Semi-automatic and Adaptive
One multiple pole A
int_{-1}^{1} sin( 1/(x-A) ) dx

Pole is 1.100

 N-point rational Fejer with N = 22.000
Exact relative error: 1.0055212044554036e-14
Execution time: 1.4562599999999998e-02

 Semi-automatic rational Fejer:
Number of poles: 100.000
Initial iteration: 1.000
Number of iterations: 22.000
Estimated relative error: 1.6758686740923289e-15
Exact relative error: 6.3310594354599494e-15
Execution time: 1.6437129999999997e-01

 Semi-automatic rational Fejer with limited number of iterations:
Number of poles: 100.000
Initial iteration: 20.000
Number of iterations: 3.000
Estimated relative error: 1.6758686740923289e-15
Exact relative error: 6.3310594354599494e-15
Execution time: 7.1796100000000002e-02

 N-point rational Fejer with N = 15.000
Exact relative error: 6.3408911983479571e-11
Execution time: 1.2087000000000001e-02

 Adaptive rational Fejer (1):
Number of subintervals: 4.000
Number of different quadrature formulae: 4.000
Number of points in each subinterval: 15.000
Estimated relative error: 1.1056078058248075e-16
Exact relative error: 1.8620763045470439e-16
Execution time: 9.2438099999999995e-02

 Adaptive rational Fejer (2):
Number of subintervals: 12.000
Number of different quadrature formulae: 1.000
Number of points in each subinterval: 15.000
Estimated relative error: 2.4730700919765422e-16
Exact relative error: 1.8620763045470439e-16
Execution time: 3.6251100000000001e-02

 Matlab's built-in QUADGK:
Minimal number of subintervals: 10.000
Number of points in each subinterval: 15.000
Estimated relative error: 1.3223651256509891e-16
Exact relative error: 1.8620763045470439e-16
Execution time: 1.4557000000000001e-03