Ultimate 5-limit again

27/25 [[1, 2, 3], [0, -2, -3]] [1200., 268.056438833948093748427143263]
3.739252 35.609240 1861.731473

135/128 [[1, 2, 1], [0, -1, 3]] [1200., 522.862345874111793591855751693]
4.132031 18.077734 1275.365360

256/243 [[5, 8, 12], [0, 0, -1]] [240., 84.6637865678588914278600509674]
5.493061 12.759741 2114.877638

25/24 [[1, 1, 2], [0, 2, 1]] [1200., 350.977500432693708872243366367]
3.025593 28.851897 799.108711

648/625 [[4, 6, 9], [0, 1, 1]] [300., 94.1343573651111175944350240576]
6.437752 11.060060 2950.938432

16875/16384 [[1, 2, 2], [0, -4, 3]] [1200., 126.238272015257926746682149917]
8.172550 5.942563 3243.743713

250/243 [[1, 2, 3], [0, -3, -5]] [1200., 162.996026370546548951179738408]
5.948286 7.975801 1678.609846

128/125 [[3, 5, 7], [0, -1, 0]] [400., 91.2018560670299909777049249654]
4.828314 9.677666 1089.323984

3125/3072 [[1, 0, 2], [0, 5, 1]] [1200., 379.967949195094816842076920201]
7.741412 4.569472 2119.954990

20000/19683 [[1, 1, 1], [0, 4, 9]] [1200., 176.282270436412295298990817071]
9.785568 2.504205 2346.540676

531441/524288 [[12, 19, 28], [0, 0, -1]] [100., 14.6637865678588914278600509674]
13.183347 1.382394 3167.444999

81/80 [[1, 2, 4], [0, -1, -4]] [1200., 503.835154026035812053011163756]
4.132031 4.217731 297.556531

2048/2025 [[2, 3, 5], [0, 1, -2]] [600., 105.446531009812541696859310996]
6.271199 2.612822 644.408867

67108864/66430125 [[3, 5, 6], [0, -1, 4]] [400., 96.7879385616949726317268914802]
15.510107 .905187 3377.402314

78732/78125 [[1, -1, -1], [0, 7, 9]] [1200., 442.979297439105373735900374126]
12.192182 1.157498 2097.802867

393216/390625 [[1, -1, 2], [0, 8, 1]] [1200., 387.819673068349143521938606127]
12.543123 1.071950 2115.395301

2109375/2097152 [[1, 0, 3], [0, 7, -3]] [1200., 271.589599585245148575185388331]
12.772341 .800410 1667.723301

4294967296/4271484375 [[1, 2, 2], [0, -9, 7]] [1200., 55.2754932571412314963954609732]
18.573955 .483108 3095.692488

15625/15552 [[1, 0, 1], [0, 6, 5]] [1200., 317.079675185758890225628070818]
9.338935 1.029625 838.631548

1600000/1594323 [[1, 3, 6], [0, -5, -13]] [1200., 339.508825625715624367834924710]
13.794200 .383104 1005.555381

``(2)^8*``(3)^14/``(5)^13 [[1, 5, 6], [0, -13, -14]] [1200., 315.250913337821936408197840098]
21.322672 .276603 2681.521263

``(2)^24*``(5)^4/``(3)^21 [[1, 0, -6], [0, 4, 21]] [1200., 475.542233398945960632986914825]
21.733049 .153767 1578.433204

``(2)^23*``(3)^6/``(5)^14 [[2, 4, 5], [0, -7, -3]] [600., 71.1460635722374759764193142621]
21.207625 .194018 1850.624306

``(5)^19/``(2)^14/``(3)^19 [[19, 30, 44], [0, 1, 1]] [63.1578947368421052631578947368, 7.29225210195322285759291880280]
30.579320 .104784 2996.244873

``(3)^18*``(5)^17/``(2)^68 [[1, 0, 4], [0, 17, -18]] [1200., 111.875426120872633513689333181]
38.845486 .058853 3449.774562

``(2)^39*``(5)^3/``(3)^29 [[1, 3, 16], [0, -3, -29]] [1200., 565.988014913065527948022354197]
30.550812 .057500 1639.596150

``(3)^8*``(5)/``(2)^15 [[1, 2, -1], [0, -1, 8]] [1200., 498.272487171563819993901705714]
9.459948 .161693 136.885775

``(3)^45/``(2)^69/``(5) [[1, 2, 21], [0, -1, -45]] [1200., 498.082318148218414995068857757]
48.911647 .026391 3088.065497

``(2)^38/``(3)^2/``(5)^15 [[1, 4, 2], [0, -15, 2]] [1200., 193.199614933859969427837273253]
24.977022 .060822 947.732642

``(3)^35/``(2)^16/``(5)^17 [[1, -1, -3], [0, 17, 35]] [1200., 182.466089137089694182158775289]
38.845486 .025466 1492.763207

``(2)*``(5)^18/``(3)^27 [[9, 15, 22], [0, -2, -3]] [133.333333333333333333333333333, 49.0088197863290461293795242156]
33.653272 .025593 975.428947

``(2)^91/``(3)^12/``(5)^31 [[1, 5, 1], [0, -31, 12]] [1200., 132.194510561451335831533197063]
55.785793 .014993 2602.883149

``(3)^10*``(5)^16/``(2)^53 [[2, 1, 6], [0, 8, -5]] [600., 162.741892126380267669129153916]
31.255737 .017725 541.228379

``(2)^37*``(3)^25/``(5)^33 [[1, 17, 14], [0, -33, -25]] [1200., 560.546969532517954992081849041]
50.788153 .012388 1622.898233

``(5)^51/``(2)^36/``(3)^52 [[1, 15, 16], [0, -51, -52]] [1200., 315.647874693157629813083932838]
82.462759 .004660 2613.109284

``(2)^54*``(5)^2/``(3)^37 [[1, 2, 10], [0, -2, -37]] [1200., 249.018447894645757478665305415]
39.665603 .005738 358.125500

``(3)^47*``(5)^14/``(2)^107 [[1, -1, 11], [0, 14, -47]] [1200., 221.567865486043404513033481373]
62.992219 .003542 885.454661

``(2)^144/``(3)^22/``(5)^47 [[1, -2, 4], [0, 47, -22]] [1200., 91.5310212152783702805100052719]
86.914326 .002842 1866.076786

``(3)^62/``(2)^17/``(5)^35 [[1, 11, 19], [0, -35, -62]] [1200., 322.801386591774163833303551406]
72.066208 .003022 1131.212237

``(5)^86/``(2)^19/``(3)^114 [[2, 14, 19], [0, -43, -57]] [600., 151.117308517283810511306888810]
151.691690 .000751 2621.929721

``(3)^54*``(5)^110/``(2)^341 [[2, -22, 17], [0, 55, -27]] [600., 274.580992585158530361667961540]
205.015253 .000385 3314.979642

``(2)^232*``(5)^25/``(3)^183 [[1, 4, 20], [0, -25, -183]] [1200., 115.921782028626355899175361808]
191.093312 .000319 2223.857514

``(2)^71*``(5)^37/``(3)^99 [[1, -9, -26], [0, 37, 99]] [1200., 343.296099168149974701274380276]
104.663080 .000511 586.422003

``(5)^49/``(2)^90/``(3)^15 [[1, -6, 0], [0, 49, 15]] [1200., 185.754178875831648371588872508]
74.858154 .000761 319.341867

``(3)^69*``(5)^61/``(2)^251 [[1, -22, 29], [0, 61, -69]] [1200., 463.966471361838581203914769766]
143.055244 .000194 566.898668

``(3)^153*``(5)^73/``(2)^412 [[1, 38, -74], [0, -73, 153]] [1200., 598.603357209211686645273006535]
235.664038 .000052 683.835625

``(2)^161/``(3)^84/``(5)^12 [[12, 19, 28], [0, 1, -7]] [100., 1.95516929663126752661956897955]
100.527798 .000120 121.841527

``(2)^734/``(3)^321/``(5)^97 [[1, 18, -52], [0, -97, 321]] [1200., 203.072628472983063961058412679]
431.645735 .000032 2593.925421

``(2)^21*``(3)^290/``(5)^207 [[1, 102, 143], [0, -207, -290]] [1200., 582.116159570683278092118297257]
374.222680 .000025 1307.744113

``(2)^140*``(5)^195/``(3)^374 [[1, 40, 76], [0, -195, -374]] [1200., 236.400230712381991918098066318]
423.433817 .000023 1718.344823

``(3)^237*``(5)^85/``(2)^573 [[1, 39, -102], [0, -85, 237]] [1200., 528.212294142246315995699039809]
332.899311 .000006 209.606840

thanks gene!

look at this:

/tuning/database?
method=reportRows&tbl=10&sortBy=5&sortDir=up

the only thing i'd like is the numerator and denominator of each
comma -- full digits. yahoo's sort doesn't recognize scientific
notation. this way i can still sort by heuristic complexity.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:
> 27/25 [[1, 2, 3], [0, -2, -3]] [1200.,
268.056438833948093748427143263]
> 3.739252 35.609240 1861.731473
>
>
> 135/128 [[1, 2, 1], [0, -1, 3]] [1200.,
522.862345874111793591855751693]
> 4.132031 18.077734 1275.365360
>
>
> 256/243 [[5, 8, 12], [0, 0, -1]] [240.,
84.6637865678588914278600509674]
> 5.493061 12.759741 2114.877638
>
>
> 25/24 [[1, 1, 2], [0, 2, 1]] [1200.,
350.977500432693708872243366367]
> 3.025593 28.851897 799.108711
>
>
> 648/625 [[4, 6, 9], [0, 1, 1]] [300.,
94.1343573651111175944350240576]
> 6.437752 11.060060 2950.938432
>
>
> 16875/16384 [[1, 2, 2], [0, -4, 3]] [1200.,
126.238272015257926746682149917]
> 8.172550 5.942563 3243.743713
>
>
> 250/243 [[1, 2, 3], [0, -3, -5]] [1200.,
162.996026370546548951179738408]
> 5.948286 7.975801 1678.609846
>
>
> 128/125 [[3, 5, 7], [0, -1, 0]] [400.,
91.2018560670299909777049249654]
> 4.828314 9.677666 1089.323984
>
>
> 3125/3072 [[1, 0, 2], [0, 5, 1]] [1200.,
379.967949195094816842076920201]
> 7.741412 4.569472 2119.954990
>
>
> 20000/19683 [[1, 1, 1], [0, 4, 9]] [1200.,
176.282270436412295298990817071]
> 9.785568 2.504205 2346.540676
>
>
> 531441/524288 [[12, 19, 28], [0, 0, -1]] [100.,
14.6637865678588914278600509674]
> 13.183347 1.382394 3167.444999
>
>
> 81/80 [[1, 2, 4], [0, -1, -4]] [1200.,
503.835154026035812053011163756]
> 4.132031 4.217731 297.556531
>
>
> 2048/2025 [[2, 3, 5], [0, 1, -2]] [600.,
105.446531009812541696859310996]
> 6.271199 2.612822 644.408867
>
>
> 67108864/66430125 [[3, 5, 6], [0, -1, 4]] [400.,
96.7879385616949726317268914802]
> 15.510107 .905187 3377.402314
>
>
> 78732/78125 [[1, -1, -1], [0, 7, 9]] [1200.,
442.979297439105373735900374126]
> 12.192182 1.157498 2097.802867
>
>
> 393216/390625 [[1, -1, 2], [0, 8, 1]] [1200.,
387.819673068349143521938606127]
> 12.543123 1.071950 2115.395301
>
>
> 2109375/2097152 [[1, 0, 3], [0, 7, -3]] [1200.,
271.589599585245148575185388331]
> 12.772341 .800410 1667.723301
>
>
> 4294967296/4271484375 [[1, 2, 2], [0, -9, 7]] [1200.,
55.2754932571412314963954609732]
> 18.573955 .483108 3095.692488
>
>
> 15625/15552 [[1, 0, 1], [0, 6, 5]] [1200.,
317.079675185758890225628070818]
> 9.338935 1.029625 838.631548
>
>
> 1600000/1594323 [[1, 3, 6], [0, -5, -13]] [1200.,
339.508825625715624367834924710]
> 13.794200 .383104 1005.555381
>
>
> ``(2)^8*``(3)^14/``(5)^13 [[1, 5, 6], [0, -13, -14]] [1200.,
315.250913337821936408197840098]
> 21.322672 .276603 2681.521263
>
>
> ``(2)^24*``(5)^4/``(3)^21 [[1, 0, -6], [0, 4, 21]] [1200.,
475.542233398945960632986914825]
> 21.733049 .153767 1578.433204
>
>
> ``(2)^23*``(3)^6/``(5)^14 [[2, 4, 5], [0, -7, -3]] [600.,
71.1460635722374759764193142621]
> 21.207625 .194018 1850.624306
>
>
> ``(5)^19/``(2)^14/``(3)^19 [[19, 30, 44], [0, 1, 1]]
[63.1578947368421052631578947368, 7.29225210195322285759291880280]
> 30.579320 .104784 2996.244873
>
>
> ``(3)^18*``(5)^17/``(2)^68 [[1, 0, 4], [0, 17, -18]] [1200.,
111.875426120872633513689333181]
> 38.845486 .058853 3449.774562
>
>
> ``(2)^39*``(5)^3/``(3)^29 [[1, 3, 16], [0, -3, -29]] [1200.,
565.988014913065527948022354197]
> 30.550812 .057500 1639.596150
>
>
> ``(3)^8*``(5)/``(2)^15 [[1, 2, -1], [0, -1, 8]] [1200.,
498.272487171563819993901705714]
> 9.459948 .161693 136.885775
>
>
> ``(3)^45/``(2)^69/``(5) [[1, 2, 21], [0, -1, -45]] [1200.,
498.082318148218414995068857757]
> 48.911647 .026391 3088.065497
>
>
> ``(2)^38/``(3)^2/``(5)^15 [[1, 4, 2], [0, -15, 2]] [1200.,
193.199614933859969427837273253]
> 24.977022 .060822 947.732642
>
>
> ``(3)^35/``(2)^16/``(5)^17 [[1, -1, -3], [0, 17, 35]] [1200.,
182.466089137089694182158775289]
> 38.845486 .025466 1492.763207
>
>
> ``(2)*``(5)^18/``(3)^27 [[9, 15, 22], [0, -2, -3]]
[133.333333333333333333333333333, 49.0088197863290461293795242156]
> 33.653272 .025593 975.428947
>
>
> ``(2)^91/``(3)^12/``(5)^31 [[1, 5, 1], [0, -31, 12]] [1200.,
132.194510561451335831533197063]
> 55.785793 .014993 2602.883149
>
>
> ``(3)^10*``(5)^16/``(2)^53 [[2, 1, 6], [0, 8, -5]] [600.,
162.741892126380267669129153916]
> 31.255737 .017725 541.228379
>
>
> ``(2)^37*``(3)^25/``(5)^33 [[1, 17, 14], [0, -33, -25]] [1200.,
560.546969532517954992081849041]
> 50.788153 .012388 1622.898233
>
>
> ``(5)^51/``(2)^36/``(3)^52 [[1, 15, 16], [0, -51, -52]] [1200.,
315.647874693157629813083932838]
> 82.462759 .004660 2613.109284
>
>
> ``(2)^54*``(5)^2/``(3)^37 [[1, 2, 10], [0, -2, -37]] [1200.,
249.018447894645757478665305415]
> 39.665603 .005738 358.125500
>
>
> ``(3)^47*``(5)^14/``(2)^107 [[1, -1, 11], [0, 14, -47]] [1200.,
221.567865486043404513033481373]
> 62.992219 .003542 885.454661
>
>
> ``(2)^144/``(3)^22/``(5)^47 [[1, -2, 4], [0, 47, -22]] [1200.,
91.5310212152783702805100052719]
> 86.914326 .002842 1866.076786
>
>
> ``(3)^62/``(2)^17/``(5)^35 [[1, 11, 19], [0, -35, -62]] [1200.,
322.801386591774163833303551406]
> 72.066208 .003022 1131.212237
>
>
> ``(5)^86/``(2)^19/``(3)^114 [[2, 14, 19], [0, -43, -57]] [600.,
151.117308517283810511306888810]
> 151.691690 .000751 2621.929721
>
>
> ``(3)^54*``(5)^110/``(2)^341 [[2, -22, 17], [0, 55, -27]] [600.,
274.580992585158530361667961540]
> 205.015253 .000385 3314.979642
>
>
> ``(2)^232*``(5)^25/``(3)^183 [[1, 4, 20], [0, -25, -183]] [1200.,
115.921782028626355899175361808]
> 191.093312 .000319 2223.857514
>
>
> ``(2)^71*``(5)^37/``(3)^99 [[1, -9, -26], [0, 37, 99]] [1200.,
343.296099168149974701274380276]
> 104.663080 .000511 586.422003
>
>
> ``(5)^49/``(2)^90/``(3)^15 [[1, -6, 0], [0, 49, 15]] [1200.,
185.754178875831648371588872508]
> 74.858154 .000761 319.341867
>
>
> ``(3)^69*``(5)^61/``(2)^251 [[1, -22, 29], [0, 61, -69]] [1200.,
463.966471361838581203914769766]
> 143.055244 .000194 566.898668
>
>
> ``(3)^153*``(5)^73/``(2)^412 [[1, 38, -74], [0, -73, 153]] [1200.,
598.603357209211686645273006535]
> 235.664038 .000052 683.835625
>
>
> ``(2)^161/``(3)^84/``(5)^12 [[12, 19, 28], [0, 1, -7]] [100.,
1.95516929663126752661956897955]
> 100.527798 .000120 121.841527
>
>
> ``(2)^734/``(3)^321/``(5)^97 [[1, 18, -52], [0, -97, 321]] [1200.,
203.072628472983063961058412679]
> 431.645735 .000032 2593.925421
>
>
> ``(2)^21*``(3)^290/``(5)^207 [[1, 102, 143], [0, -207, -290]]
[1200., 582.116159570683278092118297257]
> 374.222680 .000025 1307.744113
>
>
> ``(2)^140*``(5)^195/``(3)^374 [[1, 40, 76], [0, -195, -374]]
[1200., 236.400230712381991918098066318]
> 423.433817 .000023 1718.344823
>
>
> ``(3)^237*``(5)^85/``(2)^573 [[1, 39, -102], [0, -85, 237]] [1200.,
528.212294142246315995699039809]
> 332.899311 .000006 209.606840

> look at this:
>
> /tuning/database?
> method=reportRows&tbl=10&sortBy=5&sortDir=up

This's great! I don't see the heuristic on it,
though.

-C.

--- In tuning-math@yahoogroups.com, "Carl Lumma <clumma@y...>"
<clumma@y...> wrote:
> > look at this:
> >
> > /tuning/database?
> > method=reportRows&tbl=10&sortBy=5&sortDir=up
>
> This's great! I don't see the heuristic on it,
> though.
>
> -C.

yahoo only supports 10 columns. i deleted the heuristic error since
the RMS error has a visual correlate (distance from origin to
corresponding line) on the corresponding graph.

you're probably asking about heuristic complexity, though, since i
wrote,

"the only thing i'd like is the numerator and denominator of each
comma -- full digits. yahoo's sort doesn't recognize scientific
notation. this way i can still sort by heuristic complexity."

by which i meant that sorting by denominator is the same as sorting
by heuristic complexity. so you can now sort by heuristic complexity
only until scientific notation comes in.

> yahoo only supports 10 columns. i deleted the heuristic error
> since the RMS error has a visual correlate (distance from
> origin to corresponding line) on the corresponding graph.

Yep; another nice thing about RMS.

But how does heuristic error differ from RMS?

> you're probably asking about heuristic complexity, though,

Yep.

> by which i meant that sorting by denominator is the same as
> sorting by heuristic complexity. so you can now sort by
> heuristic complexity only until scientific notation comes in.

Understood.

-C.

--- In tuning-math@yahoogroups.com, "Carl Lumma <clumma@y...>"
<clumma@y...> wrote:
> > yahoo only supports 10 columns. i deleted the heuristic error
> > since the RMS error has a visual correlate (distance from
> > origin to corresponding line) on the corresponding graph.
>
> Yep; another nice thing about RMS.
>
> But how does heuristic error differ from RMS?

not too much -- less than a factor of 2 in every case that i've seen.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> thanks gene!
>
> look at this:
>
> /tuning/database?
> method=reportRows&tbl=10&sortBy=5&sortDir=up

Neat! What criterion did you use to select the ones you report on?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > thanks gene!
> >
> > look at this:
> >
> > /tuning/database?
> > method=reportRows&tbl=10&sortBy=5&sortDir=up
>
> Neat! What criterion did you use to select the ones you report on?

we went through this here on this list after you posted your big
list. remember? i just cut things off after atomic because there was
a big gap there.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith
> <genewardsmith@j...>" <genewardsmith@j...> wrote:
> > --- In tuning-math@yahoogroups.com, "wallyesterpaulrus
> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > > thanks gene!
> > >
> > > look at this:
> > >
> > > /tuning/database?
> > > method=reportRows&tbl=10&sortBy=5&sortDir=up
> >
> > Neat! What criterion did you use to select the ones you report on?
>
> we went through this here on this list after you posted your big
> list. remember? i just cut things off after atomic because there
was
> a big gap there.

that is, i cut things off by complexity, not by your ordering, which
was by the just size of the comma of all things.

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith
> <genewardsmith@j...>" <genewardsmith@j...> wrote:
> > --- In tuning-math@yahoogroups.com, "wallyesterpaulrus
> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > > thanks gene!
> > >
> > > look at this:
> > >
> > > /tuning/database?
> > > method=reportRows&tbl=10&sortBy=5&sortDir=up
> >
> > Neat! What criterion did you use to select the ones you report on?
>
> we went through this here on this list after you posted your big
> list. remember? i just cut things off after atomic because there
was
> a big gap there.

i would have liked ampersand in there, though . . .

--- In tuning-math@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@yahoogroups.com, "wallyesterpaulrus
> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > --- In tuning-math@yahoogroups.com, "Gene Ward Smith
> > <genewardsmith@j...>" <genewardsmith@j...> wrote:
> > > --- In tuning-math@yahoogroups.com, "wallyesterpaulrus
> > <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > > > thanks gene!
> > > >
> > > > look at this:
> > > >
> > > > /tuning/database?
> > > > method=reportRows&tbl=10&sortBy=5&sortDir=up
> > >
> > > Neat! What criterion did you use to select the ones you report
on?
> >
> > we went through this here on this list after you posted your big
> > list. remember? i just cut things off after atomic because there
> was
> > a big gap there.
>
> that is, i cut things off by complexity, not by your ordering,
which
> was by the just size of the comma of all things.

which is the same sort implemented in the url above -- maybe you just
forgot to click on "next"?