684564:
8497631728: 8283354808: |
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13 | substitute LHS of expr 1 into expr 2 |
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valid |
7107090465:
5125940051: 1525861537: |
7107090465:
5125940051: 1525861537: |
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29 | substitute LHS of expr 1 into expr 2 |
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LHS diff is -pdg2435 + pdg7882 RHS diff is 0 |
8602221482:
8497631728: 6240206408: |
8602221482:
8497631728: 6240206408: |
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18 | substitute LHS of four expressions into expr |
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no check performed |
4192519596:
4504256452: 1357848476: 7621705408: |
4192519596:
4504256452: 1357848476: 7621705408: |
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15 | change variable X to Y |
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LHS diff is pdg3192 - pdg4453 RHS diff is (Abs(pdg3192) - Abs(pdg4453))*exp(pdg1575*pdg4621) |
4182362050:
1357848476: |
4182362050:
1357848476: |
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25 | declare initial expr |
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no validation is available for declarations |
2719691582:
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2719691582:
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31 | simplify |
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valid |
6529793063:
3060393541: |
6529793063:
3060393541: |
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22 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is (-2*exp(pdg4621*(pdg1575 - pdg8586))*cos(pdg1575 - pdg8586)*Abs(pdg4453*pdg4698) + Abs(pdg4453*pdg4698*Abs(exp(pdg4621*(pdg1575 - pdg8586))*Abs(pdg4698) + Abs(pdg4453))))*exp(-pdg4621*(pdg1575 - pdg8586)) |
2700934933:
error for dim with 2700934933 3085575328: 8497631728: |
2700934933:
N/A 3085575328: 8497631728: |
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17 | conjugate both sides |
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no check performed |
4192519596:
4504256452: |
4192519596:
4504256452: |
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33 | declare final expr |
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no validation is available for declarations |
6556875579:
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6556875579:
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10 | change variable X to Y |
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Nothing to split |
3350830826:
4075539836: |
3350830826:
4075539836: |
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5 | declare initial expr |
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no validation is available for declarations |
8396997949:
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8396997949:
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19 | simplify |
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LHS diff is 0 RHS diff is -exp(-pdg1575*pdg4621 + pdg4621*pdg8586)*Abs(pdg4453*pdg4698*Abs(exp(pdg1575*pdg4621 - pdg4621*pdg8586)*Abs(pdg4698) + Abs(pdg4453))) + exp(pdg1575*pdg4621 - pdg4621*pdg8586 - re(pdg1575*pdg4621))*Abs(pdg4453*pdg4698*Abs(exp(pdg1575*pdg4621)*Abs(pdg4453) + exp(pdg4621*pdg8586)*Abs(pdg4698))) |
7621705408:
3085575328: |
7621705408:
3085575328: |
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20 | change variable X to Y |
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LHS diff is 0 RHS diff is exp(pdg1464*pdg4621)/2 - exp(-pdg1575*pdg4621 + pdg4621*pdg8586)/2 - exp(pdg1575*pdg4621 - pdg4621*pdg8586)/2 + exp(-pdg1464*pdg4621)/2 |
4585932229:
3660957533: error for dim with 3660957533 |
4585932229:
3660957533: N/A |
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6 | change variable X to Y |
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Nothing to split |
3350830826:
2236639474: |
3350830826:
2236639474: |
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32 | divide expr 1 by expr 2 |
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no check performed |
1172039918:
3060393541: 6556875579: |
1172039918:
3060393541: 6556875579: |
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11 | change variable X to Y |
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Nothing to split |
3350830826:
7107090465: |
3350830826:
7107090465: |
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27 | simplify |
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valid |
8046208134:
1172039918: |
8046208134:
1172039918: |
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3 | multiply expr 1 by expr 2 |
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Nothing to split |
4182362050:
1928085940: 9191880568: |
4182362050:
1928085940: 9191880568: |
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8 | distribute conjugate to factors |
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no check performed |
1020854560:
6306552185: |
1020854560:
6306552185: |
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23 | declare initial expr |
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no validation is available for declarations |
6774684564:
|
6774684564:
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1 | declare initial expr |
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no validation is available for declarations |
4182362050:
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4182362050:
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14 | change two variables in expr |
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Nothing to split |
7607271250:
4192519596: |
7607271250:
4192519596: |
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12 | substitute LHS of expr 1 into expr 2 |
|
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valid |
4075539836:
8065128065: 5125940051: |
4075539836:
8065128065: 5125940051: |
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28 | declare initial expr |
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no validation is available for declarations |
8602221482:
|
8602221482:
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4 | simplify |
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Nothing to split |
9191880568:
3350830826: |
9191880568:
3350830826: |
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7 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is -(pdg4453 + pdg4698)*(conjugate(pdg4453) + conjugate(pdg4698)) + Abs(pdg4453 + pdg4698)**2 |
2236639474:
8396997949: 1020854560: |
2236639474:
8396997949: 1020854560: |
|
30 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is -2*Abs(pdg4453)**2 + 2*Abs(pdg4698)**2 |
2719691582:
6240206408: 6529793063: |
2719691582:
6240206408: 6529793063: |
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26 | substitute LHS of expr 1 into expr 2 |
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LHS diff is 0 RHS diff is -4*Abs(pdg4453)**2 + 4*Abs(pdg4698)**2 |
2719691582:
8283354808: 8046208134: |
2719691582:
8283354808: 8046208134: |
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9 | simplify |
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valid |
6306552185:
8065128065: |
6306552185:
8065128065: |
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2 | conjugate both sides |
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Nothing to split |
4182362050:
1928085940: |
4182362050:
1928085940: |
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16 | conjugate both sides |
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no check performed |
1357848476:
6555185548: |
1357848476:
6555185548: |
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21 | multiply both sides by |
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valid |
3660957533:
error for dim with 3660957533 2700934933: error for dim with 2700934933 |
3660957533:
N/A 2700934933: N/A |