# Why does DeleteDuplicatesBy fail?

This is a pretty straightforward code. I just want to delete duplicates based on the final entry in each row. I have evaluated very similar numbers with no problem.

donstab = {{0,
1.1705789061117936554636283495452553721386596399741016697650834341\
6598705794795801042878980763625795299943342670025710664758586357821209\
0279004535954780800713025640594040299708920921522304084382259765530885\
7337112444042614198.64076512182706*^-11, 0162.50943944836337}, {1/
10000000000000,
1.1705789061120960550143739389297719738181660224141697965326749420\
6318294105026428103336964373648476325780945255642939285410315194256473\
0545884045080521494874592314686734833832440483935904929835831434886609\
4780411189528953198.64076512182706*^-11, \
-1.6271117548376910739081695892114426826907089948979426184793399822571\
9145416036163979220444981403040222619792567514984.7208568309512*^-78}\
, {1/5000000000000,
1.1705789061123984545651196136946655708938873825089964888495723572\
9429306955477498481962022592107954668614120537091407774361694805995059\
8634521375273677662214329567147387380735050739295407070076130142579768\
3304197646752025198.64076512182706*^-11, \
-3.1556106760507259133114418652557913911778888792185072159331697926810\
2777781978189762112150785667385779806449048934185.00852286505726*^-\
78}, {3/10000000000000,
1.1705789061127008541158653738399361633925246123339296187209136164\
7473315507563109054542531776262515004043103530809542749937611798278022\
1465111258047319729477971414349265451761029185175257145190087555552760\
3320014846009935198.64076512182706*^-11, \
-4.4868839300124237548010571391902412674536644229499051349467659896522\
3268417937503665710065066758424269949029651948485.16138428339448*^-\
78}, {1/2500000000000,
1.1705789061130032536666112193655837513407786039643263151691348864\
0163291225379040033533450004368972948907427148951870129493261265213544\
7322714921810971822134104143687148867455174011353288745402133852986392\
8811539914117782198.64076512182706*^-11, \
-5.5223186830957910322191605640070646429985812754057748470448920211544\
1932083157478717842264894527592907603410328689785.25156091374365*^-\
78}, {1/2000000000000,
1.1705789061133056532173571502716083347653502494755529642339705675\
9420514061466095997315678625817909430242657601842799827488559260462656\
2897763918492661543449517596554538123478808080341185955473578785488795\
6301068135271153198.64076512182706*^-11, \
-6.1633021016735213766588014563287506238798167366665147341008421624960\
7827578909622097257702016729822710059327221668485.29925290408158*^-\
78}, {3/5000000000000,
1.1705789061136080527681031665580099136929404409429852089724532978\
3411480642721829315408340175184283363445345106848144643030458675925088\
7038395857224241396372385538117875768783414922102504289368384441433788\
9872521422355601198.6407651218271*^-\
1125042893683844414337889872521422355601198.6407651218271*, \
-6.3112213521179956164639326181031446745916726650545216223976116981977\
9621048057267361841796333560204351272342023006785.30955286072144*^-\
78}, {7/10000000000000,
1.1705789061139104523188492682247884881502500704420079494589139557\
0584812456460645969634040348972697069360026388312324425693657478911182\
2526259111220276030299510342401332015150692030156357948657383369788585\
362904415735607198.6407651218271*^-11, \
-5.8674636008012817772294096582985882006383505206411805493562241786043\
8949647001581370936762097927362929318235329481485.27788985246622*^-\
78}, {1/1250000000000,
1.1705789061142128518695954552719440581639800300480153427849816641\
3708164036622293771237181743836588893419199943398524705146039714512582\
9613369180567129324038381895514252480733027883551286511185695057435663\
8059005702691564198.6407651218271*^-\
1112865111856950574356638059005702691564198.6407651218271*, \
-4.7334160140951350818009903145990581298590085447834512429462430448890\
5734795172091202640073443984680476204813814380485.18461412411331*^-\
78}, {9/10000000000000,
1.1705789061145152514203417276994766237608312118364108030595837939\
3905131150128732973955397055050627523384279538876144812548227157183894\
9050837909051055529956488457695995749772928721169044559059579896881851\
4799196306915679198.6407651218271*^-\
1190445590595798968818514799196306915679198.6407651218271*, \
-2.8104657583709979502753337750993064924951010756878967937934913792240\
7905168858270744964089072470429679820687093824984.95821774674636*^-\
78}, {1/1000000000000,
1.1705789061148176509710880855073861849675045078826070014089459673\
4692158983389389283044169434015582535652615894124684109866853085742302\
6119468645331954102154196477152863863161733868001026184817993041456692\
1974368729530058198.6407651218271*^-\
1110261848179930414566921974368729530058198.6407651218271*,
0162.5094394483611}};

DeleteDuplicatesBy[donstab, Last]


I acknowledge that I am dealing with some very large numbers. I have to do this because the calculation I am doing ends up relying on the difference between this numbers, so I keep a lot of extra precision around. When I try to run it I just hear a dull beep with no error output. Why I click on Help-> Why the beep? I get the following message, which isn't very helpful:

Any ideas?

• Your number representations seem weird to me: for instance, the first long number in the list carried a precision specification of number198.64076512182706*^-11. What does that mean exactly? And how did you obtain it? – MarcoB Jun 29 '16 at 22:04
• @MarcoB The precision is  198.64076512182706 . The *^-11 belongs to the whole number. – Sjoerd C. de Vries Jun 29 '16 at 22:20
• @SjoerdC.deVries D'oh! Thank you, that makes a lot more sense now! – MarcoB Jun 29 '16 at 22:23
• It looks like there are a few typos in there, but correcting those I get the same error. I believe this to be a bug in DeleteDuplicatesBy, as DeleteDuplicates[Last /@ donstab] doesn't give an error. – Sjoerd C. de Vries Jun 29 '16 at 22:24
• @SjoerdC.deVries - thank you very much for checking this out and your suggestion! – DJBunk Jun 30 '16 at 12:09