-18 using an observation from Peter Taylor (order 10 values have leading 1 or 2, while order 1 values do not).
<3Ḣ‘_L⁵*×Ḍ
“KẸ⁺dzⱮÑ2⁵İ2ṭ¬⁴²¬¶9°ß°øİẆGẊœ%X(¢ṆḢ/8¬Ɗ’b7µ18,-;_3+\⁺Ṭœṗ“SŒƥŻƭ°}MḋṘḥfyɼ{ṅĊLƝġœ⁺ḟ8ḶhỊDṭ&æ%*ɱ¬ =¦ẉ Qh"¶:ḌĊ€ĖṢė°ġṀƬmẓSṃ÷E⁴Ȥ⁼ḋ#ØĖḂ2øzẸżƈ¥Ȧƥ7¢®|ḳẊṆƙƲɦḟɼṖỊɲṁẉɗ6ẇSɗ⁴ẉİt]ẓeṆHṚƑ½>]ɦ~T¢~ẆẆA`/6ƭṡxṠKG£Ḅ+wḃḣỤw×ḌŻƲF>Ụ]5bJḤḟCḞİḶ|ȥ9Ỵ0ụKṗT⁴ƥƁṖı×ṄtTĊG©ṀḥṬƭʂd½ḊȦуŀṣ¹ʋṖẓYL²ṅṿ&ẏdDṬIɦỵ¹b,ḷṣƭ#P'µ{GTƇẹ¥L8SƥÑṆẈėẎßṀḷƓ⁷ðḳċ¿ḶM_ḲẈg9ḢĠi+LṭẹḲẎ¤g<ṘJJĿßæ⁺(ɲỴ3ɲgkSḃIƙṭ.Ỵ&_:cĿƝı’D¤Ç€
Try it online!
How?
Creates these two constants (AKA nilads):
- (A) all the decimal digits used (i.e. the numbers all joined up ignoring where they join and their decimal place separators), and
- (B) the number of significant figures used by each number
Then uses those to reconstruct floating point representations of the numbers.
The full program is of this form:
<3Ḣ‘_L⁵*×Ḍ
“...’b7µ18,-;_3+\⁺Ṭœṗ“...’D¤Ç€
(where ...
are encoded numbers for constructing B, and A)
and works like this:
<3Ḣ‘_L⁵*×Ḍ - Link 1, conversion helper: list of digits e.g. [1,2,9,6,7,6,3]
<3 - less than three? [1,1,0,0,0,0,0]
Ḣ - head 1
‘ - increment 2
L - length 7
_ - subtract -5
⁵ - literal ten 10
* - exponentiate 0.00001
Ḍ - undecimal (convert from base 10) 1296763
× - multiply 12.96763
- i.e. go from digits to a number between 3 and 30
“...’b7µ18,-;_3+\⁺Ṭœṗ“...’D¤Ç€ - Main link: no arguments
“...’ - base 250 literal = 16242329089425509505495393436399830365761075941410177200411131173280169129083782003564646
b7 - to base seven = [2,0,4,3,2,4,2,4,3,2,3,3,4,2,3,5,3,3,0,3,4,2,4,4,1,4,3,4,3,2,1,5,3,5,1,5,0,3,3,3,3,3,3,3,4,3,4,2,3,2,4,5,4,0,1,3,2,4,2,5,4,2,2,4,2,3,4,4,3,3,3,2,3,3,3,3,4,4,3,3,2,0,5,3,5,2,3,1,1,6,2,3,3,3,3,3,3,1,3,3,3,3,2,3,3]
µ - start a new monadic chain, call that x
18,- - integer list literal = [18,-1]
; - concatenate with x = [18,-1,2,0,4,3,2,4,2,4,3,2,3,3,4,2,3,5,3,3,0,3,4,2,4,4,1,4,3,4,3,2,1,5,3,5,1,5,0,3,3,3,3,3,3,3,4,3,4,2,3,2,4,5,4,0,1,3,2,4,2,5,4,2,2,4,2,3,4,4,3,3,3,2,3,3,3,3,4,4,3,3,2,0,5,3,5,2,3,1,1,6,2,3,3,3,3,3,3,1,3,3,3,3,2,3,3]
_3 - subtract three = [15,-4,-1,-3,1,0,-1,1,-1,1,0,-1,0,0,1,-1,0,2,0,0,-3,0,1,-1,1,1,-2,1,0,1,0,-1,-2,2,0,2,-2,2,-3,0,0,0,0,0,0,0,1,0,1,-1,0,-1,1,2,1,-3,-2,0,-1,1,-1,2,1,-1,-1,1,-1,0,1,1,0,0,0,-1,0,0,0,0,1,1,0,0,-1,-3,2,0,2,-1,0,-2,-2,3,-1,0,0,0,0,0,0,-2,0,0,0,0,-1,0,0]
\ - cumulative reduce with:
+ - addition = [15,11,10,7,8,8,7,8,7,8,8,7,7,7,8,7,7,9,9,9,6,6,7,6,7,8,6,7,7,8,8,7,5,7,7,9,7,9,6,6,6,6,6,6,6,6,7,7,8,7,7,6,7,9,10,7,5,5,4,5,4,6,7,6,5,6,5,5,6,7,7,7,7,6,6,6,6,6,7,8,8,8,7,4,6,6,8,7,7,5,3,6,5,5,5,5,5,5,5,3,3,3,3,3,2,2,2]
- ("B" significant figures, with 1 extra for the very first entry and a missing last entry)
⁺ - repeat (the cumulative addition to get
- partition positions) = [15,26,36,43,51,59,66,74,81,89,97,104,111,118,126,133,140,149,158,167,173,179,186,192,199,207,213,220,227,235,243,250,255,262,269,278,285,294,300,306,312,318,324,330,336,342,349,356,364,371,378,384,391,400,410,417,422,427,431,436,440,446,453,459,464,470,475,480,486,493,500,507,514,520,526,532,538,544,551,559,567,575,582,586,592,598,606,613,620,625,628,634,639,644,649,654,659,664,669,672,675,678,681,684,686,688,690]
Ṭ - untruth (1s at those indices) = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0,1]
¤ - nilad followed by link(s) as a nilad:
“...’ - base 250 literal = 1359843400513624587387936539171476193226998298019011260296145341313618054174228221564540513907677646235598576881516831048668610360011296763157596112434066354611315520656149682812674618767665174340187902467878810176398777726380939419905999301878994359788697523921181381139996049417712856948672062172666339067588570924371193873605074589083368675762348993822578635527343917860838990096610451261212984313893905548521166455769553865473552505582564371567038561498058638593905602156107761843162541595425871682506975495717864037833528438238967028958839225553104375046108287174166796728551684149317511074854072740952784245380226630675896194056265560258597385991461978628176367665065866549060168787776
D - decimal (to base 10) = [1,3,5,9,8,4,3,4,0,0,5,1,3,6,2,4,5,8,7,3,8,7,9,3,6,5,3,9,1,7,1,4,7,6,1,9,3,2,2,6,9,9,8,2,9,8,0,1,9,0,1,1,2,6,0,2,9,6,1,4,5,3,4,1,3,1,3,6,1,8,0,5,4,1,7,4,2,2,8,2,2,1,5,6,4,5,4,0,5,1,3,9,0,7,6,7,7,6,4,6,2,3,5,5,9,8,5,7,6,8,8,1,5,1,6,8,3,1,0,4,8,6,6,8,6,1,0,3,6,0,0,1,1,2,9,6,7,6,3,1,5,7,5,9,6,1,1,2,4,3,4,0,6,6,3,5,4,6,1,1,3,1,5,5,2,0,6,5,6,1,4,9,6,8,2,8,1,2,6,7,4,6,1,8,7,6,7,6,6,5,1,7,4,3,4,0,1,8,7,9,0,2,4,6,7,8,7,8,8,1,0,1,7,6,3,9,8,7,7,7,7,2,6,3,8,0,9,3,9,4,1,9,9,0,5,9,9,9,3,0,1,8,7,8,9,9,4,3,5,9,7,8,8,6,9,7,5,2,3,9,2,1,1,8,1,3,8,1,1,3,9,9,9,6,0,4,9,4,1,7,7,1,2,8,5,6,9,4,8,6,7,2,0,6,2,1,7,2,6,6,6,3,3,9,0,6,7,5,8,8,5,7,0,9,2,4,3,7,1,1,9,3,8,7,3,6,0,5,0,7,4,5,8,9,0,8,3,3,6,8,6,7,5,7,6,2,3,4,8,9,9,3,8,2,2,5,7,8,6,3,5,5,2,7,3,4,3,9,1,7,8,6,0,8,3,8,9,9,0,0,9,6,6,1,0,4,5,1,2,6,1,2,1,2,9,8,4,3,1,3,8,9,3,9,0,5,5,4,8,5,2,1,1,6,6,4,5,5,7,6,9,5,5,3,8,6,5,4,7,3,5,5,2,5,0,5,5,8,2,5,6,4,3,7,1,5,6,7,0,3,8,5,6,1,4,9,8,0,5,8,6,3,8,5,9,3,9,0,5,6,0,2,1,5,6,1,0,7,7,6,1,8,4,3,1,6,2,5,4,1,5,9,5,4,2,5,8,7,1,6,8,2,5,0,6,9,7,5,4,9,5,7,1,7,8,6,4,0,3,7,8,3,3,5,2,8,4,3,8,2,3,8,9,6,7,0,2,8,9,5,8,8,3,9,2,2,5,5,5,3,1,0,4,3,7,5,0,4,6,1,0,8,2,8,7,1,7,4,1,6,6,7,9,6,7,2,8,5,5,1,6,8,4,1,4,9,3,1,7,5,1,1,0,7,4,8,5,4,0,7,2,7,4,0,9,5,2,7,8,4,2,4,5,3,8,0,2,2,6,6,3,0,6,7,5,8,9,6,1,9,4,0,5,6,2,6,5,5,6,0,2,5,8,5,9,7,3,8,5,9,9,1,4,6,1,9,7,8,6,2,8,1,7,6,3,6,7,6,6,5,0,6,5,8,6,6,5,4,9,0,6,0,1,6,8,7,8,7,7,7,6]
- ("A" all the required digits in order)
œṗ - partition at truthy indices = [[1,3,5,9,8,4,3,4,0,0,5,1,3,6],[2,4,5,8,7,3,8,7,9,3,6],[5,3,9,1,7,1,4,7,6,1],[9,3,2,2,6,9,9],[8,2,9,8,0,1,9,0],[1,1,2,6,0,2,9,6],[1,4,5,3,4,1,3],[1,3,6,1,8,0,5,4],[1,7,4,2,2,8,2],[2,1,5,6,4,5,4,0],[5,1,3,9,0,7,6,7],[7,6,4,6,2,3,5],[5,9,8,5,7,6,8],[8,1,5,1,6,8,3],[1,0,4,8,6,6,8,6],[1,0,3,6,0,0,1],[1,2,9,6,7,6,3],[1,5,7,5,9,6,1,1,2],[4,3,4,0,6,6,3,5,4],[6,1,1,3,1,5,5,2,0],[6,5,6,1,4,9],[6,8,2,8,1,2],[6,7,4,6,1,8,7],[6,7,6,6,5,1],[7,4,3,4,0,1,8],[7,9,0,2,4,6,7,8],[7,8,8,1,0,1],[7,6,3,9,8,7,7],[7,7,2,6,3,8,0],[9,3,9,4,1,9,9,0],[5,9,9,9,3,0,1,8],[7,8,9,9,4,3,5],[9,7,8,8,6],[9,7,5,2,3,9,2],[1,1,8,1,3,8,1],[1,3,9,9,9,6,0,4,9],[4,1,7,7,1,2,8],[5,6,9,4,8,6,7,2,0],[6,2,1,7,2,6],[6,6,3,3,9,0],[6,7,5,8,8,5],[7,0,9,2,4,3],[7,1,1,9,3,8],[7,3,6,0,5,0],[7,4,5,8,9,0],[8,3,3,6,8,6],[7,5,7,6,2,3,4],[8,9,9,3,8,2,2],[5,7,8,6,3,5,5,2],[7,3,4,3,9,1,7],[8,6,0,8,3,8,9],[9,0,0,9,6,6],[1,0,4,5,1,2,6],[1,2,1,2,9,8,4,3,1],[3,8,9,3,9,0,5,5,4,8],[5,2,1,1,6,6,4],[5,5,7,6,9],[5,5,3,8,6],[5,4,7,3],[5,5,2,5,0],[5,5,8,2],[5,6,4,3,7,1],[5,6,7,0,3,8,5],[6,1,4,9,8,0],[5,8,6,3,8],[5,9,3,9,0,5],[6,0,2,1,5],[6,1,0,7,7],[6,1,8,4,3,1],[6,2,5,4,1,5,9],[5,4,2,5,8,7,1],[6,8,2,5,0,6,9],[7,5,4,9,5,7,1],[7,8,6,4,0,3],[7,8,3,3,5,2],[8,4,3,8,2,3],[8,9,6,7,0,2],[8,9,5,8,8,3],[9,2,2,5,5,5,3],[1,0,4,3,7,5,0,4],[6,1,0,8,2,8,7,1],[7,4,1,6,6,7,9,6],[7,2,8,5,5,1,6],[8,4,1,4],[9,3,1,7,5,1],[1,0,7,4,8,5],[4,0,7,2,7,4,0,9],[5,2,7,8,4,2,4],[5,3,8,0,2,2,6],[6,3,0,6,7],[5,8,9],[6,1,9,4,0,5],[6,2,6,5,5],[6,0,2,5,8],[5,9,7,3,8],[5,9,9,1,4],[6,1,9,7,8],[6,2,8,1,7],[6,3,6,7,6],[6,5,0],[6,5,8],[6,6,5],[4,9,0],[6,0,1],[6,8],[7,8],[7,7],[7,6]]
Ç€ - call the last link (1) as a monad for €ach = [13.598434005136,24.587387936000002,5.391714761,9.322699,8.298019,11.260295999999999,14.534129999999998,13.618053999999999,17.422819999999998,21.56454,5.1390766999999995,7.646235,5.985767999999999,8.151683,10.486686,10.360009999999999,12.96763,15.759611200000002,4.34066354,6.1131552000000005,6.561490000000001,6.82812,6.746187,6.76651,7.434018,7.902467799999999,7.881010000000001,7.639876999999999,7.72638,9.394199,5.9993018,7.8994349999999995,9.7886,9.752392,11.81381,13.9996049,4.177128,5.6948672,6.2172600000000005,6.633900000000001,6.758850000000001,7.09243,7.1193800000000005,7.360500000000001,7.458900000000001,8.336860000000001,7.5762339999999995,8.993822,5.7863552,7.343916999999999,8.608388999999999,9.00966,10.45126,12.129843099999999,3.893905548,5.211664,5.5769,5.538600000000001,5.473,5.525,5.582,5.6437100000000004,5.670385,6.149800000000001,5.8638,5.939050000000001,6.0215000000000005,6.1077,6.184310000000001,6.254159,5.425871,6.825069,7.549570999999999,7.8640300000000005,7.833520000000001,8.43823,8.967020000000002,8.95883,9.225553,10.437504,6.1082871,7.416679599999999,7.285515999999999,8.414,9.31751,10.7485,4.072740899999999,5.278423999999999,5.3802259999999995,6.3067,5.89,6.194050000000001,6.2655,6.0258,5.973800000000001,5.9914000000000005,6.1978,6.281700000000001,6.3676,6.5,6.58,6.65,4.9,6.01,6.800000000000001,7.800000000000001,7.7,7.6000000000000005]
2Hm, the graph shows some interesting trends, maybe that's helpful for compression... – Erik the Outgolfer – 2018-02-07T17:50:05.483
3Side note: this is a pretty experimental challenge. The scoring scheme is unique, I hope it works out well. – PhiNotPi – 2018-02-07T18:14:23.650
Very nice challenge. Unfortunately, the accuracy of the reference is so high that physically motivated approximation formulas (which can't really expect to predict more than two digits) have hardly a chance to compete against literal compression of the digits. (Short of actually solving the Schrödinger equation of course, which isn't very feasible either.) It would IMO be more interesting without the logarithm in the penalty formula, so that high-significant digits are actually more important to get right. – ceased to turn counterclockwis – 2018-02-08T13:30:06.133
@PhiNotPi The scoring scheme isn't that unique, right?
– Esolanging Fruit – 2018-02-09T05:32:14.4431@EsolangingFruit Yeah I see the similarities. I think this is unique in that the penalty is "continuous" meaning that you're not simply right or wrong for any particular output, so it's about finding how much you should fudge each number. (This scoring scheme was much more unique back in 2015 when I first sandboxed it, lol.) – PhiNotPi – 2018-02-09T06:38:44.713