Adaptive closed3 integration:
integrating sqrt(x) from  0  to  1  :
acc             =  0.0001
eps             =  0.0001
ncalls          =  27
integral        =  0.6666559338797313
exact           =  0.6666666666666666
estimated error :  0.000166666
actual error    :  1.07328e-05 

Adaptive open4 integration:
integrating sqrt(x) from  0  to  1  :
acc             =  0.0001
eps             =  0.0001
ncalls          =  28
integral        =  0.6667087639630322
exact           =  0.6666666666666666
estimated error :  0.000166671
actual error    :  4.20973e-05 

Adaptive closed3 integration:
integrating 4*sqrt(1-(1-x)*(1-x)) from  0  to  1  :
acc             =  1e-06
eps             =  1e-06
ncalls          =  345
integral        =  3.141592647979502
exact           =  3.141592653589793
estimated error :  4.14159e-06
actual error    :  5.61029e-09 

Adaptive open4 integration:
integrating 4*sqrt(1-(1-x)*(1-x)) from  0  to  1  :
acc             =  1e-06
eps             =  1e-06
ncalls          =  444
integral        =  3.141592664789677
exact           =  3.141592653589793
estimated error :  4.14159e-06
actual error    :  1.11999e-08 

Clenshaw-Curtis integration:
integrating 4*sqrt(1-(1-x)*(1-x)) from  0  to  1  :
acc             =  1e-06
eps             =  1e-06
ncalls          =  604
integral        =  3.1415926247632813
exact           =  3.141592653589793
estimated error :  4.14159e-06
actual error    :  2.88265e-08 

Adaptive open4 integration:
integrating log(x)/sqrt(x) from  0  to  1  :
acc             =  0.001
eps             =  0.001
ncalls          =  8572
integral        =  -3.999790084734025
exact           =  -4
estimated error :  0.00499979
actual error    :  0.000209915 

Clenshaw_Curtis integration:
integrating log(x)/sqrt(x) from  0  to  1  :
acc             =  0.001
eps             =  0.001
ncalls          =  72
integral        =  -3.9997193540597884
exact           =  -4
estimated error :  0.00499972
actual error    :  0.000280646 

Adaptive open4 integration:
integrating 1/sqrt(x) from  0  to  1  :
acc             =  0.001
eps             =  0.001
ncalls          =  4292
integral        =  1.999516117504203
exact           =  2
estimated error :  0.00299952
actual error    :  0.000483882 

Clenshaw-Curtis integration:
integrating 1/sqrt(x) from  0  to  1  :
acc             =  0.001
eps             =  0.001
ncalls          =  12
integral        =  1.9999563676667782
exact           =  2
estimated error :  0.00299996
actual error    :  4.36323e-05 

Adaptive open4 integration:
integrating exp(x) from -inf to  1  :
acc             =  0.0001
eps             =  0
ncalls          =  96
integral        =  2.718278963030687
exact           =  2.718281828459045
estimated error :  0.0001
actual error    :  2.86543e-06