computed in 7.5s
agree with exact (1+sin)/cos series for n<=150
1 s= 2 d= 2 pred 2 2 OK  window/d=32867.0
2 s= 4 d= 2 pred 4 2 OK  window/d=32866.0
3 s= 4 d= 8 pred 4 8 OK  window/d=8216.5
4 s= 4 d= 16 pred 4 16 OK  window/d=4108.2
5 s= 8 d= 32 pred 8 32 OK  window/d=2054.0
6 s= 8 d= 64 pred 8 64 OK  window/d=1027.0
7 s= 8 d= 128 pred 8 128 OK  window/d=513.5
8 s= 8 d= 256 pred 8 256 OK  window/d=256.8
9 s= 10 d= 512 pred 10 512 OK  window/d=128.4
10 s= 12 d= 1024 pred 12 1024 OK  window/d=64.2
11 s= 12 d= 2048 pred 12 2048 OK  window/d=32.1
12 s= 16 d= 4096 pred 16 4096 OK  window/d=16.0
13 s= 16 d= 8192 pred 16 8192 OK  window/d=8.0
14 s= 16 d= 16384 pred 16 16384 OK  window/d=4.0
fails 0 time 13.0
real 13.05
user 9.31
sys 0.09
