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Talk:Feigenbaum constant calculation: Difference between revisions
Talk:Feigenbaum constant calculation (view source)
Revision as of 00:47, 16 November 2018
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==true value of Feigenbaum's constant==
Since the true value of Feigenbaum's constant isn't shown here on this Rosetta Code task, I added the displaying of it in the REXX example, along with the displaying of the number of correct decimal digits for each (<big>'''i'''</big>) iteration. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 06:28, 19 September 2018 (UTC)
==degree of accuracy with more precision during computing==
I was experimenting with increasing the number of decimal digits (precision) with the REXX example.
For '''10''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 10 decimal digits:
correct
────i──── ──digits─── ─────d─────
2 0 3.218511415
3 1 4.385677676
4 2 4.600948689
5 2 4.65513455
6 3 4.666093465
7 3 4.668532629
8 4 4.669075367
9 3 4.661840596
10 1 4.716700473
11 1 4.865131579
12 0 33.77777778
13 0 -0.004986149584
14 0 -0.004986146524
15 0 -0.003986261738
16 0 -0.0178044264
17 0 -0.169923567
18 0 -0.2743411539
19 0 -0.2916348706
20 0 -0.2917038238
true value= 4.669201609
</pre>
For '''20''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 20 decimal digits:
correct
────i──── ──digits─── ──────────d──────────
2 0 3.2185114220380879119
3 1 4.3856775985683390848
4 2 4.6009492765380753389
5 2 4.655130495391980231
6 3 4.6661119478285698075
7 3 4.668548581446857975
8 4 4.6690606606480870955
9 4 4.6691715553802316722
10 4 4.6691951560255308919
11 6 4.6692002291211212557
12 7 4.6692013127842230631
13 7 4.6692015485437548544
14 9 4.6692016005633566634
15 7 4.6692015330312737776
16 6 4.6692023823679005527
17 4 4.6691972211443265305
18 6 4.6692074719138228098
19 4 4.6694187571119124281
20 3 4.6688146048792985728
true value= 4.6692016091029906719
</pre>
For '''30''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 30 decimal digits:
correct
────i──── ──digits─── ───────────────d───────────────
2 0 3.21851142203808791227050453077
3 1 4.3856775985683390857449485682
4 2 4.60094927653807535781169469969
5 2 4.65513049539198013648625498649
6 3 4.66611194782857138833121364654
7 3 4.66854858144684094804454708811
8 4 4.66906066064826823913257549468
9 4 4.6691715553795113888859465442
10 4 4.66919515603001717402161720542
11 6 4.66920022908685649793393149233
12 7 4.66920131329420417113719511412
13 7 4.66920154578090670783369507315
14 7 4.66920159553749390966169074155
15 9 4.66920160619815215840788706632
16 9 4.66920160848080435144581223484
17 9 4.66920160896974538458267849027
18 10 4.66920160907444981238909862845
19 10 4.66920160909687888294310165196
20 12 4.66920160910169069039564432665
true value= 4.66920160910299067185320382047
</pre>
For '''40''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 40 decimal digits:
correct
i digits d
2 0 3.218511422038087912270504530742813256018
3 1 4.385677598568339085744948568775522346173
4 2 4.600949276538075357811694698623834984934
5 2 4.655130495391980136486254995856898818963
6 3 4.666111947828571388331213696711776471107
7 3 4.668548581446840948044543680148146102083
8 4 4.669060660648268239132599822630273970875
9 4 4.669171555379511388886004609897560033836
10 4 4.669195156030017174021108801191558304938
11 6 4.669200229086856497938353781003810044639
12 7 4.66920131329420417116475494118414885682
13 7 4.669201545780906707506058109960038118631
14 7 4.669201595537493910292470639266101619701
15 9 4.669201606198152157723831098067070167449
16 9 4.669201608480804423294067936197345435789
17 9 4.66920160896974470048248536837343166496
18 10 4.669201609074452566227981315990238717244
19 10 4.66920160909687879470513360848001376754
20 12 4.669201609101681681186958959033209022075
true value= 4.669201609102990671853203820466201617258
</pre>
For '''50''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 50 decimal digits:
correct
i digits d
2 0 3.2185114220380879122705045307428132560288203779709
3 1 4.3856775985683390857449485687755223461032163565761
4 2 4.6009492765380753578116946986238349850235524966338
5 2 4.6551304953919801364862549958568988194754604973163
6 3 4.6661119478285713883312136967117764807190589709335
7 3 4.6685485814468409480445436801481462655432879036191
8 4 4.6690606606482682391325998226302726377996820048001
9 4 4.6691715553795113888860046098975670882406762637156
10 4 4.6691951560300171740211088011914920933921530026738
11 6 4.6692002290868564979383537810040672174088979117872
12 7 4.6692013132942041711647549411855711837281506913619
13 7 4.669201545780906707506058109930429736433895282946
14 7 4.6692015955374939102924706392896460400580631742226
15 9 4.669201606198152157723831097078594524390001462635
16 9 4.6692016084808044232940679458986228433868918971945
17 9 4.6692016089697447004824853219383733420478533710096
18 10 4.6692016090744525662279815203708867655911039176535
19 10 4.6692016090968787947051350378647834642184844514321
20 12 4.6692016091016816811869601608458025942520519239165
true value= 4.6692016091029906718532038204662016172581855774758
</pre>
For '''60''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 60 decimal digits:
correct
i digits d
2 0 3.21851142203808791227050453074281325602882037797108219914195
3 1 4.38567759856833908574494856877552234610321635657649780870002
4 2 4.60094927653807535781169469862383498502355249663354337228864
5 2 4.65513049539198013648625499585689881947546049738522607840669
6 3 4.66611194782857138833121369671177648071905897173694216387654
7 3 4.66854858144684094804454368014814626554328789665434875726458
8 4 4.66906066064826823913259982263027263779968209542149739645327
9 4 4.6691715553795113888860046098975670882406765731707896864092
10 4 4.66919515603001717402110880119149209339214790860575667043884
11 6 4.66920022908685649793835378100406721740888804890682292715866
12 7 4.66920131329420417116475494118557118372824888898657591993058
13 7 4.6692015457809067075060581099304297364315643304525960728651
14 7 4.66920159553749391029247063928964604007454741248894160626657
15 9 4.66920160619815215772383109707859452442133651601886184881893
16 9 4.66920160848080442329406794589862284279286838186077964235606
17 9 4.66920160896974470048248532193837334390738554123097139976161
18 10 4.66920160907445256622798152037088675394609964381174635788482
19 10 4.66920160909687879470513503786478367762266653874157074386282
20 12 4.66920160910168168118696016084580172992808891003148562640334
true value= 4.66920160910299067185320382046620161725818557747576863274565
</pre>
For '''70''' decimal digits:
<pre>
Using 10 iterations for maxJ, with 70 decimal digits:
correct
i digits d
2 0 3.218511422038087912270504530742813256028820377971082199141994437483264
3 1 4.385677598568339085744948568775522346103216356576497808699630752612707
4 2 4.600949276538075357811694698623834985023552496633543372295593454453943
5 2 4.655130495391980136486254995856898819475460497385226078363311588173369
6 3 4.666111947828571388331213696711776480719058971736942163972368911928369
7 3 4.668548581446840948044543680148146265543287896654348757317309551877191
8 4 4.669060660648268239132599822630272637799682095421497400522886796129394
9 4 4.669171555379511388886004609897567088240676573170789783804375123155331
10 4 4.669195156030017174021108801191492093392147908605756405516325953901305
11 6 4.669200229086856497938353781004067217408888048906823830162962197636106
12 7 4.669201313294204171164754941185571183728248888986548913352218691391234
13 7 4.669201545780906707506058109930429736431564330452605295006133445674219
14 7 4.669201595537493910292470639289646040074547412490596040512697122945726
15 9 4.669201606198152157723831097078594524421336516011873717994576148241557
16 9 4.669201608480804423294067945898622842792868381815074127666008519547807
17 9 4.669201608969744700482485321938373343907385540992447405914541777669855
18 10 4.669201609074452566227981520370886753946099646679618269983331571360562
19 10 4.669201609096878794705135037864783677622666525741836726551719975589237
20 12 4.669201609101681681186960160845801729928088893244076177775471467408333
true value= 4.669201609102990671853203820466201617258185577475768632745651343004134
</pre>
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