1Test of erf(x) vs double series expansion


   2000 Random arguments were tested from the interval (  0.000,  0.469)


    ERF(X) was larger   149 times,
               agreed   750 times, and
          was smaller  1101 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.4670E-15 =    2 ** -50.93
    occurred for X = 0.449955E+00
 The estimated loss of base   2 significant digits is   2.07


 The root mean square relative error was     0.1476E-15 =    2 ** -52.59
 The estimated loss of base   2 significant digits is   0.41





 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  0.469,  2.000)


   ERFC(X) was larger   706 times,
               agreed   437 times, and
          was smaller   857 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.1105E-14 =    2 ** -49.69
    occurred for X = 0.131556E+01
 The estimated loss of base   2 significant digits is   3.31


 The root mean square relative error was     0.2927E-15 =    2 ** -51.60
 The estimated loss of base   2 significant digits is   1.40


1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  0.469,  2.000)


  ERFCX(X) was larger   787 times,
               agreed   609 times, and
          was smaller   604 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.8518E-15 =    2 ** -50.06
    occurred for X = 0.195155E+01
 The estimated loss of base   2 significant digits is   2.94


 The root mean square relative error was     0.2207E-15 =    2 ** -52.01
 The estimated loss of base   2 significant digits is   0.99





 Test of erfc(x) vs exp(x+1/4) SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  2.000, 26.000)


   ERFC(X) was larger   537 times,
               agreed   487 times, and
          was smaller   976 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.9993E-15 =    2 ** -49.83
    occurred for X = 0.307650E+01
 The estimated loss of base   2 significant digits is   3.17


 The root mean square relative error was     0.2616E-15 =    2 ** -51.76
 The estimated loss of base   2 significant digits is   1.24


1Test of exp(x*x) erfc(x) vs SUM i^n erfc(x+1/2)


   2000 Random arguments were tested from the interval (  2.000, 20.000)


  ERFCX(X) was larger   482 times,
               agreed  1019 times, and
          was smaller   499 times.


 There are  53 base   2 significant digits in a floating-point number


 The maximum relative error of     0.7162E-15 =    2 ** -50.31
    occurred for X = 0.274811E+01
 The estimated loss of base   2 significant digits is   2.69


 The root mean square relative error was     0.1399E-15 =    2 ** -52.67
 The estimated loss of base   2 significant digits is   0.33


1Special Tests


       Estimated loss of base  2significant digits in

   X     Erf(x)+Erf(-x)   Erf(x)+Erfc(x)-1   Erfcx(x)-exp(x*x)*erfc(x)

  0.000            0.00            0.00            0.00
 -0.500            0.00            0.00            0.00
 -1.000            0.00            0.00            0.00
 -1.500            0.00            0.00            0.00
 -2.000            0.00            0.00            0.00
 -2.500            0.00            0.00            0.00
 -3.000            0.00            0.00            0.02
 -3.500            0.00            0.00            0.33
 -4.000            0.00            0.00            0.00
 -4.500            0.00            0.00            0.00


 Test of special arguments


   ERF ( 0.179769+309) =  0.100000E+01


   ERF ( 0.000000E+00) =  0.000000E+00


  ERFC ( 0.000000E+00) =  0.100000E+01


  ERFC (-0.179769+309) =  0.200000E+01


 Test of Error Returns



 ERFC will be called with the argument 0.199074E+02
 This should not underflow


 ERFC returned the value 0.217879-173



 ERFC will be called with the argument 0.265433E+02
 This may underflow


 ERFC returned the value 0.000000E+00



 ERFCX will be called with the argument 0.237712+308
 This should not underflow


 ERFCX returned the value 0.237341-307



 ERFCX will be called with the argument-0.239659E+02
 This should not overflow


 ERFCX returned the value 0.554007+250



 ERFCX will be called with the argument-0.266287E+02
 This may overflow


 ERFCX returned the value 0.179000+309



 This concludes the tests
