Accurate RAPr computations with Fejer quadrature

To get an accurate RAPr vector, we are going to try using a Fejer rule with a many points. A Fejer rule is like a Clenshaw-Curtis rule, but excludes the endpoints, and hence, permits singularities.

Contents

Experimental setup

This experiment should be run from the rapr/experiments/correctness directory. To reduce the computational load, we'll load the cs-stanford graph and just take the largest strong component.

cwd = pwd;
dirtail = 'experiments/correctness';
if strcmp(cwd(end-length(dirtail)+1:end),dirtail) == 0
    warning('%s should be executed from rapr/%s\n', mfilename, dirtail);
end
load ('../../data/wb-cs.stanford.mat');
% just use the largest strong component for this experiment;
P = Pcc; A = Acc;
%load ('../../data/example-small.mat');
n=size(P,1);

Add the path

addpath('../../matlab');

Generate the weight function

With the chebfun system, can generate the weight function for the beta distribution by generating a variable x and modifying it with the equation of the weight function, or we can specify it directly as an inline function. We've taken the first choice to show off a bit of the chebfun system's flexiblity in Matlab.

a=2;
b=16;
r=1;
d=alphadist('beta',a,b,0,r);

Construct the Fejer rule.

The PageRank vector is a rational of degree n in alpha (I think). After scaling it by the weight function, (a polynomial of degree (a+b)), we find the overall degree of our rational function is n+a+b. We'll build a rule to integrate polynomials of up to degree

N = 2*(n+a+b+1);
[fx fw] = fejer2_rule_compute(N);
X = zeros(n,length(fx));
Pt = P; tic;
v = ones(n,1)./n;
bw = zeros(N,1);
for i=1:N
    ti = fx(i);
    alpha = 0.5*(fx(i)+1);
    bw(i)=((r.*(ti+1)./2).^b.*(r-r.*(ti+1)./2).^a.*(r./2))/exp((a+b+1)*log(r)+betaln(a+1,b+1));
    X(:,i)=(speye(n)-alpha*Pt)\((1-alpha)*v);
    dt=toc; etr=N*dt/i-dt;
    fprintf('... solve %5i a=%7.5f time=%7f sec left=%7f sec \n',i,alpha,toc,etr);
end

save 'exact-fejer-2.mat' fx fw P X

eex = X*(bw.*fw);
... solve     1 a=0.00000 time=0.017164 sec left=95.257140 sec 
... solve     2 a=0.00000 time=0.032765 sec left=90.932865 sec 
... solve     3 a=0.00000 time=0.048359 sec left=89.484744 sec 
... solve     4 a=0.00000 time=0.063810 sec left=88.547460 sec 
... solve     5 a=0.00000 time=0.079279 sec left=87.997783 sec 
... solve     6 a=0.00000 time=0.094586 sec left=87.477250 sec 
... solve     7 a=0.00000 time=0.110108 sec left=87.272294 sec 
... solve     8 a=0.00001 time=0.125564 sec left=87.067538 sec 
... solve     9 a=0.00001 time=0.140937 sec left=86.854926 sec 
... solve    10 a=0.00001 time=0.156522 sec left=86.798782 sec 
... solve    11 a=0.00001 time=0.171949 sec left=86.670870 sec 
... solve    12 a=0.00001 time=0.187376 sec left=86.560782 sec 
... solve    13 a=0.00001 time=0.202928 sec left=86.518981 sec 
... solve    14 a=0.00002 time=0.218495 sec left=86.487264 sec 
... solve    15 a=0.00002 time=0.233981 sec left=86.427040 sec 
... solve    16 a=0.00002 time=0.249539 sec left=86.397685 sec 
... solve    17 a=0.00002 time=0.264937 sec left=86.317821 sec 
... solve    18 a=0.00003 time=0.280388 sec left=86.261426 sec 
... solve    19 a=0.00003 time=0.296956 sec left=86.534567 sec 
... solve    20 a=0.00003 time=0.312386 sec left=86.464293 sec 
... solve    21 a=0.00004 time=0.327799 sec left=86.394497 sec 
... solve    22 a=0.00004 time=0.343191 sec left=86.324363 sec 
... solve    23 a=0.00004 time=0.358642 sec left=86.273182 sec 
... solve    24 a=0.00005 time=0.373963 sec left=86.195014 sec 
... solve    25 a=0.00005 time=0.389510 sec left=86.171653 sec 
... solve    26 a=0.00005 time=0.404893 sec left=86.114436 sec 
... solve    27 a=0.00006 time=0.420436 sec left=86.092673 sec 
... solve    28 a=0.00006 time=0.436000 sec left=86.075698 sec 
... solve    29 a=0.00007 time=0.451816 sec left=86.107039 sec 
... solve    30 a=0.00007 time=0.467230 sec left=86.060819 sec 
... solve    31 a=0.00008 time=0.483062 sec left=86.091441 sec 
... solve    32 a=0.00008 time=0.498470 sec left=86.045622 sec 
... solve    33 a=0.00009 time=0.513738 sec left=85.978382 sec 
... solve    34 a=0.00009 time=0.529118 sec left=85.932552 sec 
... solve    35 a=0.00010 time=0.544527 sec left=85.892879 sec 
... solve    36 a=0.00010 time=0.560018 sec left=85.866973 sec 
... solve    37 a=0.00011 time=0.575485 sec left=85.838349 sec 
... solve    38 a=0.00012 time=0.590965 sec left=85.812161 sec 
... solve    39 a=0.00012 time=0.606332 sec left=85.770536 sec 
... solve    40 a=0.00013 time=0.621736 sec left=85.735464 sec 
... solve    41 a=0.00013 time=0.637126 sec left=85.698661 sec 
... solve    42 a=0.00014 time=0.652784 sec left=85.699113 sec 
... solve    43 a=0.00015 time=0.669405 sec left=85.822025 sec 
... solve    44 a=0.00015 time=0.684791 sec left=85.783757 sec 
... solve    45 a=0.00016 time=0.700191 sec left=85.748221 sec 
... solve    46 a=0.00017 time=0.715569 sec left=85.710925 sec 
... solve    47 a=0.00018 time=0.730823 sec left=85.660144 sec 
... solve    48 a=0.00018 time=0.746358 sec left=85.642745 sec 
... solve    49 a=0.00019 time=0.761854 sec left=85.621375 sec 
... solve    50 a=0.00020 time=0.777213 sec left=85.585044 sec 
... solve    51 a=0.00021 time=0.792524 sec left=85.544354 sec 
... solve    52 a=0.00022 time=0.807921 sec left=85.513743 sec 
... solve    53 a=0.00022 time=0.823299 sec left=85.481733 sec 
... solve    54 a=0.00023 time=0.838623 sec left=85.444735 sec 
... solve    55 a=0.00024 time=0.854281 sec left=85.442132 sec 
... solve    56 a=0.00025 time=0.869650 sec left=85.410580 sec 
... solve    57 a=0.00026 time=0.884987 sec left=85.376509 sec 
... solve    58 a=0.00027 time=0.900381 sec left=85.348487 sec 
... solve    59 a=0.00028 time=0.915811 sec left=85.324248 sec 
... solve    60 a=0.00029 time=0.931083 sec left=85.285829 sec 
... solve    61 a=0.00030 time=0.946685 sec left=85.277896 sec 
... solve    62 a=0.00031 time=0.962096 sec left=85.252879 sec 
... solve    63 a=0.00032 time=0.977455 sec left=85.223459 sec 
... solve    64 a=0.00033 time=0.992973 sec left=85.208208 sec 
... solve    65 a=0.00034 time=1.008446 sec left=85.189064 sec 
... solve    66 a=0.00035 time=1.023827 sec left=85.162544 sec 
... solve    67 a=0.00036 time=1.040371 sec left=85.231553 sec 
... solve    68 a=0.00037 time=1.055956 sec left=85.220569 sec 
... solve    69 a=0.00038 time=1.071345 sec left=85.194025 sec 
... solve    70 a=0.00039 time=1.086751 sec left=85.169053 sec 
... solve    71 a=0.00040 time=1.102061 sec left=85.136934 sec 
... solve    72 a=0.00041 time=1.117465 sec left=85.112365 sec 
... solve    73 a=0.00043 time=1.134472 sec left=85.208449 sec 
... solve    74 a=0.00044 time=1.150048 sec left=85.195688 sec 
... solve    75 a=0.00045 time=1.165457 sec left=85.170501 sec 
... solve    76 a=0.00046 time=1.180842 sec left=85.143842 sec 
... solve    77 a=0.00047 time=1.196206 sec left=85.115980 sec 
... solve    78 a=0.00049 time=1.211635 sec left=85.092934 sec 
... solve    79 a=0.00050 time=1.227120 sec left=85.074033 sec 
... solve    80 a=0.00051 time=1.242495 sec left=85.047756 sec 
... solve    81 a=0.00052 time=1.257952 sec left=85.027223 sec 
... solve    82 a=0.00054 time=1.273403 sec left=85.006414 sec 
... solve    83 a=0.00055 time=1.289054 sec left=84.998921 sec 
... solve    84 a=0.00056 time=1.304411 sec left=84.972082 sec 
... solve    85 a=0.00058 time=1.320013 sec left=84.961283 sec 
... solve    86 a=0.00059 time=1.335364 sec left=84.934407 sec 
... solve    87 a=0.00060 time=1.350883 sec left=84.918357 sec 
... solve    88 a=0.00062 time=1.366173 sec left=84.888090 sec 
... solve    89 a=0.00063 time=1.381537 sec left=84.862705 sec 
... solve    90 a=0.00065 time=1.396851 sec left=84.834567 sec 
... solve    91 a=0.00066 time=1.413385 sec left=84.879858 sec 
... solve    92 a=0.00068 time=1.429121 sec left=84.876410 sec 
... solve    93 a=0.00069 time=1.444570 sec left=84.856015 sec 
... solve    94 a=0.00071 time=1.460235 sec left=84.848044 sec 
... solve    95 a=0.00072 time=1.475836 sec left=84.836405 sec 
... solve    96 a=0.00074 time=1.491543 sec left=84.830655 sec 
... solve    97 a=0.00075 time=1.506932 sec left=84.806803 sec 
... solve    98 a=0.00077 time=1.522346 sec left=84.784516 sec 
... solve    99 a=0.00078 time=1.537754 sec left=84.762038 sec 
... solve   100 a=0.00080 time=1.553251 sec left=84.744556 sec 
... solve   101 a=0.00081 time=1.568562 sec left=84.717068 sec 
... solve   102 a=0.00083 time=1.583985 sec left=84.695754 sec 
... solve   103 a=0.00085 time=1.599319 sec left=84.670002 sec 
... solve   104 a=0.00086 time=1.614636 sec left=84.643401 sec 
... solve   105 a=0.00088 time=1.630346 sec left=84.637417 sec 
... solve   106 a=0.00090 time=1.645888 sec left=84.622767 sec 
... solve   107 a=0.00091 time=1.661266 sec left=84.599595 sec 
... solve   108 a=0.00093 time=1.677882 sec left=84.639069 sec 
... solve   109 a=0.00095 time=1.693259 sec left=84.615547 sec 
... solve   110 a=0.00097 time=1.708612 sec left=84.591084 sec 
... solve   111 a=0.00098 time=1.723961 sec left=84.566540 sec 
... solve   112 a=0.00100 time=1.739382 sec left=84.545660 sec 
... solve   113 a=0.00102 time=1.754927 sec left=84.530850 sec 
... solve   114 a=0.00104 time=1.770658 sec left=84.524858 sec 
... solve   115 a=0.00106 time=1.787052 sec left=84.550112 sec 
... solve   116 a=0.00107 time=1.802438 sec left=84.527377 sec 
... solve   117 a=0.00109 time=1.817730 sec left=84.500443 sec 
... solve   118 a=0.00111 time=1.833052 sec left=84.475044 sec 
... solve   119 a=0.00113 time=1.848645 sec left=84.462150 sec 
... solve   120 a=0.00115 time=1.864150 sec left=84.445361 sec 
... solve   121 a=0.00117 time=1.879471 sec left=84.420148 sec 
... solve   122 a=0.00119 time=1.894852 sec left=84.397859 sec 
... solve   123 a=0.00121 time=1.910246 sec left=84.376257 sec 
... solve   124 a=0.00123 time=1.925676 sec left=84.356375 sec 
... solve   125 a=0.00125 time=1.941101 sec left=84.336348 sec 
... solve   126 a=0.00127 time=1.956735 sec left=84.325314 sec 
... solve   127 a=0.00129 time=1.972105 sec left=84.302965 sec 
... solve   128 a=0.00131 time=1.987910 sec left=84.299130 sec 
... solve   129 a=0.00133 time=2.003425 sec left=84.282993 sec 
... solve   130 a=0.00135 time=2.018686 sec left=84.256264 sec 
... solve   131 a=0.00137 time=2.033980 sec left=84.230993 sec 
... solve   132 a=0.00139 time=2.049638 sec left=84.220831 sec 
... solve   133 a=0.00141 time=2.064968 sec left=84.197294 sec 
... solve   134 a=0.00143 time=2.080303 sec left=84.174041 sec 
... solve   135 a=0.00146 time=2.095651 sec left=84.151468 sec 
... solve   136 a=0.00148 time=2.110997 sec left=84.128841 sec 
... solve   137 a=0.00150 time=2.126308 sec left=84.104976 sec 
... solve   138 a=0.00152 time=2.141832 sec left=84.089598 sec 
... solve   139 a=0.00154 time=2.158219 sec left=84.107849 sec 
... solve   140 a=0.00157 time=2.173579 sec left=84.085837 sec 
... solve   141 a=0.00159 time=2.188903 sec left=84.062614 sec 
... solve   142 a=0.00161 time=2.204268 sec left=84.041026 sec 
... solve   143 a=0.00163 time=2.219662 sec left=84.020624 sec 
... solve   144 a=0.00166 time=2.235104 sec left=84.002095 sec 
... solve   145 a=0.00168 time=2.250873 sec left=83.995849 sec 
... solve   146 a=0.00170 time=2.266287 sec left=83.976206 sec 
... solve   147 a=0.00173 time=2.281643 sec left=83.954634 sec 
... solve   148 a=0.00175 time=2.296966 sec left=83.931831 sec 
... solve   149 a=0.00177 time=2.312424 sec left=83.914100 sec 
... solve   150 a=0.00180 time=2.327866 sec left=83.895786 sec 
... solve   151 a=0.00182 time=2.343171 sec left=83.872607 sec 
... solve   152 a=0.00184 time=2.358685 sec left=83.856926 sec 
... solve   153 a=0.00187 time=2.374045 sec left=83.835844 sec 
... solve   154 a=0.00189 time=2.389344 sec left=83.812732 sec 
... solve   155 a=0.00192 time=2.404538 sec left=83.786027 sec 
... solve   156 a=0.00194 time=2.420052 sec left=83.770512 sec 
... solve   157 a=0.00197 time=2.435391 sec left=83.749047 sec 
... solve   158 a=0.00199 time=2.450856 sec left=83.731931 sec 
... solve   159 a=0.00202 time=2.466253 sec left=83.712494 sec 
... solve   160 a=0.00204 time=2.481565 sec left=83.690274 sec 
... solve   161 a=0.00207 time=2.497024 sec left=83.673066 sec 
... solve   162 a=0.00210 time=2.512556 sec left=83.658310 sec 
... solve   163 a=0.00212 time=2.528916 sec left=83.670939 sec 
... solve   164 a=0.00215 time=2.544292 sec left=83.650863 sec 
... solve   165 a=0.00217 time=2.559783 sec left=83.634602 sec 
... solve   166 a=0.00220 time=2.575202 sec left=83.615979 sec 
... solve   167 a=0.00223 time=2.590495 sec left=83.593394 sec 
... solve   168 a=0.00225 time=2.605907 sec left=83.574647 sec 
... solve   169 a=0.00228 time=2.621201 sec left=83.552242 sec 
... solve   170 a=0.00231 time=2.636574 sec left=83.532393 sec 
... solve   171 a=0.00233 time=2.652311 sec left=83.524058 sec 
... solve   172 a=0.00236 time=2.667680 sec left=83.504118 sec 
... solve   173 a=0.00239 time=2.683022 sec left=83.483391 sec 
... solve   174 a=0.00242 time=2.698451 sec left=83.465417 sec 
... solve   175 a=0.00245 time=2.713743 sec left=83.443259 sec 
... solve   176 a=0.00247 time=2.729102 sec left=83.423228 sec 
... solve   177 a=0.00250 time=2.744428 sec left=83.402246 sec 
... solve   178 a=0.00253 time=2.759899 sec left=83.385709 sec 
... solve   179 a=0.00256 time=2.775404 sec left=83.370205 sec 
... solve   180 a=0.00259 time=2.790858 sec left=83.353178 sec 
... solve   181 a=0.00262 time=2.806076 sec left=83.329160 sec 
... solve   182 a=0.00264 time=2.821401 sec left=83.308250 sec 
... solve   183 a=0.00267 time=2.836739 sec left=83.288077 sec 
... solve   184 a=0.00270 time=2.852208 sec left=83.271635 sec 
... solve   185 a=0.00273 time=2.867681 sec left=83.255319 sec 
... solve   186 a=0.00276 time=2.883066 sec left=83.236444 sec 
... solve   187 a=0.00279 time=2.899491 sec left=83.247493 sec 
... solve   188 a=0.00282 time=2.914893 sec left=83.229070 sec 
... solve   189 a=0.00285 time=2.930299 sec left=83.210763 sec 
... solve   190 a=0.00288 time=2.945669 sec left=83.191499 sec 
... solve   191 a=0.00291 time=2.961112 sec left=83.174269 sec 
... solve   192 a=0.00294 time=2.976438 sec left=83.153846 sec 
... solve   193 a=0.00297 time=2.991953 sec left=83.138643 sec 
... solve   194 a=0.00300 time=3.007369 sec left=83.120757 sec 
... solve   195 a=0.00304 time=3.022708 sec left=83.100779 sec 
... solve   196 a=0.00307 time=3.038094 sec left=83.082160 sec 
... solve   197 a=0.00310 time=3.053584 sec left=83.066350 sec 
... solve   198 a=0.00313 time=3.070549 sec left=83.090484 sec 
... solve   199 a=0.00316 time=3.086093 sec left=83.075979 sec 
... solve   200 a=0.00319 time=3.101452 sec left=83.056456 sec 
... solve   201 a=0.00322 time=3.116808 sec left=83.036948 sec 
... solve   202 a=0.00326 time=3.132114 sec left=83.016129 sec 
... solve   203 a=0.00329 time=3.147508 sec left=82.997685 sec 
... solve   204 a=0.00332 time=3.163126 sec left=82.985147 sec 
... solve   205 a=0.00335 time=3.178470 sec left=82.965454 sec 
... solve   206 a=0.00339 time=3.193845 sec left=82.946556 sec 
... solve   207 a=0.00342 time=3.209346 sec left=82.930974 sec 
... solve   208 a=0.00345 time=3.224669 sec left=82.910815 sec 
... solve   209 a=0.00349 time=3.240442 sec left=82.902216 sec 
... solve   210 a=0.00352 time=3.256171 sec left=82.892403 sec 
... solve   211 a=0.00355 time=3.272408 sec left=82.895428 sec 
... solve   212 a=0.00359 time=3.287741 sec left=82.875508 sec 
... solve   213 a=0.00362 time=3.303138 sec left=82.857187 sec 
... solve   214 a=0.00365 time=3.318468 sec left=82.837271 sec 
... solve   215 a=0.00369 time=3.333754 sec left=82.816279 sec 
... solve   216 a=0.00372 time=3.349418 sec left=82.804661 sec 
... solve   217 a=0.00376 time=3.364788 sec left=82.785820 sec 
... solve   218 a=0.00379 time=3.380113 sec left=82.765886 sec 
... solve   219 a=0.00383 time=3.395469 sec left=82.746749 sec 
... solve   220 a=0.00386 time=3.410812 sec left=82.727331 sec 
... solve   221 a=0.00390 time=3.426146 sec left=82.707708 sec 
... solve   222 a=0.00393 time=3.441502 sec left=82.688725 sec 
... solve   223 a=0.00397 time=3.457209 sec left=82.678097 sec 
... solve   224 a=0.00400 time=3.472765 sec left=82.663781 sec 
... solve   225 a=0.00404 time=3.488121 sec left=82.644858 sec 
... solve   226 a=0.00408 time=3.503745 sec left=82.632216 sec 
... solve   227 a=0.00411 time=3.519125 sec left=82.613844 sec 
... solve   228 a=0.00415 time=3.534597 sec left=82.597600 sec 
... solve   229 a=0.00418 time=3.550010 sec left=82.580015 sec 
... solve   230 a=0.00422 time=3.565461 sec left=82.563328 sec 
... solve   231 a=0.00426 time=3.580832 sec left=82.544784 sec 
... solve   232 a=0.00429 time=3.596143 sec left=82.524960 sec 
... solve   233 a=0.00433 time=3.611492 sec left=82.505997 sec 
... solve   234 a=0.00437 time=3.627050 sec left=82.491796 sec 
... solve   235 a=0.00441 time=3.643273 sec left=82.492640 sec 
... solve   236 a=0.00444 time=3.658735 sec left=82.476231 sec 
... solve   237 a=0.00448 time=3.674565 sec left=82.468065 sec 
... solve   238 a=0.00452 time=3.690570 sec left=82.463746 sec 
... solve   239 a=0.00456 time=3.705885 sec left=82.443956 sec 
... solve   240 a=0.00460 time=3.721375 sec left=82.428124 sec 
... solve   241 a=0.00463 time=3.736714 sec left=82.408965 sec 
... solve   242 a=0.00467 time=3.752021 sec left=82.389090 sec 
... solve   243 a=0.00471 time=3.767551 sec left=82.374151 sec 
... solve   244 a=0.00475 time=3.782894 sec left=82.355158 sec 
... solve   245 a=0.00479 time=3.798201 sec left=82.335392 sec 
... solve   246 a=0.00483 time=3.813962 sec left=82.325441 sec 
... solve   247 a=0.00487 time=3.829347 sec left=82.307383 sec 
... solve   248 a=0.00491 time=3.844658 sec left=82.287762 sec 
... solve   249 a=0.00495 time=3.859872 sec left=82.266109 sec 
... solve   250 a=0.00499 time=3.875352 sec left=82.250152 sec 
... solve   251 a=0.00503 time=3.890706 sec left=82.231558 sec 
... solve   252 a=0.00507 time=3.906134 sec left=82.214505 sec 
... solve   253 a=0.00511 time=3.921583 sec left=82.197925 sec 
... solve   254 a=0.00515 time=3.936916 sec left=82.178913 sec 
... solve   255 a=0.00519 time=3.952232 sec left=82.159617 sec 
... solve   256 a=0.00523 time=3.967727 sec left=82.144037 sec 
... solve   257 a=0.00527 time=3.983126 sec left=82.126479 sec 
... solve   258 a=0.00531 time=3.998690 sec left=82.112326 sec 
... solve   259 a=0.00535 time=4.015133 sec left=82.116119 sec 
... solve   260 a=0.00539 time=4.030541 sec left=82.098694 sec 
... solve   261 a=0.00543 time=4.045909 sec left=82.080493 sec 
... solve   262 a=0.00547 time=4.061204 sec left=82.060799 sec 
... solve   263 a=0.00552 time=4.076828 sec left=82.047799 sec 
... solve   264 a=0.00556 time=4.092292 sec left=82.031553 sec 
... solve   265 a=0.00560 time=4.107576 sec left=82.011718 sec 
... solve   266 a=0.00564 time=4.123192 sec left=81.998520 sec 
... solve   267 a=0.00569 time=4.138922 sec left=81.987562 sec 
... solve   268 a=0.00573 time=4.154284 sec left=81.969288 sec 
... solve   269 a=0.00577 time=4.169842 sec left=81.954927 sec 
... solve   270 a=0.00581 time=4.185419 sec left=81.940909 sec 
... solve   271 a=0.00586 time=4.200758 sec left=81.922161 sec 
... solve   272 a=0.00590 time=4.216056 sec left=81.902796 sec 
... solve   273 a=0.00594 time=4.231594 sec left=81.888029 sec 
... solve   274 a=0.00599 time=4.246917 sec left=81.869130 sec 
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... solve  1100 a=0.09361 time=17.161098 sec left=69.517983 sec 
... solve  1101 a=0.09377 time=17.176770 sec left=69.502657 sec 
... solve  1102 a=0.09394 time=17.193476 sec left=69.491538 sec 
... solve  1103 a=0.09410 time=17.209121 sec left=69.476110 sec 
... solve  1104 a=0.09427 time=17.224898 sec left=69.461205 sec 
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... solve  1106 a=0.09460 time=17.257089 sec left=69.433974 sec 
... solve  1107 a=0.09476 time=17.272768 sec left=69.418667 sec 
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... solve  1111 a=0.09543 time=17.337628 sec left=69.366053 sec 
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... solve  1113 a=0.09576 time=17.369378 sec left=69.337003 sec 
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... solve  1115 a=0.09609 time=17.402088 sec left=69.311754 sec 
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... solve  1117 a=0.09642 time=17.433597 sec left=69.281710 sec 
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... solve  1119 a=0.09676 time=17.465419 sec left=69.252902 sec 
... solve  1120 a=0.09693 time=17.481758 sec left=69.240185 sec 
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... solve  1123 a=0.09743 time=17.529387 sec left=69.196529 sec 
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... solve  1125 a=0.09776 time=17.561278 sec left=69.167961 sec 
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... solve  1127 a=0.09810 time=17.593034 sec left=69.138844 sec 
... solve  1128 a=0.09827 time=17.608959 sec left=69.124472 sec 
... solve  1129 a=0.09844 time=17.624289 sec left=69.107764 sec 
... solve  1130 a=0.09860 time=17.640240 sec left=69.093483 sec 
... solve  1131 a=0.09877 time=17.655816 sec left=69.077736 sec 
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... solve  1135 a=0.09945 time=17.727770 sec left=69.052327 sec 
... solve  1136 a=0.09962 time=17.746382 sec left=69.048357 sec 
... solve  1137 a=0.09979 time=17.762819 sec left=69.035911 sec 
... solve  1138 a=0.09996 time=17.778243 sec left=69.019518 sec 
... solve  1139 a=0.10013 time=17.794422 sec left=69.006058 sec 
... solve  1140 a=0.10030 time=17.809812 sec left=68.989529 sec 
... solve  1141 a=0.10047 time=17.825694 sec left=68.974910 sec 
... solve  1142 a=0.10064 time=17.841209 sec left=68.958871 sec 
... solve  1143 a=0.10081 time=17.857064 sec left=68.944148 sec 
... solve  1144 a=0.10098 time=17.872939 sec left=68.929494 sec 
... solve  1145 a=0.10115 time=17.888294 sec left=68.912841 sec 
... solve  1146 a=0.10132 time=17.904201 sec left=68.898304 sec 
... solve  1147 a=0.10149 time=17.920141 sec left=68.883902 sec 
... solve  1148 a=0.10166 time=17.935681 sec left=68.867958 sec 
... solve  1149 a=0.10183 time=17.951762 sec left=68.854090 sec 
... solve  1150 a=0.10200 time=17.967637 sec left=68.839428 sec 
... solve  1151 a=0.10217 time=17.983508 sec left=68.824749 sec 
... solve  1152 a=0.10234 time=17.999226 sec left=68.809484 sec 
... solve  1153 a=0.10251 time=18.015094 sec left=68.794786 sec 
... solve  1154 a=0.10269 time=18.030514 sec left=68.778385 sec 
... solve  1155 a=0.10286 time=18.046360 sec left=68.763605 sec 
... solve  1156 a=0.10303 time=18.062203 sec left=68.748809 sec 
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... solve  1734 a=0.22161 time=27.444134 sec left=60.491017 sec 
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... solve  1744 a=0.22397 time=27.605753 sec left=60.340065 sec 
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... solve  1746 a=0.22444 time=27.637859 sec left=60.309385 sec 
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... solve  1748 a=0.22491 time=27.669572 sec left=60.277845 sec 
... solve  1749 a=0.22514 time=27.685595 sec left=60.262437 sec 
... solve  1750 a=0.22538 time=27.701468 sec left=60.246703 sec 
... solve  1751 a=0.22562 time=27.717361 sec left=60.231010 sec 
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... solve  1753 a=0.22609 time=27.749227 sec left=60.199800 sec 
... solve  1754 a=0.22633 time=27.766503 sec left=60.187108 sec 
... solve  1755 a=0.22656 time=27.783386 sec left=60.173557 sec 
... solve  1756 a=0.22680 time=27.799527 sec left=60.158399 sec 
... solve  1757 a=0.22704 time=27.815712 sec left=60.143331 sec 
... solve  1758 a=0.22727 time=27.831117 sec left=60.126579 sec 
... solve  1759 a=0.22751 time=27.847231 sec left=60.111358 sec 
... solve  1760 a=0.22775 time=27.863205 sec left=60.095835 sec 
... solve  1761 a=0.22798 time=27.879240 sec left=60.080442 sec 
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... solve  1771 a=0.23036 time=28.038477 sec left=59.924096 sec 
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... solve  1774 a=0.23108 time=28.087560 sec left=59.879984 sec 
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... solve  1780 a=0.23251 time=28.184958 sec left=59.790081 sec 
... solve  1781 a=0.23275 time=28.200938 sec left=59.774556 sec 
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... solve  1784 a=0.23346 time=28.248217 sec left=59.726580 sec 
... solve  1785 a=0.23370 time=28.264103 sec left=59.710857 sec 
... solve  1786 a=0.23394 time=28.279944 sec left=59.695037 sec 
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... solve  1788 a=0.23442 time=28.311694 sec left=59.663536 sec 
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... solve  1790 a=0.23490 time=28.343157 sec left=59.631437 sec 
... solve  1791 a=0.23514 time=28.359261 sec left=59.616170 sec 
... solve  1792 a=0.23538 time=28.375092 sec left=59.600329 sec 
... solve  1793 a=0.23562 time=28.391011 sec left=59.584673 sec 
... solve  1794 a=0.23586 time=28.406407 sec left=59.567919 sec 
... solve  1795 a=0.23610 time=28.422450 sec left=59.552520 sec 
... solve  1796 a=0.23634 time=28.438499 sec left=59.537136 sec 
... solve  1797 a=0.23658 time=28.454448 sec left=59.521546 sec 
... solve  1798 a=0.23682 time=28.470334 sec left=59.505817 sec 
... solve  1799 a=0.23706 time=28.486234 sec left=59.490121 sec 
... solve  1800 a=0.23730 time=28.501530 sec left=59.473163 sec 
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... solve  1802 a=0.23778 time=28.534377 sec left=59.443948 sec 
... solve  1803 a=0.23802 time=28.550257 sec left=59.428208 sec 
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... solve  1805 a=0.23850 time=28.582102 sec left=59.396902 sec 
... solve  1806 a=0.23874 time=28.598023 sec left=59.381244 sec 
... solve  1807 a=0.23899 time=28.614010 sec left=59.365726 sec 
... solve  1808 a=0.23923 time=28.630262 sec left=59.350755 sec 
... solve  1809 a=0.23947 time=28.646249 sec left=59.335234 sec 
... solve  1810 a=0.23971 time=28.662222 sec left=59.319684 sec 
... solve  1811 a=0.23995 time=28.678076 sec left=59.303889 sec 
... solve  1812 a=0.24019 time=28.694003 sec left=59.288240 sec 
... solve  1813 a=0.24043 time=28.710072 sec left=59.272889 sec 
... solve  1814 a=0.24068 time=28.725965 sec left=59.257169 sec 
... solve  1815 a=0.24092 time=28.741816 sec left=59.241367 sec 
... solve  1816 a=0.24116 time=28.757752 sec left=59.225734 sec 
... solve  1817 a=0.24140 time=28.773588 sec left=59.209901 sec 
... solve  1818 a=0.24164 time=28.789424 sec left=59.194065 sec 
... solve  1819 a=0.24188 time=28.805350 sec left=59.178415 sec 
... solve  1820 a=0.24213 time=28.821278 sec left=59.162768 sec 
... solve  1821 a=0.24237 time=28.837098 sec left=59.146900 sec 
... solve  1822 a=0.24261 time=28.852955 sec left=59.131110 sec 
... solve  1823 a=0.24285 time=28.868929 sec left=59.115555 sec 
... solve  1824 a=0.24310 time=28.884776 sec left=59.099735 sec 
... solve  1825 a=0.24334 time=28.901773 sec left=59.086277 sec 
... solve  1826 a=0.24358 time=28.917819 sec left=59.070868 sec 
... solve  1827 a=0.24382 time=28.933214 sec left=59.054130 sec 
... solve  1828 a=0.24407 time=28.949095 sec left=59.038384 sec 
... solve  1829 a=0.24431 time=28.964904 sec left=59.022494 sec 
... solve  1830 a=0.24455 time=28.980829 sec left=59.006838 sec 
... solve  1831 a=0.24480 time=28.996815 sec left=58.991305 sec 
... solve  1832 a=0.24504 time=29.012653 sec left=58.975472 sec 
... solve  1833 a=0.24528 time=29.027978 sec left=58.958596 sec 
... solve  1834 a=0.24553 time=29.043926 sec left=58.942986 sec 
... solve  1835 a=0.24577 time=29.059836 sec left=58.927299 sec 
... solve  1836 a=0.24601 time=29.075822 sec left=58.911766 sec 
... solve  1837 a=0.24626 time=29.091925 sec left=58.896469 sec 
... solve  1838 a=0.24650 time=29.107760 sec left=58.880629 sec 
... solve  1839 a=0.24674 time=29.123053 sec left=58.863695 sec 
... solve  1840 a=0.24699 time=29.138890 sec left=58.847860 sec 
... solve  1841 a=0.24723 time=29.154858 sec left=58.832288 sec 
... solve  1842 a=0.24747 time=29.170831 sec left=58.816725 sec 
... solve  1843 a=0.24772 time=29.186678 sec left=58.800911 sec 
... solve  1844 a=0.24796 time=29.202595 sec left=58.785237 sec 
... solve  1845 a=0.24821 time=29.218597 sec left=58.769733 sec 
... solve  1846 a=0.24845 time=29.234447 sec left=58.753923 sec 
... solve  1847 a=0.24870 time=29.250326 sec left=58.738170 sec 
... solve  1848 a=0.24894 time=29.266978 sec left=58.723971 sec 
... solve  1849 a=0.24918 time=29.282746 sec left=58.707996 sec 
... solve  1850 a=0.24943 time=29.298599 sec left=58.692188 sec 
... solve  1851 a=0.24967 time=29.314547 sec left=58.676575 sec 
... solve  1852 a=0.24992 time=29.330425 sec left=58.660820 sec 
... solve  1853 a=0.25016 time=29.346291 sec left=58.645040 sec 
... solve  1854 a=0.25041 time=29.362263 sec left=58.629473 sec 
... solve  1855 a=0.25065 time=29.378555 sec left=58.614545 sec 
... solve  1856 a=0.25090 time=29.394467 sec left=58.598852 sec 
... solve  1857 a=0.25114 time=29.410344 sec left=58.583097 sec 
... solve  1858 a=0.25139 time=29.426426 sec left=58.567744 sec 
... solve  1859 a=0.25163 time=29.442334 sec left=58.552046 sec 
... solve  1860 a=0.25188 time=29.458854 sec left=58.537562 sec 
... solve  1861 a=0.25212 time=29.475222 sec left=58.522778 sec 
... solve  1862 a=0.25237 time=29.491188 sec left=58.507191 sec 
... solve  1863 a=0.25262 time=29.507087 sec left=58.491476 sec 
... solve  1864 a=0.25286 time=29.522974 sec left=58.475734 sec 
... solve  1865 a=0.25311 time=29.539038 sec left=58.460340 sec 
... solve  1866 a=0.25335 time=29.555081 sec left=58.444905 sec 
... solve  1867 a=0.25360 time=29.570488 sec left=58.428214 sec 
... solve  1868 a=0.25384 time=29.586538 sec left=58.412793 sec 
... solve  1869 a=0.25409 time=29.602451 sec left=58.397101 sec 
... solve  1870 a=0.25434 time=29.618336 sec left=58.381354 sec 
... solve  1871 a=0.25458 time=29.634220 sec left=58.365602 sec 
... solve  1872 a=0.25483 time=29.650983 sec left=58.351584 sec 
... solve  1873 a=0.25508 time=29.666876 sec left=58.335851 sec 
... solve  1874 a=0.25532 time=29.682878 sec left=58.320332 sec 
... solve  1875 a=0.25557 time=29.699088 sec left=58.305220 sec 
... solve  1876 a=0.25582 time=29.715026 sec left=58.289574 sec 
... solve  1877 a=0.25606 time=29.731277 sec left=58.274541 sec 
... solve  1878 a=0.25631 time=29.746646 sec left=58.257781 sec 
... solve  1879 a=0.25656 time=29.762572 sec left=58.242109 sec 
... solve  1880 a=0.25680 time=29.779817 sec left=58.229017 sec 
... solve  1881 a=0.25705 time=29.795704 sec left=58.213270 sec 
... solve  1882 a=0.25730 time=29.811676 sec left=58.197685 sec 
... solve  1883 a=0.25754 time=29.827708 sec left=58.182220 sec 
... solve  1884 a=0.25779 time=29.843593 sec left=58.166464 sec 
... solve  1885 a=0.25804 time=29.859563 sec left=58.150876 sec 
... solve  1886 a=0.25829 time=29.875495 sec left=58.135213 sec 
... solve  1887 a=0.25853 time=29.891041 sec left=58.118799 sec 
... solve  1888 a=0.25878 time=29.906923 sec left=58.103041 sec 
... solve  1889 a=0.25903 time=29.923450 sec left=58.088532 sec 
... solve  1890 a=0.25928 time=29.939563 sec left=58.073217 sec 
... solve  1891 a=0.25952 time=29.955406 sec left=58.057381 sec 
... solve  1892 a=0.25977 time=29.971261 sec left=58.041569 sec 
... solve  1893 a=0.26002 time=29.987195 sec left=58.025906 sec 
... solve  1894 a=0.26027 time=30.003047 sec left=58.010086 sec 
... solve  1895 a=0.26052 time=30.020194 sec left=57.996766 sec 
... solve  1896 a=0.26076 time=30.036351 sec left=57.981535 sec 
... solve  1897 a=0.26101 time=30.052445 sec left=57.966179 sec 
... solve  1898 a=0.26126 time=30.068391 sec left=57.950537 sec 
... solve  1899 a=0.26151 time=30.084303 sec left=57.934829 sec 
... solve  1900 a=0.26176 time=30.100574 sec left=57.919811 sec 
... solve  1901 a=0.26201 time=30.116646 sec left=57.904404 sec 
... solve  1902 a=0.26226 time=30.132528 sec left=57.888647 sec 
... solve  1903 a=0.26250 time=30.148639 sec left=57.873295 sec 
... solve  1904 a=0.26275 time=30.164522 sec left=57.857552 sec 
... solve  1905 a=0.26300 time=30.180422 sec left=57.841819 sec 
... solve  1906 a=0.26325 time=30.196602 sec left=57.826623 sec 
... solve  1907 a=0.26350 time=30.212724 sec left=57.811312 sec 
... solve  1908 a=0.26375 time=30.228584 sec left=57.795503 sec 
... solve  1909 a=0.26400 time=30.244090 sec left=57.779016 sec 
... solve  1910 a=0.26425 time=30.260161 sec left=57.763609 sec 
... solve  1911 a=0.26450 time=30.276055 sec left=57.747863 sec 
... solve  1912 a=0.26475 time=30.292322 sec left=57.732828 sec 
... solve  1913 a=0.26500 time=30.308197 sec left=57.717047 sec 
... solve  1914 a=0.26524 time=30.324419 sec left=57.701920 sec 
... solve  1915 a=0.26549 time=30.340630 sec left=57.686766 sec 
... solve  1916 a=0.26574 time=30.356695 sec left=57.671354 sec 
... solve  1917 a=0.26599 time=30.372589 sec left=57.655606 sec 
... solve  1918 a=0.26624 time=30.389645 sec left=57.642060 sec 
... solve  1919 a=0.26649 time=30.405538 sec left=57.626309 sec 
... solve  1920 a=0.26674 time=30.421627 sec left=57.610926 sec 
... solve  1921 a=0.26699 time=30.437587 sec left=57.595302 sec 
... solve  1922 a=0.26724 time=30.454191 sec left=57.580891 sec 
... solve  1923 a=0.26749 time=30.470309 sec left=57.565563 sec 
... solve  1924 a=0.26774 time=30.486478 sec left=57.550329 sec 
... solve  1925 a=0.26799 time=30.502614 sec left=57.535032 sec 
... solve  1926 a=0.26825 time=30.518509 sec left=57.519282 sec 
... solve  1927 a=0.26850 time=30.534297 sec left=57.503326 sec 
... solve  1928 a=0.26875 time=30.550374 sec left=57.487916 sec 
... solve  1929 a=0.26900 time=30.566435 sec left=57.472474 sec 
... solve  1930 a=0.26925 time=30.582583 sec left=57.457198 sec 
... solve  1931 a=0.26950 time=30.598801 sec left=57.442050 sec 
... solve  1932 a=0.26975 time=30.614949 sec left=57.426771 sec 
... solve  1933 a=0.27000 time=30.630872 sec left=57.411068 sec 
... solve  1934 a=0.27025 time=30.646709 sec left=57.395205 sec 
... solve  1935 a=0.27050 time=30.662856 sec left=57.379921 sec 
... solve  1936 a=0.27075 time=30.678803 sec left=57.364263 sec 
... solve  1937 a=0.27100 time=30.694301 sec left=57.347763 sec 
... solve  1938 a=0.27126 time=30.710454 sec left=57.332490 sec 
... solve  1939 a=0.27151 time=30.726356 sec left=57.316747 sec 
... solve  1940 a=0.27176 time=30.742444 sec left=57.301352 sec 
... solve  1941 a=0.27201 time=30.759594 sec left=57.287931 sec 
... solve  1942 a=0.27226 time=30.775591 sec left=57.272364 sec 
... solve  1943 a=0.27251 time=30.791450 sec left=57.256539 sec 
... solve  1944 a=0.27277 time=30.807321 sec left=57.240737 sec 
... solve  1945 a=0.27302 time=30.823579 sec left=57.225652 sec 
... solve  1946 a=0.27327 time=30.839720 sec left=57.210347 sec 
... solve  1947 a=0.27352 time=30.855842 sec left=57.195006 sec 
... solve  1948 a=0.27377 time=30.871708 sec left=57.179195 sec 
... solve  1949 a=0.27403 time=30.887725 sec left=57.163656 sec 
... solve  1950 a=0.27428 time=30.903799 sec left=57.148228 sec 
... solve  1951 a=0.27453 time=30.919748 sec left=57.132565 sec 
... solve  1952 a=0.27478 time=30.935968 sec left=57.117403 sec 
... solve  1953 a=0.27503 time=30.952059 sec left=57.102004 sec 
... solve  1954 a=0.27529 time=30.967901 sec left=57.086144 sec 
... solve  1955 a=0.27554 time=30.983777 sec left=57.070346 sec 
... solve  1956 a=0.27579 time=30.999151 sec left=57.053626 sec 
... solve  1957 a=0.27604 time=31.015074 sec left=57.037914 sec 
... solve  1958 a=0.27630 time=31.031090 sec left=57.022223 sec 
... solve  1959 a=0.27655 time=31.047014 sec left=57.006666 sec 
... solve  1960 a=0.27680 time=31.062880 sec left=56.990850 sec 
... solve  1961 a=0.27706 time=31.078865 sec left=56.975250 sec 
... solve  1962 a=0.27731 time=31.094733 sec left=56.959439 sec 
... solve  1963 a=0.27756 time=31.110637 sec left=56.943691 sec 
... solve  1964 a=0.27782 time=31.127575 sec left=56.929831 sec 
... solve  1965 a=0.27807 time=31.143597 sec left=56.914300 sec 
... solve  1966 a=0.27832 time=31.160904 sec left=56.901113 sec 
... solve  1967 a=0.27858 time=31.176834 sec left=56.885413 sec 
... solve  1968 a=0.27883 time=31.192906 sec left=56.869968 sec 
... solve  1969 a=0.27908 time=31.208815 sec left=56.854209 sec 
... solve  1970 a=0.27934 time=31.224903 sec left=56.838806 sec 
... solve  1971 a=0.27959 time=31.241049 sec left=56.823492 sec 
... solve  1972 a=0.27984 time=31.257121 sec left=56.808048 sec 
... solve  1973 a=0.28010 time=31.273390 sec left=56.792956 sec 
... solve  1974 a=0.28035 time=31.289441 sec left=56.777467 sec 
... solve  1975 a=0.28061 time=31.305459 sec left=56.761922 sec 
... solve  1976 a=0.28086 time=31.321375 sec left=56.746190 sec 
... solve  1977 a=0.28111 time=31.337431 sec left=56.730711 sec 
... solve  1978 a=0.28137 time=31.353339 sec left=56.714961 sec 
... solve  1979 a=0.28162 time=31.369184 sec left=56.699101 sec 
... solve  1980 a=0.28188 time=31.385524 sec left=56.684131 sec 
... solve  1981 a=0.28213 time=31.401607 sec left=56.668698 sec 
... solve  1982 a=0.28239 time=31.417682 sec left=56.653250 sec 
... solve  1983 a=0.28264 time=31.434641 sec left=56.639394 sec 
... solve  1984 a=0.28289 time=31.450782 sec left=56.624062 sec 
... solve  1985 a=0.28315 time=31.466266 sec left=56.607548 sec 
... solve  1986 a=0.28340 time=31.482037 sec left=56.591550 sec 
... solve  1987 a=0.28366 time=31.498923 sec left=56.577554 sec 
... solve  1988 a=0.28391 time=31.515009 sec left=56.562120 sec 
... solve  1989 a=0.28417 time=31.530860 sec left=56.546268 sec 
... solve  1990 a=0.28442 time=31.547027 sec left=56.530979 sec 
... solve  1991 a=0.28468 time=31.563087 sec left=56.515496 sec 
... solve  1992 a=0.28493 time=31.579300 sec left=56.500287 sec 
... solve  1993 a=0.28519 time=31.595510 sec left=56.485072 sec 
... solve  1994 a=0.28544 time=31.611460 sec left=56.469392 sec 
... solve  1995 a=0.28570 time=31.627364 sec left=56.453631 sec 
... solve  1996 a=0.28595 time=31.643246 sec left=56.437827 sec 
... solve  1997 a=0.28621 time=31.658921 sec left=56.421656 sec 
... solve  1998 a=0.28647 time=31.674840 sec left=56.405920 sec 
... solve  1999 a=0.28672 time=31.691214 sec left=56.390993 sec 
... solve  2000 a=0.28698 time=31.707108 sec left=56.375213 sec 
... solve  2001 a=0.28723 time=31.723042 sec left=56.359501 sec 
... solve  2002 a=0.28749 time=31.739060 sec left=56.343939 sec 
... solve  2003 a=0.28774 time=31.754947 sec left=56.328144 sec 
... solve  2004 a=0.28800 time=31.771223 sec left=56.313039 sec 
... solve  2005 a=0.28826 time=31.788424 sec left=56.299569 sec 
... solve  2006 a=0.28851 time=31.804552 sec left=56.284201 sec 
... solve  2007 a=0.28877 time=31.820498 sec left=56.268509 sec 
... solve  2008 a=0.28903 time=31.836430 sec left=56.252789 sec 
... solve  2009 a=0.28928 time=31.852603 sec left=56.237491 sec 
... solve  2010 a=0.28954 time=31.869288 sec left=56.223106 sec 
... solve  2011 a=0.28979 time=31.885892 sec left=56.208568 sec 
... solve  2012 a=0.29005 time=31.902138 sec left=56.193402 sec 
... solve  2013 a=0.29031 time=31.918303 sec left=56.178090 sec 
... solve  2014 a=0.29056 time=31.934287 sec left=56.162459 sec 
... solve  2015 a=0.29082 time=31.950405 sec left=56.147061 sec 
... solve  2016 a=0.29108 time=31.966642 sec left=56.131873 sec 
... solve  2017 a=0.29133 time=31.982501 sec left=56.116023 sec 
... solve  2018 a=0.29159 time=31.998379 sec left=56.100204 sec 
... solve  2019 a=0.29185 time=32.014499 sec left=56.084808 sec 
... solve  2020 a=0.29211 time=32.030570 sec left=56.069328 sec 
... solve  2021 a=0.29236 time=32.046667 sec left=56.053892 sec 
... solve  2022 a=0.29262 time=32.062788 sec left=56.038496 sec 
... solve  2023 a=0.29288 time=32.078599 sec left=56.022559 sec 
... solve  2024 a=0.29313 time=32.094878 sec left=56.007437 sec 
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... solve  2035 a=0.29597 time=32.271958 sec left=55.837598 sec 
... solve  2036 a=0.29623 time=32.288057 sec left=55.822153 sec 
... solve  2037 a=0.29649 time=32.304106 sec left=55.806624 sec 
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... solve  2123 a=0.31892 time=33.694280 sec left=54.485356 sec 
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... solve  2127 a=0.31998 time=33.761619 sec left=54.428085 sec 
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... solve  2157 a=0.32791 time=34.251845 sec left=53.974024 sec 
... solve  2158 a=0.32818 time=34.268002 sec left=53.958580 sec 
... solve  2159 a=0.32844 time=34.284474 sec left=53.943635 sec 
... solve  2160 a=0.32871 time=34.300747 sec left=53.928372 sec 
... solve  2161 a=0.32898 time=34.317203 sec left=53.913397 sec 
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... solve  2163 a=0.32951 time=34.350474 sec left=53.884007 sec 
... solve  2164 a=0.32977 time=34.366730 sec left=53.868713 sec 
... solve  2165 a=0.33004 time=34.383072 sec left=53.853553 sec 
... solve  2166 a=0.33030 time=34.399328 sec left=53.838260 sec 
... solve  2167 a=0.33057 time=34.415214 sec left=53.822384 sec 
... solve  2168 a=0.33084 time=34.431072 sec left=53.806467 sec 
... solve  2169 a=0.33110 time=34.446924 sec left=53.790540 sec 
... solve  2170 a=0.33137 time=34.463004 sec left=53.774967 sec 
... solve  2171 a=0.33163 time=34.479792 sec left=53.760500 sec 
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... solve  2173 a=0.33217 time=34.511685 sec left=53.728935 sec 
... solve  2174 a=0.33243 time=34.526937 sec left=53.712075 sec 
... solve  2175 a=0.33270 time=34.542758 sec left=53.696098 sec 
... solve  2176 a=0.33297 time=34.559140 sec left=53.680994 sec 
... solve  2177 a=0.33323 time=34.575408 sec left=53.665709 sec 
... solve  2178 a=0.33350 time=34.591545 sec left=53.650224 sec 
... solve  2179 a=0.33377 time=34.607923 sec left=53.635109 sec 
... solve  2180 a=0.33403 time=34.624159 sec left=53.619775 sec 
... solve  2181 a=0.33430 time=34.640418 sec left=53.604469 sec 
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... solve  2185 a=0.33537 time=34.705468 sec left=53.543287 sec 
... solve  2186 a=0.33563 time=34.721737 sec left=53.527996 sec 
... solve  2187 a=0.33590 time=34.737777 sec left=53.512355 sec 
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... solve  2189 a=0.33643 time=34.771234 sec left=53.483185 sec 
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... solve  2192 a=0.33724 time=34.818666 sec left=53.435191 sec 
... solve  2193 a=0.33750 time=34.834906 sec left=53.419853 sec 
... solve  2194 a=0.33777 time=34.851785 sec left=53.405491 sec 
... solve  2195 a=0.33804 time=34.867806 sec left=53.389816 sec 
... solve  2196 a=0.33830 time=34.883708 sec left=53.373955 sec 
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... solve  2198 a=0.33884 time=34.915434 sec left=53.342119 sec 
... solve  2199 a=0.33911 time=34.931392 sec left=53.326343 sec 
... solve  2200 a=0.33938 time=34.947315 sec left=53.310516 sec 
... solve  2201 a=0.33964 time=34.963122 sec left=53.294513 sec 
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... solve  2203 a=0.34018 time=34.994755 sec left=53.262533 sec 
... solve  2204 a=0.34045 time=35.010594 sec left=53.246578 sec 
... solve  2205 a=0.34071 time=35.026576 sec left=53.230842 sec 
... solve  2206 a=0.34098 time=35.042386 sec left=53.214844 sec 
... solve  2207 a=0.34125 time=35.058233 sec left=53.198900 sec 
... solve  2208 a=0.34152 time=35.073569 sec left=53.182182 sec 
... solve  2209 a=0.34179 time=35.089342 sec left=53.166128 sec 
... solve  2210 a=0.34205 time=35.105516 sec left=53.150679 sec 
... solve  2211 a=0.34232 time=35.121536 sec left=53.135000 sec 
... solve  2212 a=0.34259 time=35.137350 sec left=53.119009 sec 
... solve  2213 a=0.34286 time=35.152661 sec left=53.102253 sec 
... solve  2214 a=0.34313 time=35.168940 sec left=53.086968 sec 
... solve  2215 a=0.34340 time=35.184787 sec left=53.071022 sec 
... solve  2216 a=0.34366 time=35.200596 sec left=53.055027 sec 
... solve  2217 a=0.34393 time=35.217657 sec left=53.040914 sec 
... solve  2218 a=0.34420 time=35.233567 sec left=53.025066 sec 
... solve  2219 a=0.34447 time=35.249389 sec left=53.009086 sec 
... solve  2220 a=0.34474 time=35.265212 sec left=52.993107 sec 
... solve  2221 a=0.34501 time=35.281023 sec left=52.977112 sec 
... solve  2222 a=0.34528 time=35.296739 sec left=52.960973 sec 
... solve  2223 a=0.34555 time=35.312648 sec left=52.945122 sec 
... solve  2224 a=0.34581 time=35.328509 sec left=52.929202 sec 
... solve  2225 a=0.34608 time=35.344310 sec left=52.913190 sec 
... solve  2226 a=0.34635 time=35.360159 sec left=52.897250 sec 
... solve  2227 a=0.34662 time=35.376007 sec left=52.881310 sec 
... solve  2228 a=0.34689 time=35.391926 sec left=52.865474 sec 
... solve  2229 a=0.34716 time=35.407711 sec left=52.849440 sec 
... solve  2230 a=0.34743 time=35.423507 sec left=52.833425 sec 
... solve  2231 a=0.34770 time=35.444034 sec left=52.824439 sec 
... solve  2232 a=0.34797 time=35.463263 sec left=52.813545 sec 
... solve  2233 a=0.34824 time=35.479253 sec left=52.797809 sec 
... solve  2234 a=0.34851 time=35.495329 sec left=52.782198 sec 
... solve  2235 a=0.34877 time=35.512821 sec left=52.768691 sec 
... solve  2236 a=0.34904 time=35.528816 sec left=52.752959 sec 
... solve  2237 a=0.34931 time=35.544826 sec left=52.737248 sec 
... solve  2238 a=0.34958 time=35.560695 sec left=52.721330 sec 
... solve  2239 a=0.34985 time=35.576507 sec left=52.705326 sec 
... solve  2240 a=0.35012 time=35.593518 sec left=52.691095 sec 
... solve  2241 a=0.35039 time=35.609881 sec left=52.675905 sec 
... solve  2242 a=0.35066 time=35.625833 sec left=52.660107 sec 
... solve  2243 a=0.35093 time=35.641689 sec left=52.644167 sec 
... solve  2244 a=0.35120 time=35.657573 sec left=52.628267 sec 
... solve  2245 a=0.35147 time=35.673522 sec left=52.612464 sec 
... solve  2246 a=0.35174 time=35.689306 sec left=52.596416 sec 
... solve  2247 a=0.35201 time=35.705782 sec left=52.581388 sec 
... solve  2248 a=0.35228 time=35.721968 sec left=52.565933 sec 
... solve  2249 a=0.35255 time=35.737829 sec left=52.550000 sec 
... solve  2250 a=0.35282 time=35.753665 sec left=52.534028 sec 
... solve  2251 a=0.35309 time=35.769726 sec left=52.518390 sec 
... solve  2252 a=0.35336 time=35.785564 sec left=52.502422 sec 
... solve  2253 a=0.35363 time=35.802474 sec left=52.488024 sec 
... solve  2254 a=0.35390 time=35.818365 sec left=52.472135 sec 
... solve  2255 a=0.35417 time=35.834163 sec left=52.456108 sec 
... solve  2256 a=0.35444 time=35.849980 sec left=52.440107 sec 
... solve  2257 a=0.35471 time=35.865416 sec left=52.423552 sec 
... solve  2258 a=0.35498 time=35.881219 sec left=52.407534 sec 
... solve  2259 a=0.35526 time=35.897015 sec left=52.391505 sec 
... solve  2260 a=0.35553 time=35.912942 sec left=52.375667 sec 
... solve  2261 a=0.35580 time=35.928736 sec left=52.359635 sec 
... solve  2262 a=0.35607 time=35.944548 sec left=52.343613 sec 
... solve  2263 a=0.35634 time=35.961583 sec left=52.329405 sec 
... solve  2264 a=0.35661 time=35.977442 sec left=52.313467 sec 
... solve  2265 a=0.35688 time=35.994583 sec left=52.299391 sec 
... solve  2266 a=0.35715 time=36.010497 sec left=52.283533 sec 
... solve  2267 a=0.35742 time=36.026407 sec left=52.267668 sec 
... solve  2268 a=0.35769 time=36.042375 sec left=52.251887 sec 
... solve  2269 a=0.35796 time=36.058178 sec left=52.235865 sec 
... solve  2270 a=0.35823 time=36.074060 sec left=52.219961 sec 
... solve  2271 a=0.35851 time=36.089908 sec left=52.204006 sec 
... solve  2272 a=0.35878 time=36.106485 sec left=52.189104 sec 
... solve  2273 a=0.35905 time=36.122425 sec left=52.173283 sec 
... solve  2274 a=0.35932 time=36.138470 sec left=52.157612 sec 
... solve  2275 a=0.35959 time=36.153796 sec left=52.140903 sec 
... solve  2276 a=0.35986 time=36.169586 sec left=52.124865 sec 
... solve  2277 a=0.36013 time=36.185487 sec left=52.108987 sec 
... solve  2278 a=0.36040 time=36.202050 sec left=52.094059 sec 
... solve  2279 a=0.36068 time=36.217919 sec left=52.078137 sec 
... solve  2280 a=0.36095 time=36.233840 sec left=52.062284 sec 
... solve  2281 a=0.36122 time=36.249692 sec left=52.046336 sec 
... solve  2282 a=0.36149 time=36.265514 sec left=52.030345 sec 
... solve  2283 a=0.36176 time=36.281332 sec left=52.014347 sec 
... solve  2284 a=0.36203 time=36.298722 sec left=52.000597 sec 
... solve  2285 a=0.36231 time=36.317342 sec left=51.988603 sec 
... solve  2286 a=0.36258 time=36.339015 sec left=51.980983 sec 
... solve  2287 a=0.36285 time=36.355000 sec left=51.965215 sec 
... solve  2288 a=0.36312 time=36.370885 sec left=51.949302 sec 
... solve  2289 a=0.36339 time=36.387990 sec left=51.935129 sec 
... solve  2290 a=0.36366 time=36.403445 sec left=51.918604 sec 
... solve  2291 a=0.36394 time=36.419494 sec left=51.902923 sec 
... solve  2292 a=0.36421 time=36.435959 sec left=51.887835 sec 
... solve  2293 a=0.36448 time=36.452363 sec left=51.872660 sec 
... solve  2294 a=0.36475 time=36.469711 sec left=51.858825 sec 
... solve  2295 a=0.36502 time=36.485622 sec left=51.842947 sec 
... solve  2296 a=0.36530 time=36.501449 sec left=51.826949 sec 
... solve  2297 a=0.36557 time=36.517407 sec left=51.811136 sec 
... solve  2298 a=0.36584 time=36.533243 sec left=51.795151 sec 
... solve  2299 a=0.36611 time=36.549030 sec left=51.779095 sec 
... solve  2300 a=0.36639 time=36.565156 sec left=51.763180 sec 
... solve  2301 a=0.36666 time=36.580676 sec left=51.747089 sec 
... solve  2302 a=0.36693 time=36.596504 sec left=51.731094 sec 
... solve  2303 a=0.36720 time=36.612573 sec left=51.715435 sec 
... solve  2304 a=0.36748 time=36.628368 sec left=51.699394 sec 
... solve  2305 a=0.36775 time=36.644201 sec left=51.683406 sec 
... solve  2306 a=0.36802 time=36.660078 sec left=51.667480 sec 
... solve  2307 a=0.36829 time=36.675908 sec left=51.651485 sec 
... solve  2308 a=0.36857 time=36.691914 sec left=51.635737 sec 
... solve  2309 a=0.36884 time=36.708764 sec left=51.621181 sec 
... solve  2310 a=0.36911 time=36.724640 sec left=51.605252 sec 
... solve  2311 a=0.36938 time=36.740473 sec left=51.589264 sec 
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... solve  2583 a=0.44485 time=41.124531 sec left=47.333791 sec 
... solve  2584 a=0.44513 time=41.143650 sec left=47.321548 sec 
... solve  2585 a=0.44541 time=41.163876 sec left=47.310572 sec 
... solve  2586 a=0.44569 time=41.181415 sec left=47.296502 sec 
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... solve  2588 a=0.44626 time=41.218006 sec left=47.270091 sec 
... solve  2589 a=0.44654 time=41.233923 sec left=47.254155 sec 
... solve  2590 a=0.44682 time=41.250167 sec left=47.238591 sec 
... solve  2591 a=0.44710 time=41.266033 sec left=47.222595 sec 
... solve  2592 a=0.44738 time=41.281889 sec left=47.206587 sec 
... solve  2593 a=0.44766 time=41.297726 sec left=47.190559 sec 
... solve  2594 a=0.44794 time=41.313523 sec left=47.174484 sec 
... solve  2595 a=0.44822 time=41.329374 sec left=47.158470 sec 
... solve  2596 a=0.44850 time=41.345368 sec left=47.142620 sec 
... solve  2597 a=0.44879 time=41.361179 sec left=47.126562 sec 
... solve  2598 a=0.44907 time=41.377112 sec left=47.110644 sec 
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... solve  2609 a=0.45216 time=41.553038 sec left=46.936281 sec 
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... solve  2617 a=0.45441 time=41.679970 sec left=46.808325 sec 
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... solve  2644 a=0.46202 time=42.128760 sec left=46.398981 sec 
... solve  2645 a=0.46230 time=42.144586 sec left=46.382929 sec 
... solve  2646 a=0.46258 time=42.160504 sec left=46.366977 sec 
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... solve  2654 a=0.46484 time=42.288456 sec left=46.240036 sec 
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... solve  2689 a=0.47471 time=42.844772 sec left=45.680892 sec 
... solve  2690 a=0.47499 time=42.860575 sec left=45.664820 sec 
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... solve  2696 a=0.47669 time=42.955403 sec left=45.568401 sec 
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... solve  2723 a=0.48431 time=43.389077 sec left=45.141834 sec 
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... solve  2730 a=0.48629 time=43.502503 sec left=45.032245 sec 
... solve  2731 a=0.48657 time=43.518726 sec left=45.016607 sec 
... solve  2732 a=0.48686 time=43.534788 sec left=45.000804 sec 
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... solve  2737 a=0.48827 time=43.614461 sec left=44.921127 sec 
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... solve  2739 a=0.48884 time=43.645595 sec left=44.888500 sec 
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... solve  2741 a=0.48940 time=43.677465 sec left=44.856630 sec 
... solve  2742 a=0.48968 time=43.693311 sec left=44.840604 sec 
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... solve  2745 a=0.49053 time=43.741014 sec left=44.792694 sec 
... solve  2746 a=0.49081 time=43.757842 sec left=44.777674 sec 
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... solve  2749 a=0.49166 time=43.805434 sec left=44.729650 sec 
... solve  2750 a=0.49194 time=43.821541 sec left=44.713891 sec 
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... solve  2757 a=0.49392 time=43.933512 sec left=44.602778 sec 
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... solve  2759 a=0.49449 time=43.965300 sec left=44.570824 sec 
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... solve  2789 a=0.50297 time=44.442906 sec left=44.092320 sec 
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... solve  2797 a=0.50523 time=44.571471 sec left=43.965908 sec 
... solve  2798 a=0.50551 time=44.587368 sec left=43.949937 sec 
... solve  2799 a=0.50579 time=44.603212 sec left=43.933911 sec 
... solve  2800 a=0.50608 time=44.619164 sec left=43.917990 sec 
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... solve  2803 a=0.50693 time=44.666572 sec left=43.869794 sec 
... solve  2804 a=0.50721 time=44.682583 sec left=43.853933 sec 
... solve  2805 a=0.50749 time=44.698373 sec left=43.837855 sec 
... solve  2806 a=0.50777 time=44.714231 sec left=43.821843 sec 
... solve  2807 a=0.50806 time=44.730074 sec left=43.805818 sec 
... solve  2808 a=0.50834 time=44.745860 sec left=43.789737 sec 
... solve  2809 a=0.50862 time=44.761899 sec left=43.773904 sec 
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... solve  2816 a=0.51060 time=44.873689 sec left=43.662594 sec 
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... solve  2826 a=0.51343 time=45.031757 sec left=43.502001 sec 
... solve  2827 a=0.51371 time=45.047551 sec left=43.485930 sec 
... solve  2828 a=0.51399 time=45.063468 sec left=43.469979 sec 
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... solve  2831 a=0.51484 time=45.111092 sec left=43.422000 sec 
... solve  2832 a=0.51512 time=45.127082 sec left=43.406119 sec 
... solve  2833 a=0.51540 time=45.142894 sec left=43.390067 sec 
... solve  2834 a=0.51569 time=45.158808 sec left=43.374112 sec 
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... solve  2836 a=0.51625 time=45.190170 sec left=43.341756 sec 
... solve  2837 a=0.51653 time=45.206153 sec left=43.325869 sec 
... solve  2838 a=0.51682 time=45.221979 sec left=43.309830 sec 
... solve  2839 a=0.51710 time=45.238056 sec left=43.294032 sec 
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... solve  2841 a=0.51766 time=45.270606 sec left=43.262814 sec 
... solve  2842 a=0.51795 time=45.286481 sec left=43.246822 sec 
... solve  2843 a=0.51823 time=45.302234 sec left=43.230714 sec 
... solve  2844 a=0.51851 time=45.318011 sec left=43.214630 sec 
... solve  2845 a=0.51879 time=45.334062 sec left=43.198805 sec 
... solve  2846 a=0.51908 time=45.349888 sec left=43.182767 sec 
... solve  2847 a=0.51936 time=45.365686 sec left=43.166703 sec 
... solve  2848 a=0.51964 time=45.381523 sec left=43.150674 sec 
... solve  2849 a=0.51992 time=45.396849 sec left=43.134162 sec 
... solve  2850 a=0.52021 time=45.412657 sec left=43.118109 sec 
... solve  2851 a=0.52049 time=45.428573 sec left=43.102157 sec 
... solve  2852 a=0.52077 time=45.444429 sec left=43.086148 sec 
... solve  2853 a=0.52105 time=45.460361 sec left=43.070212 sec 
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... solve  2857 a=0.52218 time=45.522989 sec left=43.005428 sec 
... solve  2858 a=0.52246 time=45.539006 sec left=42.989571 sec 
... solve  2859 a=0.52275 time=45.554819 sec left=42.973524 sec 
... solve  2860 a=0.52303 time=45.570627 sec left=42.957472 sec 
... solve  2861 a=0.52331 time=45.586308 sec left=42.941300 sec 
... solve  2862 a=0.52359 time=45.602136 sec left=42.925266 sec 
... solve  2863 a=0.52388 time=45.619171 sec left=42.910368 sec 
... solve  2864 a=0.52416 time=45.635063 sec left=42.894396 sec 
... solve  2865 a=0.52444 time=45.650913 sec left=42.878382 sec 
... solve  2866 a=0.52472 time=45.666782 sec left=42.862388 sec 
... solve  2867 a=0.52501 time=45.682582 sec left=42.846328 sec 
... solve  2868 a=0.52529 time=45.698419 sec left=42.830303 sec 
... solve  2869 a=0.52557 time=45.714342 sec left=42.814359 sec 
... solve  2870 a=0.52585 time=45.730123 sec left=42.798282 sec 
... solve  2871 a=0.52614 time=45.745912 sec left=42.782213 sec 
... solve  2872 a=0.52642 time=45.761780 sec left=42.766218 sec 
... solve  2873 a=0.52670 time=45.777587 sec left=42.750166 sec 
... solve  2874 a=0.52698 time=45.793353 sec left=42.734074 sec 
... solve  2875 a=0.52726 time=45.809335 sec left=42.718188 sec 
... solve  2876 a=0.52755 time=45.825141 sec left=42.702134 sec 
... solve  2877 a=0.52783 time=45.842075 sec left=42.687133 sec 
... solve  2878 a=0.52811 time=45.857935 sec left=42.671128 sec 
... solve  2879 a=0.52839 time=45.873721 sec left=42.655058 sec 
... solve  2880 a=0.52868 time=45.889647 sec left=42.639116 sec 
... solve  2881 a=0.52896 time=45.905668 sec left=42.623263 sec 
... solve  2882 a=0.52924 time=45.921535 sec left=42.607267 sec 
... solve  2883 a=0.52952 time=45.936783 sec left=42.590697 sec 
... solve  2884 a=0.52980 time=45.952571 sec left=42.574619 sec 
... solve  2885 a=0.53009 time=45.968448 sec left=42.558643 sec 
... solve  2886 a=0.53037 time=45.984870 sec left=42.543160 sec 
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... solve  4315 a=0.88173 time=68.592528 sec left=19.727302 sec 
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... solve  4883 a=0.96414 time=77.635563 sec left=10.700128 sec 
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... solve  5455 a=0.99917 time=86.607559 sec left=1.603549 sec 
... solve  5456 a=0.99919 time=86.623442 sec left=1.587673 sec 
... solve  5457 a=0.99920 time=86.639115 sec left=1.571792 sec 
... solve  5458 a=0.99922 time=86.655266 sec left=1.555921 sec 
... solve  5459 a=0.99923 time=86.670839 sec left=1.540038 sec 
... solve  5460 a=0.99925 time=86.686615 sec left=1.524160 sec 
... solve  5461 a=0.99926 time=86.702276 sec left=1.508280 sec 
... solve  5462 a=0.99928 time=86.718438 sec left=1.492408 sec 
... solve  5463 a=0.99929 time=86.734014 sec left=1.476526 sec 
... solve  5464 a=0.99931 time=86.749398 sec left=1.460641 sec 
... solve  5465 a=0.99932 time=86.764840 sec left=1.444757 sec 
... solve  5466 a=0.99934 time=86.780464 sec left=1.428877 sec 
... solve  5467 a=0.99935 time=86.796125 sec left=1.412997 sec 
... solve  5468 a=0.99937 time=86.813144 sec left=1.397139 sec 
... solve  5469 a=0.99938 time=86.828858 sec left=1.381260 sec 
... solve  5470 a=0.99940 time=86.844427 sec left=1.365378 sec 
... solve  5471 a=0.99941 time=86.860054 sec left=1.349498 sec 
... solve  5472 a=0.99942 time=86.875557 sec left=1.333616 sec 
... solve  5473 a=0.99944 time=86.891149 sec left=1.317735 sec 
... solve  5474 a=0.99945 time=86.906891 sec left=1.301857 sec 
... solve  5475 a=0.99946 time=86.923156 sec left=1.285986 sec 
... solve  5476 a=0.99948 time=86.938779 sec left=1.270106 sec 
... solve  5477 a=0.99949 time=86.954452 sec left=1.254227 sec 
... solve  5478 a=0.99950 time=86.970096 sec left=1.238347 sec 
... solve  5479 a=0.99951 time=86.986282 sec left=1.222475 sec 
... solve  5480 a=0.99953 time=87.002421 sec left=1.206603 sec 
... solve  5481 a=0.99954 time=87.018015 sec left=1.190722 sec 
... solve  5482 a=0.99955 time=87.033596 sec left=1.174842 sec 
... solve  5483 a=0.99956 time=87.049725 sec left=1.158969 sec 
... solve  5484 a=0.99957 time=87.065082 sec left=1.143086 sec 
... solve  5485 a=0.99959 time=87.080668 sec left=1.127206 sec 
... solve  5486 a=0.99960 time=87.097308 sec left=1.111340 sec 
... solve  5487 a=0.99961 time=87.112816 sec left=1.095459 sec 
... solve  5488 a=0.99962 time=87.130229 sec left=1.079602 sec 
... solve  5489 a=0.99963 time=87.145514 sec left=1.063718 sec 
... solve  5490 a=0.99964 time=87.160878 sec left=1.047835 sec 
... solve  5491 a=0.99965 time=87.177711 sec left=1.031971 sec 
... solve  5492 a=0.99966 time=87.193449 sec left=1.016092 sec 
... solve  5493 a=0.99967 time=87.208818 sec left=1.000210 sec 
... solve  5494 a=0.99968 time=87.224649 sec left=0.984333 sec 
... solve  5495 a=0.99969 time=87.239981 sec left=0.968451 sec 
... solve  5496 a=0.99970 time=87.255313 sec left=0.952569 sec 
... solve  5497 a=0.99971 time=87.270776 sec left=0.936688 sec 
... solve  5498 a=0.99972 time=87.286050 sec left=0.920806 sec 
... solve  5499 a=0.99973 time=87.301300 sec left=0.904923 sec 
... solve  5500 a=0.99974 time=87.317146 sec left=0.889047 sec 
... solve  5501 a=0.99975 time=87.333022 sec left=0.873171 sec 
... solve  5502 a=0.99976 time=87.348332 sec left=0.857290 sec 
... solve  5503 a=0.99977 time=87.363932 sec left=0.841412 sec 
... solve  5504 a=0.99978 time=87.379118 sec left=0.825529 sec 
... solve  5505 a=0.99978 time=87.394404 sec left=0.809648 sec 
... solve  5506 a=0.99979 time=87.410537 sec left=0.793775 sec 
... solve  5507 a=0.99980 time=87.426520 sec left=0.777901 sec 
... solve  5508 a=0.99981 time=87.441939 sec left=0.762021 sec 
... solve  5509 a=0.99982 time=87.457552 sec left=0.746143 sec 
... solve  5510 a=0.99982 time=87.472887 sec left=0.730264 sec 
... solve  5511 a=0.99983 time=87.488176 sec left=0.714383 sec 
... solve  5512 a=0.99984 time=87.503478 sec left=0.698504 sec 
... solve  5513 a=0.99985 time=87.519311 sec left=0.682628 sec 
... solve  5514 a=0.99985 time=87.534920 sec left=0.666751 sec 
... solve  5515 a=0.99986 time=87.551042 sec left=0.650878 sec 
... solve  5516 a=0.99987 time=87.567240 sec left=0.635005 sec 
... solve  5517 a=0.99987 time=87.582526 sec left=0.619126 sec 
... solve  5518 a=0.99988 time=87.598325 sec left=0.603250 sec 
... solve  5519 a=0.99988 time=87.613663 sec left=0.587372 sec 
... solve  5520 a=0.99989 time=87.629045 sec left=0.571494 sec 
... solve  5521 a=0.99990 time=87.644435 sec left=0.555616 sec 
... solve  5522 a=0.99990 time=87.660727 sec left=0.539744 sec 
... solve  5523 a=0.99991 time=87.676158 sec left=0.523866 sec 
... solve  5524 a=0.99991 time=87.695248 sec left=0.508010 sec 
... solve  5525 a=0.99992 time=87.719517 sec left=0.492182 sec 
... solve  5526 a=0.99992 time=87.735397 sec left=0.476305 sec 
... solve  5527 a=0.99993 time=87.751293 sec left=0.460428 sec 
... solve  5528 a=0.99993 time=87.767130 sec left=0.444551 sec 
... solve  5529 a=0.99994 time=87.782515 sec left=0.428672 sec 
... solve  5530 a=0.99994 time=87.797753 sec left=0.412792 sec 
... solve  5531 a=0.99995 time=87.813005 sec left=0.396913 sec 
... solve  5532 a=0.99995 time=87.829092 sec left=0.381037 sec 
... solve  5533 a=0.99995 time=87.844425 sec left=0.365158 sec 
... solve  5534 a=0.99996 time=87.859714 sec left=0.349280 sec 
... solve  5535 a=0.99996 time=87.875006 sec left=0.333401 sec 
... solve  5536 a=0.99996 time=87.890302 sec left=0.317523 sec 
... solve  5537 a=0.99997 time=87.905614 sec left=0.301645 sec 
... solve  5538 a=0.99997 time=87.922202 sec left=0.285771 sec 
... solve  5539 a=0.99997 time=87.938593 sec left=0.269896 sec 
... solve  5540 a=0.99998 time=87.956236 sec left=0.254025 sec 
... solve  5541 a=0.99998 time=87.972904 sec left=0.238151 sec 
... solve  5542 a=0.99998 time=87.989681 sec left=0.222276 sec 
... solve  5543 a=0.99998 time=88.011153 sec left=0.206413 sec 
... solve  5544 a=0.99999 time=88.026764 sec left=0.190534 sec 
... solve  5545 a=0.99999 time=88.043567 sec left=0.174658 sec 
... solve  5546 a=0.99999 time=88.058972 sec left=0.158779 sec 
... solve  5547 a=0.99999 time=88.083590 sec left=0.142915 sec 
... solve  5548 a=0.99999 time=88.102894 sec left=0.127041 sec 
... solve  5549 a=0.99999 time=88.118467 sec left=0.111160 sec 
... solve  5550 a=1.00000 time=88.133840 sec left=0.095280 sec 
... solve  5551 a=1.00000 time=88.149161 sec left=0.079399 sec 
... solve  5552 a=1.00000 time=88.164455 sec left=0.063519 sec 
... solve  5553 a=1.00000 time=88.180204 sec left=0.047639 sec 
... solve  5554 a=1.00000 time=88.196263 sec left=0.031760 sec 
... solve  5555 a=1.00000 time=88.211982 sec left=0.015880 sec 
... solve  5556 a=1.00000 time=88.227283 sec left=0.000000 sec 

Compare against Path Damping

Thankfully, path damping is very easy to implement. We are going to check how well our solutions compare against the exact solution.

Npd = 2e5;
m = d.mf(Npd);
Ptkx = v; ex=zeros(n,1); t=0; hpd=zeros(Npd,5); s=0; ex1=ex; ex2=ex; tic;
for k=1:Npd
    ex = ex + (m(k)-m(k+1)).*Ptkx; t=norm(ex,1); s=s+(m(k)-m(k+1)); r=m(1)-m(k+1);
    ex1 = ex1 + m(k).*Ptkx; ex2 = ex2 + m(k+1).*Ptkx;
    y = P'*(Ptkx); Ptkx = y + (1-sum(y))*v;
    z1 = ex + (1-t)*Ptkx; z2 = ex + (1-s)*Ptkx; z3=ex./t; z4=ex1-ex2 + m(k+1).*Ptkx;
    hpd(k,1) = norm(eex-ex,1); hpd(k,2)=norm(eex-z1,1);
    hpd(k,3)=norm(eex-z2,1); hpd(k,4)=norm(eex-z3,1); hpd(k,5)=norm(eex-z4,1);
    dt=toc; etr=Npd*dt/k-dt;
    if mod(k,1000)==0, fprintf('k = %6i ; erry = %8e ; errz = %8e ; etr=%7f sec\n',...
            k,t,1-s,etr); end
end

save 'exact-pd-hist.mat' eex m hpd P
k =   1000 ; erry = 9.999945e-01 ; errz = 5.511022e-06 ; etr=160.226442 sec
k =   2000 ; erry = 9.999993e-01 ; errz = 7.074759e-07 ; etr=159.701058 sec
k =   3000 ; erry = 9.999998e-01 ; errz = 2.115034e-07 ; etr=159.536313 sec
k =   4000 ; erry = 9.999999e-01 ; errz = 8.962832e-08 ; etr=158.248048 sec
k =   5000 ; erry = 1.000000e-00 ; errz = 4.601326e-08 ; etr=157.133067 sec
k =   6000 ; erry = 1.000000e-00 ; errz = 2.667586e-08 ; etr=156.119431 sec
k =   7000 ; erry = 1.000000e-00 ; errz = 1.682034e-08 ; etr=155.155457 sec
k =   8000 ; erry = 1.000000e-00 ; errz = 1.127916e-08 ; etr=154.242288 sec
k =   9000 ; erry = 1.000000e-00 ; errz = 7.927643e-09 ; etr=153.351014 sec
k =  10000 ; erry = 1.000000e-00 ; errz = 5.782714e-09 ; etr=152.478154 sec
k =  11000 ; erry = 1.000000e-00 ; errz = 4.346767e-09 ; etr=151.614632 sec
k =  12000 ; erry = 1.000000e-00 ; errz = 3.349485e-09 ; etr=150.762104 sec
k =  13000 ; erry = 1.000000e-00 ; errz = 2.635371e-09 ; etr=149.921467 sec
k =  14000 ; erry = 1.000000e-00 ; errz = 2.110649e-09 ; etr=149.085377 sec
k =  15000 ; erry = 1.000000e-00 ; errz = 1.716477e-09 ; etr=148.255608 sec
k =  16000 ; erry = 1.000000e-00 ; errz = 1.414650e-09 ; etr=147.431288 sec
k =  17000 ; erry = 1.000000e-00 ; errz = 1.179637e-09 ; etr=146.603625 sec
k =  18000 ; erry = 1.000000e-00 ; errz = 9.939264e-10 ; etr=145.782111 sec
k =  19000 ; erry = 1.000000e-00 ; errz = 8.452385e-10 ; etr=144.967568 sec
k =  20000 ; erry = 1.000000e-00 ; errz = 7.247886e-10 ; etr=144.148437 sec
k =  21000 ; erry = 1.000000e-00 ; errz = 6.261799e-10 ; etr=143.332741 sec
k =  22000 ; erry = 1.000000e-00 ; errz = 5.446775e-10 ; etr=142.519972 sec
k =  23000 ; erry = 1.000000e-00 ; errz = 4.767271e-10 ; etr=141.706954 sec
k =  24000 ; erry = 1.000000e-00 ; errz = 4.196256e-10 ; etr=140.896206 sec
k =  25000 ; erry = 1.000000e-00 ; errz = 3.712908e-10 ; etr=140.083251 sec
k =  26000 ; erry = 1.000000e-00 ; errz = 3.301029e-10 ; etr=139.273475 sec
k =  27000 ; erry = 1.000000e-00 ; errz = 2.947891e-10 ; etr=138.464145 sec
k =  28000 ; erry = 1.000000e-00 ; errz = 2.643377e-10 ; etr=137.656256 sec
k =  29000 ; erry = 1.000000e-00 ; errz = 2.379397e-10 ; etr=136.848487 sec
k =  30000 ; erry = 1.000000e-00 ; errz = 2.149432e-10 ; etr=136.042069 sec
k =  31000 ; erry = 1.000000e-00 ; errz = 1.948175e-10 ; etr=135.235757 sec
k =  32000 ; erry = 1.000000e-00 ; errz = 1.771272e-10 ; etr=134.429263 sec
k =  33000 ; erry = 1.000000e-00 ; errz = 1.615166e-10 ; etr=133.622621 sec
k =  34000 ; erry = 1.000000e-00 ; errz = 1.476869e-10 ; etr=132.816795 sec
k =  35000 ; erry = 1.000000e-00 ; errz = 1.353916e-10 ; etr=132.012092 sec
k =  36000 ; erry = 1.000000e-00 ; errz = 1.244251e-10 ; etr=131.207170 sec
k =  37000 ; erry = 1.000000e-00 ; errz = 1.146113e-10 ; etr=130.402295 sec
k =  38000 ; erry = 1.000000e-00 ; errz = 1.058036e-10 ; etr=129.599314 sec
k =  39000 ; erry = 1.000000e-00 ; errz = 9.787515e-11 ; etr=128.795591 sec
k =  40000 ; erry = 1.000000e-00 ; errz = 9.071932e-11 ; etr=127.992148 sec
k =  41000 ; erry = 1.000000e-00 ; errz = 8.424272e-11 ; etr=127.190972 sec
k =  42000 ; erry = 1.000000e-00 ; errz = 7.837042e-11 ; etr=126.386871 sec
k =  43000 ; erry = 1.000000e-00 ; errz = 7.303269e-11 ; etr=125.583800 sec
k =  44000 ; erry = 1.000000e-00 ; errz = 6.816725e-11 ; etr=124.780755 sec
k =  45000 ; erry = 1.000000e-00 ; errz = 6.372403e-11 ; etr=123.978817 sec
k =  46000 ; erry = 1.000000e-00 ; errz = 5.966039e-11 ; etr=123.177037 sec
k =  47000 ; erry = 1.000000e-00 ; errz = 5.593370e-11 ; etr=122.373801 sec
k =  48000 ; erry = 1.000000e-00 ; errz = 5.250744e-11 ; etr=121.571500 sec
k =  49000 ; erry = 1.000000e-00 ; errz = 4.936229e-11 ; etr=120.769178 sec
k =  50000 ; erry = 1.000000e-00 ; errz = 4.646139e-11 ; etr=119.967258 sec
k =  51000 ; erry = 1.000000e-00 ; errz = 4.378187e-11 ; etr=119.165000 sec
k =  52000 ; erry = 1.000000e-00 ; errz = 4.129941e-11 ; etr=118.363034 sec
k =  53000 ; erry = 1.000000e-00 ; errz = 3.901268e-11 ; etr=117.561189 sec
k =  54000 ; erry = 1.000000e-00 ; errz = 3.687839e-11 ; etr=116.759972 sec
k =  55000 ; erry = 1.000000e-00 ; errz = 3.491107e-11 ; etr=115.958343 sec
k =  56000 ; erry = 1.000000e-00 ; errz = 3.307576e-11 ; etr=115.156687 sec
k =  57000 ; erry = 1.000000e-00 ; errz = 3.136535e-11 ; etr=114.355866 sec
k =  58000 ; erry = 1.000000e-00 ; errz = 2.977163e-11 ; etr=113.555260 sec
k =  59000 ; erry = 1.000000e-00 ; errz = 2.828515e-11 ; etr=112.754056 sec
k =  60000 ; erry = 1.000000e-00 ; errz = 2.689482e-11 ; etr=111.954488 sec
k =  61000 ; erry = 1.000000e-00 ; errz = 2.558720e-11 ; etr=111.152931 sec
k =  62000 ; erry = 1.000000e-00 ; errz = 2.436595e-11 ; etr=110.351655 sec
k =  63000 ; erry = 1.000000e-00 ; errz = 2.323619e-11 ; etr=109.550523 sec
k =  64000 ; erry = 1.000000e-00 ; errz = 2.215350e-11 ; etr=108.749374 sec
k =  65000 ; erry = 1.000000e-00 ; errz = 2.115430e-11 ; etr=107.948405 sec
k =  66000 ; erry = 1.000000e-00 ; errz = 2.020506e-11 ; etr=107.147452 sec
k =  67000 ; erry = 1.000000e-00 ; errz = 1.931688e-11 ; etr=106.346155 sec
k =  68000 ; erry = 1.000000e-00 ; errz = 1.846934e-11 ; etr=105.545717 sec
k =  69000 ; erry = 1.000000e-00 ; errz = 1.769218e-11 ; etr=104.745225 sec
k =  70000 ; erry = 1.000000e-00 ; errz = 1.691502e-11 ; etr=103.944702 sec
k =  71000 ; erry = 1.000000e-00 ; errz = 1.623801e-11 ; etr=103.144139 sec
k =  72000 ; erry = 1.000000e-00 ; errz = 1.557188e-11 ; etr=102.343337 sec
k =  73000 ; erry = 1.000000e-00 ; errz = 1.490574e-11 ; etr=101.542709 sec
k =  74000 ; erry = 1.000000e-00 ; errz = 1.434086e-11 ; etr=100.742457 sec
k =  75000 ; erry = 1.000000e-00 ; errz = 1.378575e-11 ; etr=99.941810 sec
k =  76000 ; erry = 1.000000e-00 ; errz = 1.323064e-11 ; etr=99.141552 sec
k =  77000 ; erry = 1.000000e-00 ; errz = 1.269218e-11 ; etr=98.340714 sec
k =  78000 ; erry = 1.000000e-00 ; errz = 1.224809e-11 ; etr=97.540057 sec
k =  79000 ; erry = 1.000000e-00 ; errz = 1.180400e-11 ; etr=96.740716 sec
k =  80000 ; erry = 1.000000e-00 ; errz = 1.135991e-11 ; etr=95.940424 sec
k =  81000 ; erry = 1.000000e-00 ; errz = 1.091582e-11 ; etr=95.140305 sec
k =  82000 ; erry = 1.000000e-00 ; errz = 1.049016e-11 ; etr=94.340060 sec
k =  83000 ; erry = 1.000000e-00 ; errz = 1.015710e-11 ; etr=93.539624 sec
k =  84000 ; erry = 1.000000e-00 ; errz = 9.824030e-12 ; etr=92.739592 sec
k =  85000 ; erry = 1.000000e-00 ; errz = 9.490964e-12 ; etr=91.939450 sec
k =  86000 ; erry = 1.000000e-00 ; errz = 9.157897e-12 ; etr=91.139538 sec
k =  87000 ; erry = 1.000000e-00 ; errz = 8.824830e-12 ; etr=90.339350 sec
k =  88000 ; erry = 1.000000e-00 ; errz = 8.491763e-12 ; etr=89.539498 sec
k =  89000 ; erry = 1.000000e-00 ; errz = 8.158696e-12 ; etr=88.739630 sec
k =  90000 ; erry = 1.000000e-00 ; errz = 7.934764e-12 ; etr=87.939994 sec
k =  91000 ; erry = 1.000000e-00 ; errz = 7.712719e-12 ; etr=87.140113 sec
k =  92000 ; erry = 1.000000e-00 ; errz = 7.490675e-12 ; etr=86.340082 sec
k =  93000 ; erry = 1.000000e-00 ; errz = 7.268630e-12 ; etr=85.540380 sec
k =  94000 ; erry = 1.000000e-00 ; errz = 7.046586e-12 ; etr=84.741064 sec
k =  95000 ; erry = 1.000000e-00 ; errz = 6.824541e-12 ; etr=83.941390 sec
k =  96000 ; erry = 1.000000e-00 ; errz = 6.602496e-12 ; etr=83.142505 sec
k =  97000 ; erry = 1.000000e-00 ; errz = 6.380452e-12 ; etr=82.342222 sec
k =  98000 ; erry = 1.000000e-00 ; errz = 6.158407e-12 ; etr=81.543077 sec
k =  99000 ; erry = 1.000000e-00 ; errz = 5.936363e-12 ; etr=80.743007 sec
k = 100000 ; erry = 1.000000e-00 ; errz = 5.714318e-12 ; etr=79.943024 sec
k = 101000 ; erry = 1.000000e-00 ; errz = 5.492273e-12 ; etr=79.143327 sec
k = 102000 ; erry = 1.000000e-00 ; errz = 5.365153e-12 ; etr=78.343409 sec
k = 103000 ; erry = 1.000000e-00 ; errz = 5.254130e-12 ; etr=77.543639 sec
k = 104000 ; erry = 1.000000e-00 ; errz = 5.143108e-12 ; etr=76.744051 sec
k = 105000 ; erry = 1.000000e-00 ; errz = 5.032086e-12 ; etr=75.944172 sec
k = 106000 ; erry = 1.000000e-00 ; errz = 4.921064e-12 ; etr=75.144887 sec
k = 107000 ; erry = 1.000000e-00 ; errz = 4.810041e-12 ; etr=74.345010 sec
k = 108000 ; erry = 1.000000e-00 ; errz = 4.699019e-12 ; etr=73.545292 sec
k = 109000 ; erry = 1.000000e-00 ; errz = 4.587997e-12 ; etr=72.745565 sec
k = 110000 ; erry = 1.000000e-00 ; errz = 4.476974e-12 ; etr=71.945876 sec
k = 111000 ; erry = 1.000000e-00 ; errz = 4.365952e-12 ; etr=71.146121 sec
k = 112000 ; erry = 1.000000e-00 ; errz = 4.254930e-12 ; etr=70.346520 sec
k = 113000 ; erry = 1.000000e-00 ; errz = 4.143907e-12 ; etr=69.546804 sec
k = 114000 ; erry = 1.000000e-00 ; errz = 4.032885e-12 ; etr=68.747088 sec
k = 115000 ; erry = 1.000000e-00 ; errz = 3.921863e-12 ; etr=67.947422 sec
k = 116000 ; erry = 1.000000e-00 ; errz = 3.810841e-12 ; etr=67.148016 sec
k = 117000 ; erry = 1.000000e-00 ; errz = 3.699818e-12 ; etr=66.348446 sec
k = 118000 ; erry = 1.000000e-00 ; errz = 3.588796e-12 ; etr=65.549020 sec
k = 119000 ; erry = 1.000000e-00 ; errz = 3.477774e-12 ; etr=64.749289 sec
k = 120000 ; erry = 1.000000e-00 ; errz = 3.366751e-12 ; etr=63.949797 sec
k = 121000 ; erry = 1.000000e-00 ; errz = 3.255729e-12 ; etr=63.149982 sec
k = 122000 ; erry = 1.000000e-00 ; errz = 3.144707e-12 ; etr=62.350399 sec
k = 123000 ; erry = 1.000000e-00 ; errz = 3.033684e-12 ; etr=61.550918 sec
k = 124000 ; erry = 1.000000e-00 ; errz = 2.922662e-12 ; etr=60.751347 sec
k = 125000 ; erry = 1.000000e-00 ; errz = 2.811640e-12 ; etr=59.951864 sec
k = 126000 ; erry = 1.000000e-00 ; errz = 2.700618e-12 ; etr=59.152339 sec
k = 127000 ; erry = 1.000000e-00 ; errz = 2.589595e-12 ; etr=58.352879 sec
k = 128000 ; erry = 1.000000e-00 ; errz = 2.478573e-12 ; etr=57.553450 sec
k = 129000 ; erry = 1.000000e-00 ; errz = 2.367551e-12 ; etr=56.753964 sec
k = 130000 ; erry = 1.000000e-00 ; errz = 2.256528e-12 ; etr=55.954382 sec
k = 131000 ; erry = 1.000000e-00 ; errz = 2.145506e-12 ; etr=55.154835 sec
k = 132000 ; erry = 1.000000e-00 ; errz = 2.034484e-12 ; etr=54.355330 sec
k = 133000 ; erry = 1.000000e-00 ; errz = 1.923461e-12 ; etr=53.555800 sec
k = 134000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=52.756278 sec
k = 135000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=51.956900 sec
k = 136000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=51.157313 sec
k = 137000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=50.357897 sec
k = 138000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=49.558317 sec
k = 139000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=48.758778 sec
k = 140000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=47.959394 sec
k = 141000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=47.159814 sec
k = 142000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=46.360363 sec
k = 143000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=45.560829 sec
k = 144000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=44.761449 sec
k = 145000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=43.962012 sec
k = 146000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=43.162514 sec
k = 147000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=42.363146 sec
k = 148000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=41.563802 sec
k = 149000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=40.764271 sec
k = 150000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=39.964930 sec
k = 151000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=39.165437 sec
k = 152000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=38.366043 sec
k = 153000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=37.566601 sec
k = 154000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=36.767329 sec
k = 155000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=35.967880 sec
k = 156000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=35.168489 sec
k = 157000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=34.369043 sec
k = 158000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=33.569716 sec
k = 159000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=32.770409 sec
k = 160000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=31.971011 sec
k = 161000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=31.171655 sec
k = 162000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=30.372359 sec
k = 163000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=29.572997 sec
k = 164000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=28.773696 sec
k = 165000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=27.974291 sec
k = 166000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=27.174871 sec
k = 167000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=26.375585 sec
k = 168000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=25.576283 sec
k = 169000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=24.777168 sec
k = 170000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=23.977928 sec
k = 171000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=23.178567 sec
k = 172000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=22.379315 sec
k = 173000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=21.580106 sec
k = 174000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=20.780783 sec
k = 175000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=19.981479 sec
k = 176000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=19.182162 sec
k = 177000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=18.382849 sec
k = 178000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=17.583574 sec
k = 179000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=16.784267 sec
k = 180000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=15.984980 sec
k = 181000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=15.185667 sec
k = 182000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=14.386431 sec
k = 183000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=13.587164 sec
k = 184000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=12.787901 sec
k = 185000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=11.988615 sec
k = 186000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=11.189336 sec
k = 187000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=10.390073 sec
k = 188000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=9.590805 sec
k = 189000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=8.791552 sec
k = 190000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=7.992302 sec
k = 191000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=7.193069 sec
k = 192000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=6.393837 sec
k = 193000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=5.594592 sec
k = 194000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=4.795353 sec
k = 195000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=3.996122 sec
k = 196000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=3.196891 sec
k = 197000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=2.397663 sec
k = 198000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=1.598439 sec
k = 199000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=0.799216 sec
k = 200000 ; erry = 1.000000e-00 ; errz = 1.910028e-12 ; etr=0.000000 sec

Plot the results loglog(1:Npd,hpd(:,1),'-',1:Npd,hpd(:,2),'--',... 1:Npd,hpd(:,3),'-.',1:Npd,1-m(1)+m(2:end),'.:');

loglog(1:Npd,hpd(:,1),'-',1:Npd,hpd(:,2),'--',...
    1:Npd,hpd(:,3),'-.',1:Npd,hpd(:,4),'.:', ...
    1:Npd,hpd(:,5),'--');

Test against GQ

gqNs=0:10:100;
gqconv=zeros(length(gqNs),2);
for Ni=1:length(gqNs)
    N=gqNs(Ni);
    [ex stdx] = gqrapr(P,N+1,d,'direct');
    %[ex1 stdx1] = gqrapr(P,N+2,db,'direct');
    gqconv(Ni,:) = [N,norm(ex-eex,1)];
end
semilogy(gqconv(:,1),gqconv(:,2),'.-');