commatic efficiency

One measure I would propose of how 'easy' or 'efficient' a comma can be
produced, 'commatic efficiency':

In the 7-limit, we take a 'decrease' in the size of the minimum 'comma'
available for a 'taxicab distance' of 1 (8/7 in the 7-limit) minus our target
comma, and divide that 'gain' by the 'pain' of getting there (the number of
'taxicab steps' to produce it).

I hope that wasn't too confusing....

formula:

commatic_efficiency"=(smallest_available_interval_in_given_limit_by_taxicab_distance_of_1-target_interval)/target_interval_taxicab_distance

so for the 7-limit, if we sort by decreasing commatic efficiency, we see that
64/63 is the most efficient:

decimal ratio monzo dist. efficiency
1.01587 64/63 [ 6, -2, 0, -1> 3 0.04233
1.02083 49/48 [ -4, -1, 0, 2> 3 0.04067
1.02400 128/125 [ 7, 0, -3, 0> 3 0.03962
1.06667 16/15 [ 4, -1, -1, 0> 2 0.03810
1.04167 25/24 [ -3, -1, 2, 0> 3 0.03373
1.04490 256/245 [ 8, 0, -1, -2> 3 0.03265
1.05000 21/20 [ -2, 1, -1, 1> 3 0.03095
1.02041 50/49 [ 1, 0, 2, -2> 4 0.03061
1.02539 525/512 [ -9, 1, 2, 1> 4 0.02937
1.02857 36/35 [ 2, 2, -1, -1> 4 0.02857
1.00446 225/224 [ -5, 2, 2, -1> 5 0.02768
1.03704 28/27 [ 2, -3, 0, 1> 4 0.02646
1.01250 81/80 [ -4, 4, -1, 0> 5 0.02607
1.09375 35/32 [ -5, 0, 1, 1> 2 0.02455
1.07143 15/14 [ -1, 1, 1, -1> 3 0.02381
1.00310 6144/6125 [ 11, 1, -3, -2> 6 0.02329
1.00800 126/125 [ 1, 2, -3, 1> 6 0.02248
1.05469 135/128 [ -7, 3, 1, 0> 4 0.02204
1.01136 2048/2025 [ 11, -4, -2, 0> 6 0.02192
1.00042 2401/2400 [ -5, -1, -2, 4> 7 0.02035
1.00352 3136/3125 [ 6, 0, -5, 2> 7 0.01991
1.02357 12288/12005 [ 12, 1, -1, -4> 6 0.01988
1.00758 1728/1715 [ 6, 3, -1, -3> 7 0.01933
1.01094 65536/64827 [ 16, -3, 0, -4> 7 0.01885
1.01273 875/864 [ -5, -3, 3, 1> 7 0.01859
1.03200 4096/3969 [ 12, -4, 0, -2> 6 0.01848
1.03359 1323/1280 [ -8, 3, -1, 2> 6 0.01821
1.05350 256/243 [ 8, -5, 0, 0> 5 0.01787
1.07187 343/320 [ -6, 0, -1, 3> 4 0.01775
1.01902 131072/128625 [ 17, -1, -3, -3> 7 0.01769
1.00333 5120/5103 [ 10, -6, 1, -1> 8 0.01744
1.04025 8192/7875 [ 13, -2, -3, -1> 6 0.01710
1.00823 245/243 [ 0, -5, 1, 2> 8 0.01683
1.04210 2401/2304 [ -8, -2, 0, 4> 6 0.01679
1.02900 1029/1000 [ -3, 1, -3, 3> 7 0.01627
1.04533 392/375 [ 3, -1, -3, 2> 6 0.01625
1.04632 1875/1792 [ -8, 1, 4, -1> 6 0.01609
1.01545 51200/50421 [ 11, -1, 2, -5> 8 0.01593
1.01630 686/675 [ 1, -3, -2, 3> 8 0.01582
1.01702 3645/3584 [ -9, 6, 1, -1> 8 0.01573
1.04858 16384/15625 [ 14, 0, -6, 0> 6 0.01571
1.03316 405/392 [ -3, 4, 1, -2> 7 0.01567
1.04956 360/343 [ 3, 2, 1, -3> 6 0.01555
1.01860 4194304/4117715 [ 22, 0, -1, -7> 8 0.01553
1.01945 28672/28125 [ 12, -2, -5, 1> 8 0.01543
1.06622 2560/2401 [ 9, 0, 1, -4> 5 0.01533
1.03661 3200/3087 [ 7, -2, 2, -3> 7 0.01518
1.03982 262144/252105 [ 18, -1, -1, -5> 7 0.01472
1.02881 250/243 [ 1, -5, 3, 0> 8 0.01426
1.05820 200/189 [ 3, -3, 2, -1> 6 0.01411
1.08844 160/147 [ 5, -1, 1, -2> 4 0.01361
1.06148 16384/15435 [ 14, -2, -1, -3> 6 0.01356
1.03680 648/625 [ 3, 4, -4, 0> 8 0.01326
1.06337 1225/1152 [ -7, -2, 2, 2> 6 0.01325
1.05326 4608/4375 [ 9, 2, -4, -1> 7 0.01280
1.04123 2500/2401 [ 2, 0, 4, -4> 8 0.01270
1.08000 27/25 [ 0, 3, -2, 0> 5 0.01257
1.04446 122880/117649 [ 13, 1, 1, -6> 8 0.01230
1.06998 32768/30625 [ 15, 0, -4, -2> 6 0.01215
1.05864 343/324 [ -2, -4, 0, 3> 7 0.01203
1.08360 1024/945 [ 10, -3, -1, -1> 5 0.01185
1.06193 3584/3375 [ 9, -3, -3, 1> 7 0.01156
1.05044 16807/16000 [ -7, 0, -3, 5> 8 0.01155
1.09714 192/175 [ 6, 1, -2, -1> 4 0.01143
1.06293 625/588 [ -2, -1, 4, -2> 7 0.01142
1.07520 672/625 [ 5, 1, -4, 1> 6 0.01128
1.08889 49/45 [ 0, -2, -1, 2> 5 0.01079
1.05796 1296/1225 [ 4, 4, -2, -2> 8 0.01061
1.11111 10/9 [ 1, -2, 1, 0> 3 0.01058
1.09227 2048/1875 [ 11, -1, -4, 0> 5 0.01012
1.06313 1701/1600 [ -6, 5, -2, 1> 8 0.00997
1.07475 9216/8575 [ 10, 2, -2, -3> 7 0.00973
1.08482 243/224 [ -5, 5, 0, -1> 6 0.00967
1.08507 625/576 [ -6, -2, 4, 0> 6 0.00963
1.07022 16384/15309 [ 14, -7, 0, -1> 8 0.00908
1.08025 175/162 [ -1, -4, 2, 1> 7 0.00894
1.12500 9/8 [ -3, 2, 0, 0> 2 0.00893
1.09181 65536/60025 [ 16, 0, -2, -4> 6 0.00851
1.07545 784/729 [ 4, -6, 0, 2> 8 0.00843
1.07621 3375/3136 [ -6, 3, 3, -2> 8 0.00833
1.10204 54/49 [ 1, 3, 0, -2> 5 0.00816
1.07878 32768/30375 [ 15, -5, -3, 0> 8 0.00801
1.07955 2592/2401 [ 5, 4, 0, -4> 8 0.00791
1.12000 28/25 [ 2, 0, -2, 1> 3 0.00762
1.08315 163840/151263 [ 15, -2, 1, -5> 8 0.00746
1.10742 567/512 [ -9, 4, 0, 1> 5 0.00709
1.09329 375/343 [ 0, 1, 3, -3> 7 0.00708
1.10250 441/400 [ -4, 2, -2, 2> 6 0.00673
1.11607 125/112 [ -4, 0, 3, -1> 4 0.00670
1.09669 18432/16807 [ 11, 2, 0, -5> 7 0.00660
1.09760 686/625 [ 1, 0, -4, 3> 7 0.00647
1.10617 448/405 [ 6, -4, -1, 1> 6 0.00611
1.11953 384/343 [ 7, 1, 0, -3> 4 0.00583
1.09739 800/729 [ 5, -6, 2, 0> 8 0.00568
1.11456 4096/3675 [ 12, -1, -2, -2> 5 0.00566
1.10571 10240/9261 [ 11, -3, 1, -3> 7 0.00531
1.11654 1715/1536 [ -9, -1, 1, 3> 5 0.00526
1.10080 65536/59535 [ 16, -5, -1, -2> 8 0.00526
1.11409 131072/117649 [ 17, 0, 0, -6> 6 0.00479
1.10592 3456/3125 [ 7, 3, -5, 0> 8 0.00462
1.10960 131072/118125 [ 17, -3, -4, -1> 8 0.00416
1.11065 8000/7203 [ 6, -1, 3, -4> 8 0.00403
1.11157 2401/2160 [ -4, -3, -1, 4> 8 0.00391
1.11502 6272/5625 [ 7, -2, -4, 2> 8 0.00348
1.11848 262144/234375 [ 18, -1, -7, 0> 8 0.00305
1.12347 24576/21875 [ 13, 1, -5, -1> 7 0.00277
1.12373 4096/3645 [ 12, -6, -1, 0> 7 0.00273
1.12547 7203/6400 [ -8, 1, -2, 4> 7 0.00248
1.12875 640/567 [ 7, -4, 1, -1> 6 0.00235
1.13002 2025/1792 [ -8, 4, 2, -1> 7 0.00183
1.12849 6912/6125 [ 8, 3, -3, -2> 8 0.00180
1.13426 245/216 [ -3, -3, 1, 2> 6 0.00143
1.13225 262144/231525 [ 18, -3, -2, -3> 8 0.00133
1.13379 500/441 [ 2, -2, 3, -2> 7 0.00130
1.13778 256/225 [ 8, -2, -2, 0> 4 0.00127
1.13730 8192/7203 [ 13, -1, 0, -4> 5 0.00111
1.13400 567/500 [ -2, 4, -3, 1> 8 0.00111
1.13932 875/768 [ -8, -1, 3, 1> 5 0.00071
1.13906 729/640 [ -7, 6, -1, 0> 7 0.00054
1.13885 3125/2744 [ -3, 0, 5, -3> 8 0.00050
1.14131 524288/459375 [ 19, -1, -5, -2> 8 0.00019
1.14238 19200/16807 [ 8, 1, 2, -5> 8 0.00006
1.41312 46305/32768 [-15, 3, 1, 3> 7 -0.03861
1.41253 10125/7168 [-10, 4, 3, -1> 8 -0.03371
1.40684 7203/5120 [-10, 1, -1, 4> 6 -0.04400
1.40249 2941225/2097152 [-21, 0, 2, 6> 8 -0.03245
1.40190 91875/65536 [-16, 1, 4, 2> 7 -0.03701
1.39567 8575/6144 [-11, -1, 2, 3> 6 -0.04214
1.38428 2835/2048 [-11, 4, 1, 1> 6 -0.04024
1.37444 5764801/4194304 [-22, 0, 0, 8> 8 -0.02895
1.37386 180075/131072 [-17, 1, 2, 4> 7 -0.03300
1.37329 5625/4096 [-12, 2, 4, 0> 6 -0.03841
1.36776 16807/12288 [-12, -1, 0, 5> 6 -0.03748
1.36239 78125/57344 [-13, 0, 7, -1> 8 -0.02744
1.35659 27783/20480 [-12, 4, -1, 3> 8 -0.02672
1.34639 352947/262144 [-18, 1, 0, 6> 7 -0.02908
1.34583 11025/8192 [-13, 2, 2, 2> 6 -0.03383
1.33514 21875/16384 [-14, 0, 5, 1> 6 -0.03205
1.33484 10935/8192 [-13, 7, 1, 0> 8 -0.02400
1.31891 21609/16384 [-14, 2, 0, 4> 6 -0.02934
1.30844 42875/32768 [-15, 0, 3, 3> 6 -0.02760
1.30790 9375/7168 [-10, 1, 5, -1> 7 -0.02358
1.30263 12005/9216 [-10, -2, 1, 4> 7 -0.02282
1.29776 42525/32768 [-15, 5, 2, 1> 8 -0.01936
1.29199 1323/1024 [-10, 3, 0, 2> 5 -0.02983
1.28746 84375/65536 [-16, 3, 5, 0> 8 -0.01808
1.28227 84035/65536 [-16, 0, 1, 5> 6 -0.02324
1.28174 2625/2048 [-11, 1, 3, 1> 5 -0.02778
1.27180 83349/65536 [-16, 5, 0, 3> 8 -0.01612
1.27157 15625/12288 [-12, -1, 6, 0> 7 -0.01839
1.26171 165375/131072 [-17, 3, 3, 2> 8 -0.01486
1.25663 823543/655360 [-17, 0, -1, 7> 8 -0.01422
1.25610 5145/4096 [-12, 1, 1, 3> 5 -0.02265
1.25170 328125/262144 [-18, 1, 6, 1> 8 -0.01361
1.24613 30625/24576 [-13, -1, 4, 2> 7 -0.01475
1.24585 5103/4096 [-12, 6, 0, 1> 7 -0.01471
1.23648 324135/262144 [-18, 3, 1, 4> 8 -0.01170
1.23596 10125/8192 [-13, 4, 3, 0> 7 -0.01330
1.23098 50421/40960 [-13, 1, -1, 5> 7 -0.01259
1.22666 643125/524288 [-19, 1, 4, 3> 8 -0.01048
1.22121 60025/49152 [-14, -1, 2, 4> 7 -0.01119
1.21124 19845/16384 [-14, 4, 1, 2> 7 -0.00977
1.20213 1260525/1048576 [-20, 1, 2, 5> 8 -0.00741
1.20163 39375/32768 [-15, 2, 4, 1> 7 -0.00840
1.19679 117649/98304 [-15, -1, 0, 6> 7 -0.00770
1.19629 1225/1024 [-10, 0, 2, 2> 4 -0.01336
1.19209 78125/65536 [-16, 0, 7, 0> 7 -0.00703
1.18679 21875/18432 [-11, -2, 5, 1> 8 -0.00549
1.18652 1215/1024 [-10, 5, 1, 0> 6 -0.00728
1.17809 2470629/2097152 [-21, 1, 0, 7> 8 -0.00440
1.17760 77175/65536 [-16, 2, 2, 3> 7 -0.00496
1.17711 16875/14336 [-11, 3, 4, -1> 8 -0.00428
1.17236 2401/2048 [-11, 0, 0, 4> 4 -0.00738
1.16825 153125/131072 [-17, 0, 5, 2> 7 -0.00363
1.16306 42875/36864 [-12, -2, 3, 3> 8 -0.00253
1.16279 11907/10240 [-11, 5, -1, 2> 8 -0.00249
1.15405 151263/131072 [-17, 2, 0, 5> 7 -0.00160
1.15356 4725/4096 [-12, 3, 2, 1> 6 -0.00178
1.14892 117649/102400 [-12, 0, -2, 6> 8 -0.00076
1.14489 300125/262144 [-18, 0, 3, 4> 7 -0.00029
1.14441 9375/8192 [-13, 1, 5, 0> 6 -0.00026
1.14286 8/7 [ 3, 0, 0, -1> 1 0.00000
1.13980 84035/73728 [-13, -2, 1, 5> 8 0.00038
1.13049 9261/8192 [-13, 3, 0, 3> 6 0.00206
1.12199 588245/524288 [-19, 0, 1, 6> 7 0.00298
1.12152 18375/16384 [-14, 1, 3, 2> 6 0.00356
1.11262 109375/98304 [-15, -1, 6, 1> 8 0.00378
1.11237 18225/16384 [-14, 6, 2, 0> 8 0.00381
1.09909 36015/32768 [-15, 1, 1, 4> 6 0.00729
1.09863 1125/1024 [-10, 2, 3, 0> 5 0.00884
1.09421 16807/15360 [-10, -1, -1, 5> 7 0.00695
1.09037 214375/196608 [-16, -1, 4, 3> 8 0.00656
1.09012 35721/32768 [-15, 6, 0, 2> 8 0.00659
1.08991 15625/14336 [-11, 0, 6, -1> 7 0.00756
1.08147 70875/65536 [-16, 4, 3, 1> 8 0.00767
1.07711 352947/327680 [-16, 1, -1, 6> 8 0.00822
1.07666 2205/2048 [-11, 2, 1, 2> 5 0.01324
1.07288 140625/131072 [-17, 2, 6, 0> 8 0.00875
1.06856 420175/393216 [-17, -1, 2, 5> 8 0.00929
1.06812 4375/4096 [-12, 0, 4, 1> 5 0.01495
1.06787 2187/2048 [-11, 7, 0, 0> 7 0.01071
1.05984 138915/131072 [-17, 4, 1, 3> 8 0.01038
1.05513 21609/20480 [-12, 2, -1, 4> 7 0.01253
1.05143 275625/262144 [-18, 2, 4, 2> 8 0.01143
1.04719 823543/786432 [-18, -1, 0, 7> 8 0.01196
1.04675 8575/8192 [-13, 0, 2, 3> 5 0.01922
1.04308 546875/524288 [-19, 0, 7, 1> 8 0.01247
1.03821 8505/8192 [-13, 5, 1, 1> 7 0.01495
1.03040 540225/524288 [-19, 2, 2, 4> 8 0.01406
1.02997 16875/16384 [-14, 3, 4, 0> 7 0.01613
1.02582 16807/16384 [-14, 0, 0, 5> 5 0.02341
1.02222 1071875/1048576 [-20, 0, 5, 3> 8 0.01508
1.01725 3125/3072 [-10, -1, 5, 0> 6 0.02093
1.00979 1058841/1048576 [-20, 2, 0, 6> 8 0.01663
1.00937 33075/32768 [-15, 3, 2, 2> 7 0.01907
1.00488 1029/1024 [-10, 1, 0, 3> 4 0.03449
1.00178 2100875/2097152 [-21, 0, 3, 5> 8 0.01764
1.00136 65625/65536 [-16, 1, 5, 1> 7 0.02021
1.14333 343/300 [ -2, -1, -2, 3> 6 -0.00008
1.14640 49152/42875 [ 14, 1, -3, -3> 7 -0.00051
1.14688 3584/3125 [ 9, 0, -5, 1> 6 -0.00067
1.14796 225/196 [ -2, 2, 2, -2> 6 -0.00085
1.15152 13824/12005 [ 9, 3, -1, -4> 8 -0.00108
1.15226 280/243 [ 3, -5, 1, 1> 7 -0.00134
1.15536 524288/453789 [ 19, -3, 0, -5> 8 -0.00156
1.15200 144/125 [ 4, 2, -3, 0> 5 -0.00183
1.15584 16384/14175 [ 14, -4, -2, -1> 7 -0.00185
1.14844 147/128 [ -7, 1, 0, 2> 3 -0.00186
1.15714 81/70 [ -1, 4, -1, -1> 6 -0.00238
1.15741 125/108 [ -2, -3, 3, 0> 6 -0.00243
1.16148 784/675 [ 4, -3, -2, 2> 7 -0.00266
1.16460 1048576/900375 [ 20, -1, -3, -4> 8 -0.00272
1.16257 3125/2688 [ -7, -1, 5, -1> 7 -0.00282
1.16508 32768/28125 [ 15, -2, -5, 0> 7 -0.00318
1.17055 2560/2187 [ 9, -7, 1, 0> 8 -0.00346
1.16980 98304/84035 [ 15, 1, -1, -5> 7 -0.00385
1.16100 512/441 [ 9, -2, 0, -2> 4 -0.00454
1.17965 18432/15625 [ 11, 2, -6, 0> 8 -0.00460
1.17992 7168/6075 [ 10, -5, -2, 1> 8 -0.00463
1.16618 400/343 [ 4, 0, 2, -3> 5 -0.00466
1.18076 405/343 [ 0, 4, 1, -3> 8 -0.00474
1.17943 32768/27783 [ 15, -4, 0, -3> 7 -0.00522
1.18469 25600/21609 [ 10, -2, 2, -4> 8 -0.00523
1.17600 147/125 [ 0, 1, -3, 2> 6 -0.00552
1.18837 2097152/1764735 [ 21, -1, -1, -6> 8 -0.00569
1.17551 288/245 [ 5, 2, -1, -2> 5 -0.00653
1.18886 65536/55125 [ 16, -2, -3, -2> 7 -0.00657
1.17029 1024/875 [ 10, 0, -3, -1> 4 -0.00686
1.19579 1875/1568 [ -5, 1, 4, -2> 7 -0.00756
1.20372 36864/30625 [ 12, 2, -4, -2> 8 -0.00761
1.18125 189/160 [ -5, 3, -1, 1> 5 -0.00768
1.19837 131072/109375 [ 17, 0, -6, -1> 7 -0.00793
1.19950 2880/2401 [ 6, 2, 1, -4> 7 -0.00809
1.20050 2401/2000 [ -4, 0, -3, 4> 7 -0.00823
1.20960 756/625 [ 2, 3, -4, 1> 8 -0.00834
1.21477 1250/1029 [ 1, -1, 4, -3> 8 -0.00899
1.21578 16807/13824 [ -9, -3, 0, 5> 8 -0.00912
1.20937 1600/1323 [ 6, -3, 2, -2> 7 -0.00950
1.21956 1372/1125 [ 2, -2, -3, 3> 8 -0.00959
1.19097 343/288 [ -5, -2, 0, 3> 5 -0.00962
1.17188 75/64 [ -6, 1, 2, 0> 3 -0.00967
1.22042 2187/1792 [ -8, 7, 0, -1> 8 -0.00970
1.21312 131072/108045 [ 17, -2, -1, -4> 7 -0.01004
1.22334 57344/46875 [ 13, -1, -6, 1> 8 -0.01006
1.20400 2048/1701 [ 11, -5, 0, -1> 6 -0.01019
1.21500 243/200 [ -3, 5, -2, 0> 7 -0.01031
1.19467 448/375 [ 6, -1, -3, 1> 5 -0.01036
1.20586 3087/2560 [ -9, 2, -1, 3> 6 -0.01050
1.22829 73728/60025 [ 13, 2, -2, -4> 8 -0.01068
1.20988 98/81 [ 1, -4, 0, 2> 6 -0.01117
1.22283 262144/214375 [ 18, 0, -4, -3> 7 -0.01142
1.21363 4096/3375 [ 12, -3, -3, 0> 6 -0.01180
1.19048 25/21 [ 0, -1, 2, -1> 4 -0.01190
1.16667 7/6 [ -1, -1, 0, 1> 2 -0.01190
1.24031 3969/3200 [ -7, 4, -2, 2> 8 -0.01218
1.24060 8575/6912 [ -8, -3, 2, 3> 8 -0.01222
1.22908 896/729 [ 7, -6, 0, 1> 7 -0.01232
1.20536 135/112 [ -4, 3, 1, -1> 5 -0.01250
1.21854 20480/16807 [ 12, 0, 1, -5> 6 -0.01261
1.19417 2048/1715 [ 11, 0, -1, -3> 4 -0.01283
1.24562 15625/12544 [ -8, 0, 6, -2> 8 -0.01284
1.24859 8192/6561 [ 13, -8, 0, 0> 8 -0.01322
1.24948 3000/2401 [ 3, 1, 3, -4> 8 -0.01333
1.25336 147456/117649 [ 14, 2, 0, -6> 8 -0.01381
1.23980 243/196 [ -2, 5, 0, -2> 7 -0.01385
1.24008 625/504 [ -3, -2, 4, -1> 7 -0.01389
1.18519 32/27 [ 5, -3, 0, 0> 3 -0.01411
1.25829 98304/78125 [ 15, 1, -7, 0> 8 -0.01443
1.21528 175/144 [ -4, -2, 2, 1> 5 -0.01448
1.24778 524288/420175 [ 19, 0, -2, -5> 7 -0.01499
1.26367 81920/64827 [ 14, -3, 1, -4> 8 -0.01510
1.23429 216/175 [ 3, 3, -2, -1> 6 -0.01524
1.23457 100/81 [ 2, -4, 2, 0> 6 -0.01529
1.26591 4375/3456 [ -7, -3, 4, 1> 8 -0.01538
1.23840 8192/6615 [ 13, -3, -1, -2> 6 -0.01592
1.22880 768/625 [ 8, 1, -4, 0> 5 -0.01719
1.24830 16384/13125 [ 14, -1, -4, -1> 6 -0.01757
1.28397 196608/153125 [ 16, 1, -5, -2> 8 -0.01764
1.28426 32768/25515 [ 15, -6, -1, -1> 8 -0.01768
1.25052 2401/1920 [ -7, -1, -1, 4> 6 -0.01794
1.27037 343/270 [ -1, -3, -1, 3> 7 -0.01822
1.29024 4032/3125 [ 6, 2, -5, 1> 8 -0.01842
1.29053 1568/1215 [ 5, -5, -1, 2> 8 -0.01846
1.29145 2025/1568 [ -5, 4, 2, -2> 8 -0.01857
1.25440 784/625 [ 4, 0, -4, 2> 6 -0.01859
1.27325 1048576/823543 [ 20, 0, 0, -7> 7 -0.01863
1.27431 7168/5625 [ 10, -2, -4, 1> 7 -0.01878
1.25558 1125/896 [ -7, 2, 3, -1> 6 -0.01879
1.29454 65536/50625 [ 16, -4, -4, 0> 8 -0.01896
1.29576 4000/3087 [ 5, -2, 3, -3> 8 -0.01911
1.25948 432/343 [ 4, 3, 0, -3> 6 -0.01944
1.22070 625/512 [ -9, 0, 4, 0> 4 -0.01946
1.30179 729/560 [ -4, 6, -1, -1> 8 -0.01987
1.24393 1280/1029 [ 8, -1, 1, -3> 5 -0.02021
1.22449 60/49 [ 2, 1, 1, -2> 4 -0.02041
1.31017 393216/300125 [ 17, 1, -3, -4> 8 -0.02091
1.29000 5120/3969 [ 10, -4, 1, -2> 7 -0.02102
1.27378 32768/25725 [ 15, -1, -2, -3> 6 -0.02182
1.29600 162/125 [ 1, 4, -3, 0> 7 -0.02188
1.23047 315/256 [ -8, 2, 1, 1> 4 -0.02190
1.25388 1536/1225 [ 9, 1, -2, -2> 5 -0.02220
1.32096 131072/99225 [ 17, -4, -2, -2> 8 -0.02226
1.32300 1323/1000 [ -3, 3, -3, 2> 8 -0.02252
1.32330 1715/1296 [ -4, -4, 1, 3> 8 -0.02256
1.32866 3125/2352 [ -4, -1, 5, -2> 8 -0.02322
1.26000 63/50 [ -1, 2, -2, 1> 5 -0.02343
1.33153 262144/196875 [ 18, -2, -5, -1> 8 -0.02358
1.33389 2401/1800 [ -3, -2, -2, 4> 8 -0.02388
1.28625 1029/800 [ -5, 1, -2, 3> 6 -0.02390
1.31195 450/343 [ 1, 2, 2, -3> 7 -0.02416
1.33691 786432/588245 [ 18, 1, -1, -6> 8 -0.02426
1.26420 512/405 [ 9, -4, -1, 0> 5 -0.02427
1.31305 16807/12800 [ -9, 0, -2, 5> 7 -0.02431
1.33803 12544/9375 [ 8, -1, -5, 2> 8 -0.02440
1.34218 524288/390625 [ 19, 0, -8, 0> 8 -0.02492
1.24444 56/45 [ 3, -2, -1, 1> 4 -0.02540
1.21905 128/105 [ 7, -1, -1, -1> 3 -0.02540
1.34792 262144/194481 [ 18, -4, 0, -4> 8 -0.02563
1.32245 324/245 [ 2, 4, -1, -2> 7 -0.02566
1.32275 250/189 [ 1, -3, 3, -1> 7 -0.02570
1.35031 875/648 [ -3, -4, 3, 1> 8 -0.02593
1.29978 65536/50421 [ 16, -1, 0, -5> 6 -0.02615
1.27551 125/98 [ -1, 0, 3, -2> 5 -0.02653
1.32891 1701/1280 [ -8, 5, -1, 1> 7 -0.02658
1.32921 6125/4608 [ -9, -2, 3, 2> 7 -0.02662
1.35870 524288/385875 [ 19, -2, -3, -3> 8 -0.02698
1.27947 3072/2401 [ 10, 1, 0, -4> 5 -0.02732
1.22500 49/40 [ -3, 0, -1, 2> 3 -0.02738
1.36662 1875/1372 [ -2, 1, 4, -3> 8 -0.02797
1.36957 1048576/765625 [ 20, 0, -6, -2> 8 -0.02834
1.37086 23040/16807 [ 9, 2, 1, -5> 8 -0.02850
1.20000 6/5 [ 1, 1, -1, 0> 2 -0.02857
1.31657 1152/875 [ 7, 2, -3, -1> 6 -0.02895
1.31687 320/243 [ 6, -5, 1, 0> 6 -0.02900
1.37626 21504/15625 [ 10, 1, -6, 1> 8 -0.02917
1.34848 8192/6075 [ 13, -5, -2, 0> 7 -0.02937
1.38214 12800/9261 [ 9, -3, 2, -3> 8 -0.02991
1.38643 1048576/756315 [ 20, -2, -1, -5> 8 -0.03045
1.35603 1215/896 [ -7, 5, 1, -1> 7 -0.03045
1.35634 3125/2304 [ -8, -2, 5, 0> 7 -0.03050
1.29630 35/27 [ 0, -3, 1, 1> 5 -0.03069
1.26562 81/64 [ -6, 4, 0, 0> 4 -0.03069
1.38857 243/175 [ 0, 5, -2, -1> 8 -0.03071
1.32741 896/675 [ 7, -3, -2, 1> 6 -0.03076
1.30032 2048/1575 [ 11, -2, -2, -1> 5 -0.03149
1.33278 3200/2401 [ 7, 0, 2, -4> 6 -0.03165
1.26984 80/63 [ 4, -2, 1, -1> 4 -0.03175
1.39752 2097152/1500625 [ 21, 0, -4, -4> 8 -0.03183
1.30667 98/75 [ 1, -1, -2, 2> 5 -0.03276
1.27604 245/192 [ -6, -1, 1, 2> 4 -0.03330
1.37600 16384/11907 [ 14, -5, 0, -2> 7 -0.03331
1.34344 2304/1715 [ 8, 2, -1, -3> 6 -0.03343
1.41120 882/625 [ 1, 2, -4, 2> 8 -0.03354
1.31072 4096/3125 [ 12, 0, -5, 0> 5 -0.03357
1.41152 343/243 [ 0, -5, 0, 3> 8 -0.03358
1.38240 864/625 [ 5, 3, -4, 0> 7 -0.03422
1.38701 32768/23625 [ 15, -3, -3, -1> 7 -0.03488
1.31836 675/512 [ -9, 3, 2, 0> 5 -0.03510
1.38947 2401/1728 [ -6, -3, 0, 4> 7 -0.03523
1.39262 163840/117649 [ 15, 0, 1, -6> 7 -0.03568
1.39378 1568/1125 [ 5, -2, -3, 2> 7 -0.03585
1.39810 65536/46875 [ 16, -1, -6, 0> 7 -0.03646
1.32685 4096/3087 [ 12, -2, 0, -3> 5 -0.03680
1.37200 343/250 [ -1, 0, -3, 3> 6 -0.03819
1.41061 1728/1225 [ 6, 3, -2, -2> 7 -0.03825
1.41093 800/567 [ 5, -4, 2, -1> 7 -0.03830
1.33747 8192/6125 [ 13, 0, -3, -2> 5 -0.03892
1.37755 135/98 [ -1, 3, 1, -2> 6 -0.03912
1.30208 125/96 [ -5, -1, 3, 0> 4 -0.03981
1.34400 168/125 [ 3, 1, -3, 1> 5 -0.04023
1.36054 200/147 [ 3, -1, 2, -2> 5 -0.04354
1.40434 6144/4375 [ 11, 1, -4, -1> 6 -0.04358
1.40466 1024/729 [ 10, -6, 0, 0> 6 -0.04363
1.36476 16384/12005 [ 14, 0, -1, -4> 5 -0.04438
1.37813 441/320 [ -6, 2, -1, 2> 5 -0.04705
1.28571 9/7 [ 0, 2, 0, -1> 3 -0.04762
1.38272 112/81 [ 4, -4, 0, 1> 5 -0.04797
1.33929 75/56 [ -3, 1, 2, -1> 4 -0.04911
1.39509 625/448 [ -6, 0, 4, -1> 5 -0.05045
1.39942 480/343 [ 5, 1, 1, -3> 5 -0.05131
1.35000 27/20 [ -2, 3, -1, 0> 4 -0.05179
1.35450 256/189 [ 8, -3, 0, -1> 4 -0.05291
1.36111 49/36 [ -2, -2, 0, 2> 4 -0.05456
1.36533 512/375 [ 9, -1, -3, 0> 4 -0.05562
1.38889 25/18 [ -1, -2, 2, 0> 4 -0.06151
1.39320 1024/735 [ 10, -1, -1, -2> 4 -0.06259
1.33984 343/256 [ -8, 0, 0, 3> 3 -0.06566
1.28000 32/25 [ 5, 0, -2, 0> 2 -0.06857
1.36719 175/128 [ -7, 0, 2, 1> 3 -0.07478
1.37143 48/35 [ 4, 1, -1, -1> 3 -0.07619
1.30612 64/49 [ 6, 0, 0, -2> 2 -0.08163
1.31250 21/16 [ -4, 1, 0, 1> 2 -0.08482
1.40625 45/32 [ -5, 2, 1, 0> 3 -0.08780
1.25000 5/4 [ -2, 0, 1, 0> 1 -0.10714
1.40000 7/5 [ 0, 0, -1, 1> 2 -0.12857
1.33333 4/3 [ 2, -1, 0, 0> 1 -0.19048