9 September 2023   7:21:47.489 AM      
 
ball_monte_carlo_test():
  FORTRAN77 version
  Test ball_monte_carlo().
 
TEST01
  Estimate integrals over the interior of the unit ball
  using the Monte Carlo method.
 
         N        1              X^2             Y^2             Z^2             X^4           X^2Y^2           Z^4
 
         1     4.18879         1.95456        0.154962        0.222153        0.912032        0.723078E-01    0.117819E-01
         2     4.18879         1.62731         1.05487        0.664254         1.26129        0.136638        0.210351    
         4     4.18879        0.734514        0.199887        0.971398        0.368033        0.651732E-01    0.305456    
         8     4.18879        0.517291        0.891092        0.408330        0.127877        0.109757        0.923969E-01
        16     4.18879        0.983047        0.931486         1.06439        0.477341        0.159812        0.488477    
        32     4.18879         1.03570        0.703630        0.877538        0.497207        0.108907        0.378070    
        64     4.18879        0.789039        0.675452        0.839127        0.333270        0.656307E-01    0.350401    
       128     4.18879        0.915054        0.825066        0.886565        0.403059        0.112893        0.405476    
       256     4.18879        0.763896        0.872109        0.916547        0.300699        0.125996        0.422931    
       512     4.18879        0.815962        0.903185        0.817093        0.349506        0.120456        0.357843    
      1024     4.18879        0.855916        0.814805        0.822955        0.375218        0.117958        0.340883    
      2048     4.18879        0.843579        0.835054        0.831435        0.359523        0.122554        0.356660    
      4096     4.18879        0.853495        0.810376        0.844804        0.370678        0.119071        0.366617    
      8192     4.18879        0.843629        0.822722        0.843863        0.361941        0.119218        0.361640    
     16384     4.18879        0.820308        0.842325        0.838738        0.347649        0.118054        0.356431    
     32768     4.18879        0.839988        0.834583        0.842454        0.358756        0.120813        0.362220    
     65536     4.18879        0.842308        0.837056        0.838084        0.360922        0.120189        0.360257    
 
     Exact     4.18879        0.837758        0.837758        0.837758        0.359039        0.119680        0.359039    
 
ball_monte_carlo_test():
  Normal end of execution.
 
 9 September 2023   7:21:47.531 AM