本文尝试拟合神经网络迭代次数n对应收敛标准δ的曲线n(δ),和准确率p-max对应收敛标准δ的p-max(δ)曲线,去估算网络准确率达到99.9%的时间和迭代次数。
δ:神经网络输出与收敛对象的差值的绝对值
制作一个带一个3*3卷积核的神经网络,测试集是mnist的3,4,5图片集,将28*28的图片缩小成9*9,网络结构是49*30*3,将这个网络画成图
这个网络分成三个部分让mnist 3,4,5分别向(1,0,0),(0,1,0),(0,0,1)收敛,让三个网络的权重实现同步更新,实现权重共享,前面的实验已经用证实这种做法相当于将弹簧并联,模拟了一个振子力学系统,最终收敛相当于3个弹性系数是k的弹簧并联成一个弹性系数是3k的弹簧。
将上图简写成
S(mnist3)81-(con3*3)49-30-3-(1,0,0)
S(mnist4)81-(con3*3)49-30-3-(0,1,0)
S(mnist5)81-(con3*3)49-30-3-(0,0,1)
w=w,w1=w1,w2=w2
将这个写法进一步的简化
d3(mnist3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1)
测试集由1010张3,982张4,892张5共2884张测试图片。
具体进样顺序 |
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迭代次数 |
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δ=0.1 |
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minst 3-1 |
1 |
判断是否达到收敛标准 |
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minst 4-1 |
2 |
判断是否达到收敛标准 |
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minst 5-1 |
3 |
判断是否达到收敛标准 |
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梯度下降 |
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minst 3-2 |
4 |
判断是否达到收敛标准 |
|
minst 4-2 |
5 |
判断是否达到收敛标准 |
|
minst 5-2 |
6 |
判断是否达到收敛标准 |
|
梯度下降 |
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minst 3-3 |
7 |
判断是否达到收敛标准 |
|
minst 4-3 |
8 |
判断是否达到收敛标准 |
|
minst 5-3 |
9 |
判断是否达到收敛标准 |
|
… |
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minst 3-4999 |
14995 |
判断是否达到收敛标准 |
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minst 4-4999 |
14996 |
判断是否达到收敛标准 |
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minst 5-4999 |
14997 |
判断是否达到收敛标准 |
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梯度下降 |
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… |
|
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如果4999图片内没有达到收敛标准再次从头循环 |
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minst 3-1 |
14998 |
判断是否达到收敛标准 |
|
minst 4-1 |
14999 |
判断是否达到收敛标准 |
|
minst 5-1 |
15000 |
判断是否达到收敛标准 |
|
… |
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达到收敛标准测试准确率记录迭代次数 |
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δ=0.01 |
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… |
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δ=1e-7 |
这个网络的收敛标准是
if (Math.abs(f2[0]-y[0])< δ && Math.abs(f2[1]-y[1])< δ && Math.abs(f2[2]-y[2])< δ)
得到的数据表格
f2[0] |
f2[1] |
f2[2] |
迭代次数n |
平均准确率p-ave |
δ |
耗时ms/pc |
耗时min/200 |
最大准确率p-max |
0.052117 |
0.930084 |
0.091221 |
9887.53 |
0.740473 |
0.1 |
3695.15 |
12.31717 |
0.828363 |
0.278115 |
0.695626 |
0.036957 |
16477.4 |
0.807139 |
0.01 |
5715.36 |
19.0512 |
0.896671 |
0.450262 |
0.340408 |
0.210466 |
33735.23 |
0.846673 |
0.001 |
10724.84 |
35.74945 |
0.92233 |
0.435248 |
0.355336 |
0.210449 |
33855.88 |
0.845035 |
9.00E-04 |
10912.98 |
36.3766 |
0.92129 |
0.425236 |
0.395299 |
0.180408 |
37486.52 |
0.848351 |
8.00E-04 |
12293.83 |
40.97943 |
0.920596 |
0.545123 |
0.290297 |
0.165372 |
37743.51 |
0.857165 |
7.00E-04 |
12503.9 |
41.67967 |
0.919903 |
0.570118 |
0.335231 |
0.095355 |
38853.78 |
0.854445 |
6.00E-04 |
11846.63 |
39.48875 |
0.923024 |
0.525108 |
0.340191 |
0.135284 |
42011.69 |
0.852828 |
5.00E-04 |
13265.66 |
44.21887 |
0.925104 |
0.520092 |
0.380134 |
0.100245 |
46537.22 |
0.855017 |
4.00E-04 |
14817.89 |
49.39297 |
0.922677 |
0.580052 |
0.255132 |
0.165159 |
50546.64 |
0.860267 |
3.00E-04 |
15535.38 |
51.78458 |
0.926144 |
0.625022 |
0.275083 |
0.100124 |
59306.3 |
0.875378 |
2.00E-04 |
18614.03 |
62.04677 |
0.927878 |
0.705002 |
0.240043 |
0.055066 |
72432.41 |
0.886512 |
1.00E-04 |
21980.39 |
73.26797 |
0.931345 |
0.670003 |
0.210041 |
0.120051 |
74827.21 |
0.88659 |
9.00E-05 |
23119.77 |
77.06588 |
0.932039 |
0.650003 |
0.260032 |
0.090049 |
76215 |
0.887975 |
8.00E-05 |
23458.73 |
78.19575 |
0.932386 |
0.665002 |
0.25503 |
0.080044 |
82560.16 |
0.895055 |
7.00E-05 |
25700.81 |
85.66935 |
0.932386 |
0.739997 |
0.170025 |
0.090035 |
81525.21 |
0.892389 |
6.00E-05 |
24866.65 |
82.88882 |
0.937587 |
0.759995 |
0.195021 |
0.045035 |
85679.71 |
0.898838 |
5.00E-05 |
26353.14 |
87.8438 |
0.937587 |
0.635001 |
0.285016 |
0.080024 |
94710.29 |
0.898015 |
4.00E-05 |
29016.53 |
96.72175 |
0.933426 |
0.684997 |
0.230012 |
0.085017 |
102116.6 |
0.903518 |
3.00E-05 |
31293.59 |
104.312 |
0.936893 |
0.709998 |
0.240008 |
0.050012 |
111092.7 |
0.90594 |
2.00E-05 |
33340.97 |
111.1366 |
0.944521 |
0.619999 |
0.325004 |
0.055006 |
145284.1 |
0.912632 |
1.00E-05 |
44158.16 |
147.1939 |
0.949029 |
0.635 |
0.29 |
0.075 |
290646 |
0.931931 |
1.00E-06 |
86017.45 |
286.7248 |
0.961165 |
0.51 |
0.385 |
0.105 |
572369.5 |
0.946196 |
1.00E-07 |
169200.9 |
564.0031 |
0.972261 |
P –ave是200次收敛准确率的平均值,对应网络的平均性能
P-max是200次收敛准确率的最大值,对应网络最大性能
δ |
迭代次数n |
平均准确率p-ave |
耗时min/200 |
最大准确率p-max |
1.00E-07 |
572369.51 |
0.946196279999999 |
564.00305 |
0.972261 |
δ=1e-7的这组数据可以理解成
让网络d3(minst 3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1)
的收敛标准δ=1e-7,在564min可以实现200次收敛其中至少有一次的准确率可以达到0.972261;或者也可以理解成将网络的收敛标准设定在δ=1e-7准确率达到0.972261的概率是5‰,需要2.87min。
第一步
拟合迭代次数n与δ的曲线 n(δ),前面的大量实验已经证实一个网络对应一个特定的收敛标准δ的迭代次数n是特征的,所以n(δ)曲线是稳定存在可重现的,因此用于评估网络性能。
n(δ)曲线的图
迭代次数n随着δ减小在加速变大
用δ∈[1e-5,1e-3] 的数据去拟合n(δ)
x |
δ |
0.00001,0.00002,3E-05,4E-05,5E-05,6E-05,7E-05,8E-05,9E-05,1E-04,0.0002,0.0003,0.0004,0.0005,0.0006,0.0007,0.0008,0.0009,0.001 |
y |
n |
145284.115,111092.705,102116.6,94710.29,85679.71,81525.21,82560.155,76215,74827.21,72432.405,59306.3,50546.635,46537.22,42011.69,38853.775,37743.51,37486.515,33855.875,33735.23 |
拟合方程式:y=ax^b |
a = 3879.73942909131 |
b = -0.314884805502776 |
相关系数 R2:0.995488933786717 |
比较实测值与计算值之间的差异
迭代次数n实测 |
迭代次数计算值 |
实测值/计算值 |
9887.53 |
8011.011663 |
1.234242367 |
16477.395 |
16541.39641 |
0.996130834 |
33735.23 |
34155.21119 |
0.987703745 |
33855.875 |
35307.36551 |
0.958889866 |
37486.515 |
36641.43431 |
1.023063526 |
37743.51 |
38214.94585 |
0.987663574 |
38853.775 |
40115.64463 |
0.968544202 |
42011.69 |
42486.08823 |
0.988834034 |
46537.22 |
45578.73182 |
1.021029286 |
50546.635 |
49900.34486 |
1.012951617 |
59306.3 |
56695.94636 |
1.046041275 |
72432.405 |
70524.78657 |
1.027048908 |
74827.21 |
72903.79214 |
1.02638296 |
76215 |
75658.42062 |
1.007356476 |
82560.155 |
78907.45822 |
1.046290894 |
81525.21 |
82832.08263 |
0.984222627 |
85679.71 |
87726.65137 |
0.976666824 |
94710.29 |
94112.44205 |
1.006352486 |
102116.6 |
103035.8487 |
0.991078361 |
111092.705 |
117067.6268 |
0.948961793 |
145284.115 |
145621.8641 |
0.997680643 |
290645.97 |
300684.7425 |
0.966613628 |
572369.51 |
620863.5975 |
0.921892526 |
在δ∈[1e-7,0.1]的整个区间上都相对精确
所以d3(mnist3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1) 这个网络的n(δ)的表达式就是
第二步拟合准确率p-max和δ的曲线p-max(δ)
可以看到这两条曲线随着n的增加δ的减小几乎都在单调的增加
用δ∈[1e-5,0.1] 的数据去拟合p-max(δ)
x |
-lnδ |
11.51292546,10.81977828,10.41431318,10.1266311,9.903487553,9.721165996,9.567015316,9.433483923,9.315700888,9.210340372,8.517193191,8.111728083,7.824046011,7.60090246,7.418580903,7.264430223,7.13089883,7.013115795,6.907755279,4.605170186,2.302585093, |
y |
p-max |
0.949029126,0.944521498,0.936893204,0.933425798,0.937586685,0.937586685,0.932385576,0.932385576,0.932038835,0.931345354,0.927877947,0.926144244,0.922676838,0.925104022,0.923023578,0.919902913,0.920596394,0.921289875,0.922330097,0.89667129,0.828363384, |
拟合方程式:y=ax^b |
|
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a = 0.788241939009081 |
|
|||
b = 0.0764411686463573 |
|
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相关系数 R2:0.950865104968765 |
|
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实测δ |
最大准确率p-max |
计算δ |
实测值/计算值 |
|
0.1 |
0.828363 |
0.147411 |
0.678374648 |
|
0.01 |
0.896671 |
0.004525 |
2.209945484 |
|
0.001 |
0.92233 |
4.06E-04 |
2.460211481 |
|
1.00E-04 |
0.931345 |
1.41E-04 |
0.70975493 |
|
1.00E-05 |
0.949029 |
1.19E-05 |
0.842376765 |
|
1.00E-06 |
0.961165 |
1.53E-06 |
0.655015704 |
|
1.00E-07 |
0.972261 |
1.74E-07 |
0.573565718 |
|
计算值偏大导致预估的时间会比实际的时间短。
所以d3(mnist3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1) 这个网络的p-max( δ)的表达式
所以由n(δ)和p-max(δ)两个表达式可以计算网络
d3(mnist3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1)
对应任意预期准确率p-max的耗时,
预期p-max |
计算收敛标准δ |
计算迭代次数n |
预期耗时min |
预期耗时 hour |
0.96 |
1.88495E-06 |
246276.8568 |
242.67697 |
4.044616166 |
0.97 |
2.78076E-07 |
449920.4671 |
443.3438736 |
7.38906456 |
0.98 |
3.18267E-08 |
890347.615 |
877.3331941 |
14.6222199 |
0.99 |
2.74104E-09 |
1926960.173 |
1898.793342 |
31.6465557 |
0.999 |
2.30044E-10 |
4204570.835 |
4143.111632 |
69.05186054 |
0.999653259 |
1.90123E-10 |
4464641.455 |
4399.380739 |
73.32301231 |
也就是让网络d3(mnist 3,4,5)81-con(3*3)49-30-3-(3*k) ,k∈(0,1)
的准确率p-max达到0.999可以将网络的收敛标准设定在2.30044E-10,在69小时内内这个网络可以收敛200次,其中至少有一次的准确率可以达到0.999.
或者也可以理解成将网络的收敛标准设定在2.30044E-10,网络的准确率达到0.999的概率是5‰,需要时间20.7min,需要迭代4204570次。
关于调参
δ收敛标准
r学习率
x权重分母,(1-99的随机数)/x
num隐藏层节点数量
n迭代次数
p-ave 网络收敛199次的准确率的平均值
p-max网络收敛199次的准确率的最大值
t收敛时间
δ |
r |
x |
num |
n |
p-ave |
p-max |
t |
减小 |
不变 |
不变 |
不变 |
增加 |
增加 |
增加 |
增加 |
减小 |
减小 |
不变 |
不变 |
增加 |
增加 |
增加 |
增加 |
减小 |
不变 |
减小 |
不变 |
增加 |
增加 |
增加 |
增加 |
减小 |
不变 |
不变 |
减小 |
增加 |
增加 |
增加 |
可能有极小值 |
减小 |
减小 |
减小 |
减小 |
增加 |
增加 |
增加 |
可能有极小值 |
不变 |
减小 |
不变 |
不变 |
增加 |
增加 |
小幅增加,几乎是定值 |
增加 |
不变 |
不变 |
减小 |
不变 |
增加 |
增加 |
几乎是定值 |
增加 |
不变 |
不变 |
不变 |
减小 |
增加 |
增加 |
几乎是定值 |
开口向上有极小值 |
不变 |
减小 |
减小 |
减小 |
增加 |
增加 |
几乎是定值 |
可能有极小值 |
1.δ,r,x,num的减小都会使网络的平均性能p-ave和最大性能p-max增加
2.当δ保持不变并且非常小时,虽然r,x,num减小同样会使最大性能p-max增加但是幅度相当小,几乎可以认为当δ保持不变并且非常小时最大性能p-max是定值
3.在网络的平均性能p-ave和收敛时间之间存在一种平衡,若想网络平均性能p-ave稳定就要增加收敛时间,或者希望网络收敛加快就会导致网络平均性能p-ave不稳定。
4.隐藏层节点数num增加会导致迭代次数n减小,n减小会使收敛时间t减小。但num增加会使单次迭代运算量增加导致t增加,所以num增加可能使收敛时间曲线出现一个极小值,使num出现一个效率最优解。隐藏层节点数应该在同一个单调递减区间。
比如这个网络
d2(minst0,3)81-con(3*3)49-30-2-(2*k) ,k∈(0,1)
先让学习率r=1e-3,再次让学习率r=0.1,会导致网络看起来收敛速度快好多,但性能时好时坏。
因为r增大会导致迭代次数n减小,使得网络在更短的时间里可能达到更小的δ,而δ减小导致准确率增加;
r增大也会导致平均性能下降,使网络性能不稳定。
实验数据 |
学习率 0.1 |
权重初始化方式 |
Random rand1 =new Random(); |
int ti1=rand1.nextInt(98)+1; |
int xx=1; |
if(ti1%2==0) |
{ xx=-1;} |
tw[a][b]=xx*((double)ti1/x); |
第一层第二层和卷积核的权重的初始化的x分别为1000,1000,200 |
0.1
f2[0] f2[1] f2[2] 迭代次数n p-max
0.012827 0.96441 0.089603 9974 0.788488
0.031441 0.915709 0.077609 9824 0.813107
0.020802 0.93349 0.09931 9536 0.799931
0.008112 0.988325 0.089144 9707 0.679612
0.002962 0.994776 0.097958 9620 0.752774
0.017134 0.964293 0.093444 7556 0.761096
0.015488 0.955754 0.097767 9737 0.770458
0.918436 0.014388 0.095227 9223 0.787101
0.004613 0.983155 0.082351 11825 0.754508
0.003877 0.99427 0.092755 7031 0.662275
0.00698 0.983622 0.092608 9140 0.737864
0.035545 0.932161 0.088047 9641 0.759709
0.02577 0.962937 0.096524 4664 0.682732
0.061369 0.916823 0.089663 6962 0.756588
0.005511 0.991375 0.099822 9620 0.695215
0.015159 0.981255 0.097859 7331 0.73509
0.003402 0.995983 0.092068 10634 0.726422
0.015924 0.98039 0.098445 8348 0.700416
0.0185 0.944527 0.098601 11825 0.726768
0.007194 0.991799 0.087106 7745 0.743065
0.005483 0.994767 0.080316 9140 0.755895
0.038374 0.957633 0.080649 11723 0.766644
0.016394 0.933796 0.089638 11801 0.730929
0.002952 0.996135 0.091026 10691 0.727809
0.015704 0.968888 0.092811 7793 0.692094
0.006765 0.988987 0.099408 11546 0.73613
0.003841 0.993202 0.084675 10034 0.712899
0.026445 0.969735 0.089596 8756 0.736824
0.011839 0.984824 0.086533 5786 0.694175
0.017053 0.960208 0.0928 8951 0.765603
0.017166 0.970101 0.092146 9140 0.692094
0.020977 0.913143 0.097007 9797 0.794383
0.003832 0.995257 0.082048 7031 0.708391
0.004329 0.992111 0.086731 11411 0.778086
0.022771 0.964165 0.085294 12614 0.720527
0.01696 0.936819 0.085238 16982 0.756241
0.026895 0.909846 0.072664 8195 0.804785
0.01008 0.977969 0.088773 10592 0.74896
0.069432 0.914766 0.094267 4664 0.662968
0.008611 0.981779 0.097303 10943 0.729542
0.004483 0.994833 0.09836 9551 0.724341
0.008747 0.988043 0.080949 10034 0.716019
0.023349 0.93646 0.09568 6815 0.818308
0.01703 0.982632 0.092562 7031 0.670943
0.024706 0.961836 0.099034 6575 0.715673
0.936789 0.011318 0.08007 17137 0.777393
0.931689 0.013035 0.097533 18568 0.777046
0.0041 0.994438 0.075247 7556 0.70111
0.010191 0.970219 0.091426 13532 0.818308
0.004137 0.993027 0.090874 10034 0.732316
0.012 0.978519 0.099883 10613 0.734743
0.02603 0.959347 0.086926 11825 0.716713
0.008386 0.991091 0.085893 9140 0.758669
0.01859 0.977652 0.098246 7031 0.675451
0.019731 0.951697 0.093927 9641 0.755548
0.936125 0.017022 0.094268 12469 0.768377
0.003115 0.9944 0.081719 7793 0.772885
0.017502 0.970434 0.099409 7793 0.707351
0.004441 0.996043 0.086009 10691 0.698336
0.00664 0.991786 0.093164 7031 0.666782
0.0036 0.9946 0.077596 7793 0.720527
0.014466 0.951693 0.0749 13532 0.814147
0.00375 0.995194 0.079871 7031 0.706311
0.012917 0.974851 0.09825 10034 0.758669
0.009039 0.982302 0.091919 7793 0.785021
0.00331 0.997223 0.08853 9140 0.729889
0.020768 0.947083 0.094765 18710 0.772538
0.008381 0.98902 0.090978 7745 0.753814
0.016042 0.970407 0.0957 11546 0.759362
0.00477 0.99064 0.076519 7793 0.695215
0.002851 0.996334 0.084609 7031 0.733356
0.023179 0.975908 0.086913 7031 0.679958
0.020219 0.957616 0.097704 12614 0.722607
0.00545 0.992173 0.087705 9818 0.694868
0.01526 0.978302 0.079698 6698 0.748613
0.017927 0.972085 0.099699 5786 0.73509
0.022453 0.916097 0.076655 15440 0.76595
0.013655 0.976572 0.098351 18701 0.720527
8.69E-04 0.998633 0.095391 8717 0.792996
0.028955 0.917522 0.093725 11159 0.800971
0.012101 0.982083 0.076882 7793 0.666089
0.026632 0.924207 0.091707 8549 0.760055
0.008955 0.967816 0.094027 11723 0.799237
0.014314 0.965416 0.097349 10226 0.727115
0.005781 0.988894 0.099738 11663 0.693828
0.007687 0.976106 0.093508 11288 0.745839
0.029332 0.943497 0.091109 14534 0.740291
0.028885 0.923879 0.091788 10943 0.725035
0.013197 0.967597 0.098159 7517 0.762136
0.015552 0.968071 0.095718 11723 0.77982
0.012308 0.977774 0.096064 5897 0.732663
0.004786 0.994341 0.084676 8717 0.745839
0.009094 0.975892 0.099555 9473 0.785714
0.020683 0.908495 0.099759 9353 0.773925
0.040761 0.909651 0.07922 8774 0.739945
0.004176 0.984281 0.096594 14228 0.730236
0.042675 0.914063 0.098459 8288 0.742718
0.027144 0.935049 0.096938 11360 0.783634
0.004266 0.992093 0.084666 7556 0.71914
0.012937 0.976928 0.097618 10460 0.773578
0.023402 0.958074 0.093704 5939 0.722261
0.00893 0.974253 0.093574 11825 0.767684
0.014487 0.974271 0.090006 6116 0.769071
0.01853 0.965924 0.078884 8774 0.753467
0.025246 0.938508 0.09756 5918 0.821775
0.030244 0.928453 0.099726 8489 0.731623
0.021258 0.933875 0.099095 8390 0.78086
0.018967 0.977521 0.096254 7031 0.62448
0.009778 0.979861 0.088648 11825 0.723648
0.019501 0.964979 0.094911 9278 0.730929
0.017212 0.974055 0.096599 7793 0.666436
0.011124 0.982726 0.075871 7556 0.712552
0.946755 0.019727 0.076061 9046 0.782247
0.919891 0.008116 0.098741 13528 0.782594
0.019241 0.965534 0.08547 10433 0.747573
0.006991 0.980225 0.097947 9140 0.731969
0.006428 0.988803 0.095322 10034 0.705964
0.008431 0.984134 0.087914 8390 0.75208
0.009976 0.985402 0.099679 10109 0.729542
0.039806 0.923234 0.088908 17531 0.644938
0.015443 0.97443 0.09357 16982 0.729196
0.00357 0.994912 0.091558 11663 0.717406
0.008375 0.986987 0.093318 13049 0.68932
0.04645 0.9113 0.096623 6815 0.790222
0.025147 0.965249 0.093505 5786 0.693828
0.038716 0.914284 0.08434 14192 0.784674
0.003942 0.986901 0.09933 9572 0.790569
0.018261 0.970623 0.097484 5897 0.666436
0.031863 0.93717 0.090267 11825 0.750347
0.037508 0.940471 0.072046 12614 0.715673
0.00724 0.964876 0.095985 9488 0.807906
0.047271 0.936788 0.0726 8774 0.737517
0.00264 0.992901 0.087917 9620 0.726075
0.008752 0.978796 0.097844 8390 0.775659
0.008701 0.973215 0.093971 9374 0.756935
0.021281 0.971198 0.098796 4955 0.732663
0.005358 0.990063 0.099412 7229 0.805825
0.012994 0.986745 0.09097 7793 0.715326
0.031841 0.90164 0.091246 12065 0.789182
0.00331 0.986425 0.071953 9518 0.828363
0.001415 0.99903 0.098656 24812 0.692094
0.020269 0.960183 0.092548 9386 0.805825
0.005185 0.989311 0.09968 9518 0.76595
0.00426 0.98706 0.098652 13292 0.791956
0.031127 0.919875 0.075798 9641 0.783287
0.023823 0.945157 0.090905 9737 0.764216
0.003867 0.992525 0.080883 11825 0.760402
0.008837 0.985815 0.090654 7556 0.743759
0.006836 0.987751 0.090172 9707 0.722607
0.042328 0.944765 0.09288 10559 0.664702
0.004087 0.993416 0.099656 7190 0.747226
0.908405 0.012913 0.093338 11386 0.791956
0.020819 0.920347 0.086002 13829 0.745146
0.013071 0.970995 0.099455 9473 0.79889
0.005217 0.992229 0.099461 7031 0.721221
0.023826 0.912439 0.096299 8351 0.776699
0.006589 0.972057 0.098989 11825 0.773578
0.002372 0.99685 0.098317 9818 0.726422
0.040762 0.928299 0.0903 12245 0.748266
0.006135 0.992624 0.099302 10559 0.741678
0.025961 0.929203 0.085027 8549 0.787101
0.003928 0.991675 0.096728 9140 0.758322
0.011612 0.984469 0.086291 7031 0.691748
0.021223 0.943315 0.086819 10244 0.723648
0.007357 0.99193 0.086805 7004 0.769417
0.042012 0.937487 0.099465 8699 0.729196
0.013727 0.962332 0.098142 9518 0.780166
0.003761 0.997241 0.066355 7556 0.722954
0.012995 0.982352 0.09964 7793 0.718793
0.921575 0.012328 0.098306 14827 0.77982
0.012791 0.986903 0.075571 7031 0.728502
0.027376 0.963576 0.099444 5786 0.65742
0.009098 0.991452 0.070932 7031 0.68932
0.003955 0.995079 0.094361 9620 0.740291
0.011408 0.973353 0.095323 6137 0.786061
0.012585 0.982657 0.098817 7793 0.755201
0.028041 0.93635 0.088059 17192 0.712552
0.04436 0.951442 0.094876 12413 0.734743
0.023736 0.934216 0.092267 9974 0.696602
0.017502 0.984593 0.072552 7031 0.645284
0.012701 0.982634 0.092179 6029 0.723648
0.007394 0.977546 0.091848 13532 0.801664
0.021214 0.945138 0.092845 10034 0.758322
0.003386 0.995114 0.094881 11663 0.701456
0.027655 0.947345 0.080993 11546 0.806865
0.00745 0.984857 0.09853 10034 0.723648
0.007459 0.989533 0.09598 8348 0.79473
0.003634 0.991733 0.083683 18677 0.656033
0.004212 0.995312 0.087025 9620 0.73509
0.003749 0.995002 0.094711 9818 0.639043
0.010209 0.979845 0.094366 9974 0.735784
0.005446 0.989488 0.099487 9518 0.740985
0.029489 0.930853 0.082922 10709 0.742372
0.029368 0.918938 0.098905 7391 0.735784
0.024283 0.9538 0.088555 16982 0.752774
0.017368 0.973337 0.096931 6575 0.734397
0.020987 0.96943 0.097887 10409 0.755201
0.008934 0.978982 0.095947 7745 0.767684
0.003471 0.994565 0.093273 11249 0.64251
0.001959 0.997363 0.098906 14228 0.71706
0.052117 0.930084 0.091221 9887.53 0.828363
0.01
0.008435 0.999779 0.006228 23342 0.850555
0.007281 0.996897 0.007635 15038 0.878294
0.993851 0.008452 0.0047 10663 0.881761
0.008307 0.998859 0.009029 8936 0.833564
0.007228 0.997963 0.008065 14228 0.764216
0.006601 0.999066 0.007722 13292 0.856103
0.008281 0.999381 0.006653 13115 0.779126
0.008261 0.999504 0.007162 16823 0.786061
0.991968 0.003298 0.008157 17350 0.84258
0.992333 0.006768 0.006466 18568 0.815534
0.008918 0.993924 0.009911 21449 0.727809
0.995287 0.005623 0.004781 17137 0.863731
0.002886 0.999631 0.009933 15974 0.840153
0.991619 0.008175 0.004423 12010 0.878294
0.009174 0.996366 0.007299 18677 0.741331
0.009375 0.996261 0.009448 14294 0.883842
0.995382 0.003745 0.008606 17155 0.71706
0.008717 0.99983 0.002972 34742 0.695908
0.008007 0.999348 0.009542 16523 0.852635
0.003972 0.999501 0.00638 22025 0.772538
0.992341 0.009703 0.007064 13018 0.877947
0.997034 0.001528 0.009107 15406 0.846741
0.006907 0.999347 0.003909 12413 0.795423
0.002398 0.998972 0.008178 16850 0.867892
0.008544 0.993995 0.009243 11849 0.84466
0.003152 0.999587 0.004153 24614 0.730929
0.998172 0.00446 0.005868 21328 0.761096
0.002718 0.999922 0.007211 19748 0.739251
0.006427 0.998357 0.008821 14393 0.830791
0.009049 0.999079 0.00866 10034 0.811026
0.005078 0.999174 0.009087 18929 0.821429
0.994727 0.00149 0.005555 14827 0.844313
0.007179 0.99887 0.006899 10034 0.8138
0.006468 0.998664 0.008321 12794 0.817961
0.009874 0.999535 0.003783 19748 0.725035
0.009066 0.997916 0.009817 15233 0.867198
0.004239 0.998978 0.00853 13604 0.853675
0.003896 0.997378 0.008916 13292 0.819695
0.006475 0.999277 0.008399 10034 0.821429
0.009704 0.999322 0.00554 22025 0.748266
0.003637 0.997612 0.009062 13550 0.85749
0.005974 0.999177 0.006802 14912 0.791956
0.008701 0.998828 0.003248 19748 0.691401
0.994748 0.008258 0.001697 14827 0.869279
0.995378 0.005362 0.005198 10756 0.856103
0.004346 0.998628 0.009747 18131 0.85957
0.994198 0.001155 0.008372 12472 0.854369
0.994935 0.007296 0.00483 14473 0.864424
0.991634 0.003402 0.007952 17137 0.850902
0.005975 0.998196 0.007978 14228 0.794036
0.004789 0.999189 0.006463 17489 0.79785
0.007276 0.007628 0.990351 13761 0.882108
0.993698 0.008271 0.009152 17155 0.720874
0.992393 0.001743 0.009365 17137 0.814147
0.991374 0.006974 0.009244 27670 0.824549
0.99564 0.005595 0.003861 20629 0.878294
0.005961 0.999439 0.008126 16823 0.808946
0.006419 0.999818 0.004694 19748 0.694175
0.009086 0.997263 0.009419 14900 0.838766
0.993763 9.60E-04 0.008521 14827 0.872053
0.009181 0.998445 0.007767 16142 0.769071
0.993943 0.002718 0.00592 18568 0.800971
0.00994 0.997054 0.009956 13523 0.831137
0.008532 0.998661 0.007081 16472 0.770804
0.006493 0.996726 0.009476 17489 0.795076
0.009185 0.997108 0.009628 16724 0.759362
0.006756 0.005002 0.993494 13761 0.852288
0.004908 0.99936 0.005906 17489 0.799237
0.009852 0.997151 0.007222 21266 0.785714
0.008798 0.996524 0.009077 16310 0.824549
0.99607 0.008713 0.005327 17137 0.792302
0.008428 0.997942 0.007226 17000 0.848821
0.009278 0.999399 0.007707 16850 0.896671
0.994782 0.005052 0.009174 16777 0.806865
0.002497 0.999594 0.008601 21410 0.730929
0.990776 0.005235 0.00931 12427 0.804438
0.006949 0.998206 0.008272 14228 0.821775
0.00927 0.99641 0.006558 13892 0.859917
0.005808 0.998156 0.009734 16142 0.727115
0.004878 0.998474 0.009955 15038 0.868239
0.007222 0.997736 0.007462 9140 0.852288
0.007025 0.998505 0.007848 16679 0.783287
0.007238 0.999492 0.006348 22025 0.708738
0.003822 0.999759 0.005219 15470 0.780513
0.9946 0.006777 0.008438 20728 0.8457
0.003801 0.99873 0.008339 16142 0.71706
0.004494 0.999009 0.007273 10559 0.825243
0.9929 0.008747 0.004117 14827 0.825936
0.009557 0.994723 0.009875 10559 0.809986
0.006542 0.997989 0.009549 14228 0.79889
0.006046 0.998395 0.006465 13550 0.879681
0.007421 0.99703 0.008727 10574 0.874827
0.008667 0.998027 0.007724 31136 0.701803
0.005215 0.998462 0.009475 14228 0.785021
0.007546 0.99952 0.002305 22025 0.677531
0.008024 0.999568 0.004428 10559 0.790915
0.992556 0.003953 0.006498 14701 0.852288
0.004788 0.998897 0.004628 13292 0.814147
0.990082 0.005347 0.009725 14014 0.825243
0.99155 0.003198 0.009059 14014 0.874827
0.004042 0.999561 0.005552 18929 0.81172
0.996822 0.005656 0.009644 35092 0.806172
0.006871 0.998473 0.009275 15038 0.86165
0.003511 0.997625 0.009572 13760 0.885576
0.008874 0.999707 0.007221 17930 0.79889
0.996451 0.002706 0.008205 16804 0.729889
0.004503 0.999207 0.009487 13427 0.839112
0.990445 0.007088 0.009778 17992 0.869279
0.991293 0.006746 0.007788 20383 0.82767
0.007822 0.999546 0.007035 16724 0.757628
0.00547 0.999202 0.009189 14228 0.795423
0.995813 0.008069 0.00705 17788 0.645978
0.994044 0.008109 0.004734 12427 0.833911
0.005185 0.99724 0.005791 13949 0.795423
0.995264 0.006352 0.003777 17137 0.838766
0.007034 0.996222 0.007596 18131 0.877254
0.006158 0.997432 0.009249 22949 0.788835
0.991784 0.009286 0.007648 24478 0.708044
0.993897 0.005804 0.009823 24478 0.740291
0.00922 0.999324 0.004405 13673 0.835992
0.009235 0.999661 0.005971 19748 0.696949
0.005386 0.999191 0.004864 14702 0.765603
0.005085 0.999627 0.009001 10034 0.800624
0.00871 0.998773 0.008118 12413 0.848821
0.009178 0.996023 0.009647 18101 0.787448
0.994225 0.005651 0.00798 24478 0.735784
0.006865 0.994484 0.009714 13604 0.820042
0.994586 0.001574 0.009552 18535 0.864424
0.005001 0.9987 0.005438 15227 0.763176
0.00679 0.998786 0.00978 12413 0.81276
0.004921 0.998438 0.008646 29387 0.682386
0.005394 0.996532 0.00769 13292 0.822469
0.007669 0.002998 0.997793 19821 0.863384
0.993633 0.002932 0.007442 14827 0.811026
0.003438 0.998032 0.007073 13472 0.857836
0.99474 0.008815 0.008332 16777 0.753121
0.99223 0.009589 0.004048 18568 0.81172
0.008487 0.997982 0.00886 14228 0.825936
0.009911 0.996059 0.009547 12302 0.871359
0.009213 0.996809 0.006766 16142 0.759362
0.007057 0.998028 0.008824 13673 0.809293
0.008816 0.998915 0.004295 13292 0.865465
0.006229 0.998479 0.004381 11663 0.789528
0.007569 0.999583 0.008656 20684 0.79473
0.007403 0.999254 0.007472 16724 0.721567
0.005984 0.999498 0.005281 10034 0.772191
9.80E-04 0.999788 0.008189 15227 0.81484
0.99502 0.005199 0.004642 14395 0.828017
0.007758 0.99583 0.009334 18854 0.718447
0.008959 0.999502 0.008876 10034 0.831137
0.991334 0.002965 0.009446 14827 0.806172
0.007079 0.999416 0.007827 19121 0.85957
0.007895 0.005775 0.993846 13761 0.867545
0.006864 0.999372 0.007178 22025 0.724341
0.005787 0.999283 0.005052 10034 0.850208
0.005072 0.99872 0.008427 13292 0.847087
0.006886 0.998028 0.005527 13292 0.851248
0.996073 0.004926 0.00711 18673 0.820042
0.008694 0.002969 0.994886 13761 0.841886
0.993852 0.004379 0.008073 20107 0.827323
0.003171 0.999832 0.00761 22550 0.775659
0.998171 0.001242 0.009636 15544 0.869972
0.00331 0.999786 0.004182 22025 0.769417
0.007438 0.99756 0.006166 13292 0.84258
0.004151 0.999664 0.005182 19748 0.690361
0.00381 0.997803 0.009075 14786 0.704924
0.995108 0.002652 0.009189 11542 0.801664
0.992335 0.009256 0.009016 10756 0.85749
0.998266 0.004438 0.007727 36322 0.769417
0.005853 0.998602 0.006287 13472 0.839112
0.991973 0.008067 0.004495 14827 0.840846
0.005523 0.999678 0.00684 19748 0.695215
0.008937 0.998172 0.006199 10559 0.786061
0.00872 0.998715 0.008529 11612 0.786061
0.994663 0.007675 0.009128 10756 0.87656
0.00858 0.998445 0.007677 13292 0.849515
0.004607 0.999114 0.006265 13760 0.839112
0.006127 0.999151 0.00665 13472 0.834605
0.006109 0.999124 0.004714 10034 0.858877
0.003962 0.999292 0.003718 22025 0.668863
0.998355 0.004871 0.007127 26536 0.762829
0.004912 0.999553 0.006175 22025 0.760749
0.008593 0.998818 0.005533 14228 0.789182
0.006077 0.999628 0.007806 15920 0.844313
0.007165 0.99831 0.009057 10034 0.85749
0.991351 0.003779 0.009207 17656 0.79785
0.003611 0.999241 0.008033 19748 0.771151
0.008881 0.999442 0.009011 18116 0.870666
0.002088 0.997862 0.008795 15101 0.841886
0.005582 0.997669 0.009669 13760 0.884535
0.004427 0.999813 0.003576 19748 0.717753
0.005829 0.009528 0.992416 13761 0.881068
0.005525 0.999272 0.0071 17489 0.848474
0.004457 0.999628 0.00308 15227 0.791609
0.006094 0.998817 0.004222 15038 0.850902
0.007218 0.99954 0.006942 19748 0.714979
0.002418 0.999602 0.008641 24812 0.768031
0.00462 0.999811 0.005746 19748 0.728502
0.009382 0.99769 0.008902 25586 0.772191
0.006389 0.997569 0.00854 15233 0.884882
0.278115 0.695626 0.036957 16477.4 0.896671
0.001
1.00E-03 8.53E-04 0.999747 24801 0.87344
0.999897 6.06E-04 7.24E-04 25750 0.889736
3.90E-04 0.999997 9.00E-04 73415 0.885229
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6.00E-04
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5.66E-04 4.26E-04 0.999708 33165 0.907074
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4.80E-04 0.999959 2.94E-04 54602 0.793343
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3.49E-04 0.999995 4.36E-04 45215 0.792996
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5.00E-04
3.46E-04 0.999942 3.59E-04 34469 0.869279
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4.25E-04 2.43E-04 0.999654 43749 0.849515
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1.77E-04 2.73E-04 0.999728 35913 0.826283
4.84E-04 0.999979 2.54E-04 35900 0.88835
3.96E-04 0.999964 4.28E-04 39608 0.895978
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1.52E-04 0.999979 4.68E-04 32921 0.866505
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3.91E-04 0.999993 3.05E-04 48089 0.840846
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3.86E-04 0.999993 2.86E-04 47915 0.869279
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4.00E-04
3.75E-04 0.99999 3.35E-04 39806 0.841886
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3.78E-04 0.999989 3.77E-04 39806 0.770111
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1.73E-04 0.999994 3.76E-04 45287 0.881415
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2.17E-04 0.999994 2.67E-04 39806 0.7181
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2.48E-04 0.999995 1.97E-04 39806 0.787101
2.98E-04 0.999983 3.36E-04 31844 0.917822
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2.81E-04 0.999996 1.55E-04 49736 0.685853
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3.82E-04 0.999994 1.26E-04 35900 0.878294
1.98E-04 3.06E-04 0.9999 24801 0.834258
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7.60E-05 0.999991 3.59E-04 156053 0.859223
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3.62E-04 0.999995 2.84E-04 39806 0.781207
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3.72E-04 0.999991 3.80E-04 30221 0.866852
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3.31E-04 2.52E-04 0.999733 58743 0.854369
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1.97E-04 0.999931 3.92E-04 35900 0.903259
2.33E-04 0.999999 1.59E-04 62909 0.841886
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3.97E-04 0.999996 2.69E-04 60956 0.82871
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3.00E-04
0.999947 8.48E-05 2.19E-04 47143 0.806519
2.22E-04 0.999994 2.55E-04 40562 0.911928
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1.52E-04 1.65E-04 0.999905 39795 0.84258
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1.91E-04 2.61E-04 0.999788 80895 0.838419
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1.87E-04 0.999996 2.04E-04 49736 0.769764
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2.60E-04 0.999975 2.98E-04 45215 0.816227
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1.96E-04 1.09E-04 0.9999 43749 0.867198
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1.90E-04 9.07E-05 0.999946 61860 0.895631
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1.19E-04 0.999989 2.78E-04 47915 0.8457
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1.82E-04 1.89E-04 0.999908 39795 0.848474
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2.94E-04 2.15E-04 0.99993 39795 0.815881
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2.67E-04 2.48E-04 0.999809 38160 0.925798
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2.47E-04 2.48E-04 0.999896 39795 0.828017
2.63E-04 0.999991 1.99E-04 47906 0.883842
0.999981 2.86E-04 1.95E-04 50971 0.867545
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5.08E-05 0.999996 2.69E-04 64730 0.718793
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1.61E-04 2.63E-04 0.999884 39795 0.843967
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1.35E-04 8.40E-05 0.999968 54789 0.849861
2.09E-04 0.999996 7.04E-05 64730 0.75
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2.39E-04 2.96E-04 0.999866 39795 0.862691
1.88E-04 0.999989 2.11E-04 35900 0.87656
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2.56E-04 0.999997 2.02E-04 45215 0.832178
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2.50E-04 8.74E-05 0.999925 39795 0.886963
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2.62E-04 0.999998 1.32E-04 38894 0.821429
0.999965 1.75E-04 2.44E-04 65965 0.856796
2.66E-04 2.57E-04 0.999773 37992 0.851942
0.999969 1.96E-04 1.20E-04 62137 0.765257
0.99998 2.09E-04 1.85E-04 47185 0.89147
1.79E-04 0.999998 2.82E-04 39806 0.787448
1.94E-04 2.27E-04 0.99989 33366 0.926144
2.85E-04 0.999982 2.38E-04 54800 0.79681
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0.999949 8.78E-05 1.99E-04 63655 0.866505
2.28E-04 0.999997 1.75E-04 54800 0.84362
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2.66E-04 1.32E-04 0.999832 23166 0.921637
1.84E-04 0.999994 2.58E-04 39806 0.811026
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2.85E-04 0.999998 1.36E-04 49736 0.715326
2.15E-04 2.53E-04 0.99989 39795 0.838419
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1.24E-04 1.50E-04 0.999969 39795 0.816574
2.93E-04 0.999987 1.95E-04 49463 0.884189
2.01E-04 0.999999 1.56E-04 34742 0.744452
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1.72E-04 0.999996 2.55E-04 51188 0.916782
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1.24E-04 0.99999 1.32E-04 54602 0.852635
1.83E-04 2.72E-04 0.999908 24801 0.816574
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7.26E-05 0.999998 2.45E-04 45215 0.834951
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1.20E-04 2.72E-04 0.99992 39795 0.85957
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2.00E-04
0.999961 1.56E-04 1.73E-04 48661 0.916436
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1.21E-04 1.74E-04 0.999832 53154 0.918516
0.999974 1.95E-05 1.34E-04 108637 0.875173
1.61E-04 0.999998 1.54E-04 64730 0.723994
1.54E-04 5.61E-05 0.999881 38160 0.918863
0.99999 1.11E-04 6.19E-05 63655 0.89147
1.57E-04 0.999994 1.15E-04 66089 0.833911
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8.84E-05 0.999996 1.38E-04 50894 0.881761
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1.96E-04 0.999997 1.60E-04 63083 0.903953
0.999923 6.08E-05 1.69E-04 57775 0.915742
1.97E-04 0.999982 9.77E-05 39608 0.863731
1.31E-04 0.999998 1.66E-04 36194 0.914008
1.70E-04 0.999999 1.62E-04 48680 0.902219
1.44E-04 0.999988 1.41E-04 51188 0.917129
1.70E-04 0.999998 1.45E-04 56972 0.89251
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1.00E-04
0.999953 8.98E-05 9.13E-05 60526 0.896325
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7.00E-05
0.999979 4.07E-05 3.56E-05 93643 0.914702
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6.83E-05 6.58E-05 0.99998 114765 0.82871
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6.00E-05
0.999955 2.75E-05 4.37E-05 90514 0.912968
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5.45E-05 4.54E-05 0.999953 110685 0.904993
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3.10E-05 0.999999 5.50E-05 77903 0.870666
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3.64E-05 0.999998 2.38E-05 91820 0.92233
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3.79E-05 1.37E-05 0.999986 68148 0.930999
5.85E-05 0.999996 5.94E-05 116948 0.921637
4.95E-05 0.999997 5.20E-05 96077 0.825936
0.999978 4.69E-05 3.67E-05 93643 0.916782
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5.00E-05
0.999954 1.27E-05 3.51E-05 89206 0.907767
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3.67E-05 0.999998 3.74E-05 95993 0.897712
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3.89E-05 0.999999 2.32E-05 101954 0.919556
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1.96E-05 0.999999 4.42E-05 105938 0.9043
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3.96E-05 0.999999 4.67E-05 85136 0.92025
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3.98E-05 0.999998 2.88E-05 96998 0.87656
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4.00E-05
1.53E-05 0.999999 3.83E-05 75950 0.914355
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3.00E-05
2.68E-05 2.67E-05 0.999976 98136 0.924064
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2.00E-05
1.88E-05 0.999998 1.34E-05 128183 0.899098
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