Open jzhan039 opened 4 years ago
giordano
commented
4 years ago Hi Jin,
I'm not aware of this limitation, I'm not the author of the original C library and I've never gone that far with the number of components :slightly_smiling_face: Could you please provide a minimal reproducible example? Thanks!
giordano
commented
4 years ago Ok, I managed to reproduce the issue:
julia> using Cuba
julia> function integrand(x, f)
for i in eachindex(f)
f[i] = x[1]
end
end
integrand (generic function with 1 method)
julia> cuhre(integrand, 2, 1024)
Components:
1: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
2: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
3: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
4: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
5: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
6: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
7: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
8: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
9: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
10: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
11: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
12: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
13: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
14: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
15: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
16: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
17: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
18: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
19: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
20: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
21: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
22: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
23: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
24: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
25: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
26: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
27: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
28: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
29: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
30: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
31: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
32: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
33: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
34: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
35: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
36: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
37: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
38: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
39: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
40: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
41: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
42: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
43: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
44: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
45: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
46: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
47: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
48: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
49: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
50: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
51: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
52: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
53: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
54: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
55: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
56: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
57: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
58: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
59: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
60: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
61: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
62: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
63: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
64: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
65: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
66: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
67: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
68: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
69: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
70: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
71: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
72: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
73: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
74: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
75: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
76: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
77: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
78: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
79: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
80: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
81: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
82: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
83: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
84: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
85: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
86: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
87: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
88: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
89: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
90: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
91: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
92: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
93: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
94: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
95: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
96: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
97: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
98: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
99: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
100: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
101: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
102: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
103: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
104: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
105: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
106: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
107: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
108: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
109: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
110: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
111: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
112: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
113: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
114: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
115: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
116: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
117: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
118: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
119: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
120: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
121: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
122: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
123: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
124: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
125: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
126: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
127: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
128: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
129: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
130: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
131: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
132: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
133: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
134: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
135: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
136: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
137: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
138: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
139: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
140: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
141: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
142: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
143: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
144: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
145: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
146: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
147: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
148: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
149: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
150: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
151: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
152: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
153: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
154: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
155: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
156: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
157: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
158: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
159: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
160: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
161: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
162: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
163: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
164: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
165: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
166: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
167: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
168: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
169: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
170: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
171: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
172: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
173: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
174: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
175: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
176: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
177: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
178: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
179: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
180: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
181: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
182: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
183: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
184: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
185: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
186: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
187: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
188: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
189: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
190: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
191: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
192: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
193: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
194: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
195: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
196: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
197: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
198: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
199: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
200: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
201: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
202: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
203: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
204: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
205: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
206: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
207: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
208: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
209: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
210: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
211: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
212: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
213: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
214: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
215: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
216: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
217: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
218: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
219: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
220: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
221: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
222: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
223: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
224: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
225: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
226: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
227: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
228: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
229: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
230: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
231: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
232: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
233: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
234: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
235: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
236: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
237: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
238: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
239: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
240: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
241: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
242: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
243: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
244: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
245: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
246: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
247: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
248: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
249: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
250: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
251: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
252: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
253: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
254: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
255: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
256: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
257: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
258: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
259: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
260: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
261: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
262: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
263: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
264: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
265: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
266: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
267: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
268: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
269: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
270: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
271: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
272: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
273: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
274: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
275: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
276: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
277: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
278: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
279: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
280: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
281: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
282: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
283: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
284: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
285: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
286: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
287: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
288: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
289: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
290: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
291: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
292: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
293: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
294: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
295: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
296: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
297: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
298: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
299: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
300: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
301: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
302: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
303: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
304: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
305: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
306: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
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928: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
929: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
930: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
931: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
932: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
933: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
934: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
935: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
936: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
937: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
938: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
939: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
940: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
941: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
942: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
943: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
944: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
945: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
946: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
947: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
948: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
949: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
950: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
951: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
952: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
953: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
954: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
955: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
956: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
957: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
958: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
959: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
960: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
961: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
962: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
963: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
964: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
965: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
966: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
967: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
968: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
969: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
970: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
971: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
972: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
973: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
974: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
975: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
976: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
977: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
978: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
979: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
980: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
981: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
982: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
983: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
984: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
985: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
986: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
987: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
988: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
989: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
990: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
991: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
992: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
993: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
994: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
995: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
996: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
997: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
998: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
999: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1000: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1001: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1002: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1003: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1004: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1005: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1006: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1007: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1008: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1009: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1010: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1011: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1012: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1013: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1014: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1015: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1016: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1017: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1018: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1019: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1020: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1021: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1022: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1023: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
1024: 0.5 ± 4.291960664289122e-15 (prob.: 0.0)
Integrand evaluations: 195
Number of subregions: 2
Note: The desired accuracy was reached
julia> cuhre(integrand, 2, 1025)
Components:
1: 1.0e-323 ± 2.6582969e-316 (prob.: 3.181697100895784e107)
2: 6.9225739581205e-310 ± 2.37420064e-316 (prob.: -1.5261292110010404e176)
3: NaN ± 5.736e-321 (prob.: -3.0533142086506293e171)
4: 2.63943623e-316 ± NaN (prob.: 1.5792447235956503e44)
5: 2.6394323e-316 ± 0.0 (prob.: -1.0853051458509069e293)
6: 8.957e-321 ± 0.0 (prob.: 2.3154661861578768e-130)
7: 4.4e-323 ± NaN (prob.: 2.950287248468539e-153)
8: 2.29e-321 ± 1.1791178574683886e-307 (prob.: 2.3081130043758142e-36)
9: NaN ± 2.65830005e-316 (prob.: 4.133590865535919e39)
10: 2.65386215e-316 ± 2.37420064e-316 (prob.: -6.905522643028877e15)
11: 2.6542503e-316 ± NaN (prob.: -2.6995513957278123e307)
12: 5.5e-322 ± 0.0 (prob.: 1.001091914194852e-309)
13: 2.5e-323 ± 5.0e-324 (prob.: -1.4537345263617328e-266)
14: 5.4e-322 ± 0.0 (prob.: 3.54936952253e-313)
15: 3.08e-321 ± -2.1219957944e-314 (prob.: -1.4925084834725364e82)
16: 1.0e-323 ± 1.2347447039310686e-307 (prob.: 6.814582066837622e305)
17: 6.92257395812703e-310 ± 2.6583032e-316 (prob.: -7.187538103692136e-264)
18: 9.93e-322 ± 2.37420064e-316 (prob.: -8.384723485103756e80)
19: 2.5e-323 ± 5.736e-321 (prob.: 4.460691083174233e43)
20: 1.44e-321 ± 0.0 (prob.: 2.7977170889221333e-306)
21: NaN ± 5.0e-324 (prob.: -7.171307625967033e-264)
22: 0.0 ± 0.0 (prob.: 3.881450834186189e47)
23: 2.6538748e-316 ± 2.1219957944e-314 (prob.: -6.9744556466635676e-264)
24: NaN ± 1.2903715503937486e-307 (prob.: -2.5243706271072766e-29)
25: 6.92260767504386e-310 ± 2.65830637e-316 (prob.: 3.280483651242142e43)
26: 2.63937773e-316 ± 2.37420064e-316 (prob.: 9.1e-322)
27: NaN ± 5.736e-321 (prob.: -454.0452354587469)
28: 7.29114287962383e-304 ± 0.0 (prob.: 2.7528843516212226e41)
29: 2.653874e-316 ± 2.0e-323 (prob.: 3.374368219391306e-76)
30: 6.2e-322 ± 0.0 (prob.: 3.815460340537556e248)
31: 2.5e-323 ± 2.1219957944e-314 (prob.: -2.435594034356285e-156)
32: 6.47e-322 ± 1.3459983968564287e-307 (prob.: -1.4702819925499117e82)
33: NaN ± 2.65830954e-316 (prob.: 1.4402451455707735e41)
34: 2.6605783e-316 ± 2.37420064e-316 (prob.: -1.91871335183198e83)
35: 6.922572414842e-310 ± 5.736e-321 (prob.: 3.6032899820148115e-85)
36: 1.06e-321 ± 0.0 (prob.: 4.2779677e-317)
37: 2.5e-323 ± 1.2e-322 (prob.: 7.70733537814983e249)
38: 1.59e-321 ± 0.0 (prob.: 7.671349735616455e39)
39: NaN ± 2.1219957944e-314 (prob.: -1.8088832901759735e-302)
40: 2.65387955e-316 ± 1.4016252433191087e-307 (prob.: 1.2165775182807046e43)
41: 2.6541428e-316 ± 2.6583127e-316 (prob.: -17.025532314615287)
42: NaN ± 2.37420064e-316 (prob.: 7.406959381198235e6)
43: 5.0e-324 ± 2.65514243e-316 (prob.: 3.373812617795425e42)
44: 2.65387955e-316 ± 0.0 (prob.: -6.187527810972812e-264)
45: 3.626e-321 ± 1.2e-322 (prob.: 1.1823560776595915e51)
46: 2.5e-323 ± 0.0 (prob.: 3.600274376648485e-305)
47: 6.77e-322 ± -2.1219957944e-314 (prob.: -2.524354896707238e-29)
48: 7.01e-321 ± 9.012009175239832e-308 (prob.: -3.305544048687633e307)
49: 2.5e-323 ± 2.65831586e-316 (prob.: -4.111538201221135e233)
50: 6.23e-322 ± 2.37420064e-316 (prob.: 2.4269394740819694e-299)
51: 2.806e-321 ± NaN (prob.: 3.91044036854e-312)
52: 1.0e-323 ± NaN (prob.: 2.401080677393025e-309)
53: 6.9225739581209e-310 ± 1.2e-322 (prob.: 1.8492092661651294e187)
54: 4.07e-321 ± 0.0 (prob.: 4.2779677e-317)
55: 2.5e-323 ± 2.1219957944e-314 (prob.: 2.3536142380232684e70)
56: 1.68e-321 ± 9.568277639866633e-308 (prob.: -2.5580795433476178e-254)
57: 7.455e-321 ± 2.658319e-316 (prob.: 4.55616139313353e-153)
58: 2.5e-323 ± 2.37420064e-316 (prob.: 3.91052634928e-312)
59: 2.653e-321 ± 5.736e-321 (prob.: -6.409558347403985e31)
60: NaN ± 0.0 (prob.: 3.931727997794e-312)
61: 0.0 ± 1.2e-322 (prob.: -3.3053897514481974e307)
62: 0.0 ± 0.0 (prob.: 3.7005615259616e-310)
63: 3.696e-321 ± 2.1219957944e-314 (prob.: 3.181697100895784e107)
64: 2.5e-323 ± 1.0124546104493433e-307 (prob.: -1.5261292110010404e176)
65: 8.4e-322 ± 2.6583222e-316 (prob.: 2.73575862233e-312)
66: 7.08e-321 ± 2.37420064e-316 (prob.: -1.0116223001480086e28)
67: 2.5e-323 ± 5.736e-321 (prob.: 3.0502176066069363e-248)
68: 6.47e-322 ± 0.0 (prob.: 3.3551817223910385e18)
69: NaN ± 1.2e-322 (prob.: -3.1830304566630274e-301)
70: 0.0 ± 0.0 (prob.: 9.916383467466166e-115)
71: 9.54898105934e-313 ± 4.0317920029e-313 (prob.: 1.6491030997209667e-36)
72: 7.525e-321 ± 0.0 (prob.: -1.6171483477000026e-263)
73: 2.5e-323 ± 0.0 (prob.: -1.343059456277364e-244)
74: 2.75e-321 ± 5.0e-324 (prob.: -2.397670127039312e233)
75: 8.38e-321 ± 0.0 (prob.: 3.910517880146e-312)
76: 1.0e-323 ± 0.0 (prob.: 9.444657098335766e-277)
77: 6.9225739581746e-310 ± 5.0e-324 (prob.: 1.255420500133095e58)
78: NaN ± 0.0 (prob.: 5.922912193232405e42)
79: 0.0 ± 0.0 (prob.: 2.797701385396905e-306)
80: 2.65389536e-316 ± 2.1219957944e-314 (prob.: 2.0547715973305232e-113)
81: NaN ± 1.3473081160881192e-307 (prob.: 3.374367888951715e-76)
82: 2.65390484e-316 ± 2.6583289e-316 (prob.: 6.814704098582699e305)
83: 5.0e-324 ± 2.37420064e-316 (prob.: 9.551385419952489e-187)
84: 3.355e-321 ± 2.65514243e-316 (prob.: -2.641182643580031e-254)
85: 2.5e-323 ± 2.121995791e-314 (prob.: -1.4824647955804004e82)
86: 2.9e-322 ± 5.9e-322 (prob.: 3.832089626450007e58)
87: 4.21e-321 ± 0.0 (prob.: 3.600481609082e-311)
88: 2.5e-323 ± 2.1219957944e-314 (prob.: 3.0550225828966323e171)
89: 3.226e-321 ± 1.4029349625507992e-307 (prob.: 1.001091926497764e-309)
90: 8.86e-321 ± 2.65833207e-316 (prob.: -1.4702816322997461e82)
91: 1.0e-323 ± 2.37420064e-316 (prob.: 6.814582050487698e305)
92: 6.92257395817545e-310 ± 2.65514243e-316 (prob.: -7.187538103692136e-264)
93: 2.124e-321 ± 0.0 (prob.: 2.2771441608802432e17)
94: 1.0e-323 ± 5.9e-322 (prob.: -1.522911660876011e178)
95: 6.9225739581205e-310 ± 0.0 (prob.: 3.8149663006622334e248)
96: 1.714e-321 ± 2.1219957944e-314 (prob.: -2.4355940343563013e-156)
97: 1.0e-323 ± 9.025106367556738e-308 (prob.: -1.4702819925499117e82)
98: 6.9225739581143e-310 ± 2.65833523e-316 (prob.: 1.222464430741373e41)
99: NaN ± 2.37420064e-316 (prob.: -1.91871335183198e83)
100: 2.6539064e-316 ± 5.736e-321 (prob.: 1.7935571014896854e-307)
101: 2.54608786e-316 ± 0.0 (prob.: 7.70733537814983e249)
102: 8.94e-322 ± 8.3e-322 (prob.: 7.67134973561646e39)
103: 2.5e-323 ± 0.0 (prob.: -1.8088832901759735e-302)
104: 1.21e-321 ± 4.4e-323 (prob.: 1.2165775182807046e43)
105: 4.84e-322 ± 2.65834116e-316 (prob.: 2.0667980246433124e39)
106: 1.0e-323 ± 3.518913817613768e150 (prob.: -6.793502048450274e117)
107: 6.9225739581117e-310 ± 2.0158960041e-313 (prob.: 7.931253021255816e6)
108: NaN ± 1.5717498880000003e11 (prob.: -1.138910405840611e-244)
109: 0.0 ± NaN (prob.: -4.044353716061486e7)
110: 0.0 ± 2.65833977e-316 (prob.: 2.2774628152410115e17)
111: NaN ± 1.09313506e-316 (prob.: 5.9992613e-317)
112: 2.6495539e-316 ± NaN (prob.: 3.663758358e-314)
113: 2.6393872e-316 ± NaN (prob.: -1.0848291433738378e157)
114: NaN ± 1.43e-321 (prob.: 2.862338169205023e43)
115: 8.0710441471e-313 ± 0.0 (prob.: 6.80564738756529e38)
116: 2.65402974e-316 ± NaN (prob.: 9.1e-322)
117: 1.1e-322 ± 0.0 (prob.: -6.946912723407004e-264)
118: 9.0e-323 ± 2.65508507e-316 (prob.: 3.7005615701563e-310)
119: 0.0 ± 2.65834116e-316 (prob.: 2.3536142380232684e70)
120: 9.63e-322 ± -2.1219957944e-314 (prob.: -2.5580795433476178e-254)
121: 2.5e-323 ± 9.581374832183538e-308 (prob.: 4.55616139313353e-153)
122: 1.39e-321 ± 2.6583447e-316 (prob.: 3.0368990550341976e20)
123: NaN ± 2.37420064e-316 (prob.: 1.5358380217e-314)
124: 2.65391117e-316 ± 5.736e-321 (prob.: 7.56191232e8)
125: 1.29088484e-316 ± 0.0 (prob.: 1.5358313755e-314)
126: NaN ± 8.3e-322 (prob.: -9.877906918534788e86)
127: 6.92260764328774e-310 ± 0.0 (prob.: 3.6032903126412187e-85)
128: 2.65391117e-316 ± 5.0e-324 (prob.: 4.2779677e-317)
129: 3.53e-321 ± 0.0 (prob.: 3.181697100895784e107)
130: 2.5e-323 ± NaN (prob.: -1.5261292110010404e176)
131: 6.23e-322 ± 0.0 (prob.: 4.772874581654e-312)
132: 5.647e-321 ± 0.0 (prob.: -8.306757478905456e-287)
133: 1.0e-323 ± 0.0 (prob.: -2.8248287794355013e-248)
134: 6.92257395814546e-310 ± 2.65834313e-316 (prob.: -9.612394232143579e-210)
135: 3.97e-321 ± 2.65834788e-316 (prob.: -1.2888113561150625e-55)
136: 2.5e-323 ± 2.1219957944e-314 (prob.: 4.8014427793213545e-222)
137: 1.54e-321 ± 1.0137643296810338e-307 (prob.: -1.5988405828341027e288)
138: 7.357e-321 ± 2.65835104e-316 (prob.: 6.805651195692952e38)
139: 2.5e-323 ± 2.3740797e-316 (prob.: -2.4178529375585005e24)
140: 1.645e-321 ± 5.736e-321 (prob.: 5.548414683404104e-134)
141: 6.91e-321 ± 3.2593855349227e-311 (prob.: 2.1988871429459544e23)
142: 2.5e-323 ± 0.0 (prob.: 5.444517870758819e40)
143: 6.23e-322 ± 0.0 (prob.: 6.80564734208483e38)
144: 2.1e-322 ± 2.1219957944e-314 (prob.: 1.32636480396e-313)
145: 1.0e-323 ± 1.0693911761437139e-307 (prob.: 4.460019776714643e43)
146: 6.9225739581046e-310 ± 2.6583542e-316 (prob.: 7.85645652286031e-134)
147: 3.597e-321 ± 2.3740797e-316 (prob.: NaN)
148: 2.5e-323 ± 5.736e-321 (prob.: 4.4600197764552816e43)
149: 7.16e-322 ± 0.0 (prob.: 2.9859795147023507e-294)
150: 1.92e-321 ± 7.0e-323 (prob.: -2.9836763068786495e-254)
151: 1.0e-323 ± 0.0 (prob.: 9.559241001664397e-187)
152: 6.92257395811626e-310 ± 2.1219957944e-314 (prob.: -1.0575046477566869e-174)
153: 4.04e-321 ± 1.1250180226063939e-307 (prob.: -6.946914607817815e-264)
154: 2.5e-323 ± 2.65835736e-316 (prob.: 2.5136223908520635e7)
155: 1.66e-321 ± 2.3740797e-316 (prob.: 1.7190135512946123e-305)
156: 7.426e-321 ± 5.736e-321 (prob.: 4.052916386671515e59)
157: 2.5e-323 ± 6.922586868866e-310 (prob.: -2.73474496784293e101)
158: 2.554e-321 ± 7.0e-323 (prob.: 4.011413794395482e116)
159: 4.45e-321 ± 0.0 (prob.: -9.871886654241323e304)
160: 1.0e-323 ± 2.1219957944e-314 (prob.: 2.61520462356375e-310)
161: 6.92257395813845e-310 ± 1.180644869069074e-307 (prob.: 1.74603514666324e-310)
162: 2.8e-322 ± 2.6583605e-316 (prob.: 1.31145040867355e-310)
163: 2.5e-323 ± 2.3740797e-316 (prob.: -2.574171855273491e237)
164: 2.955e-321 ± 2.65514243e-316 (prob.: 2.28982576157962e-309)
165: NaN ± 0.0 (prob.: 6.485300685404406e62)
166: 2.63937773e-316 ± 2.4e-322 (prob.: 1.2554211708627635e58)
167: 2.65393804e-316 ± 0.0 (prob.: 1.96568360485163e-236)
168: 6.98e-321 ± 2.1219957944e-314 (prob.: -3.4405868452306585e45)
169: 2.5e-323 ± 1.236271715531754e-307 (prob.: 2.474524260229675e-309)
170: 1.89e-321 ± 2.6583637e-316 (prob.: 9.766277746820058e61)
171: NaN ± 2.3740797e-316 (prob.: 1.0132949516125e-311)
172: 2.6539349e-316 ± NaN (prob.: 3.05870091215e-312)
173: 2.6538985e-316 ± NaN (prob.: 1.006505206927293e-309)
174: 9.066e-321 ± 2.4e-322 (prob.: -6.058451752097371e-28)
175: 4.4e-323 ± 0.0 (prob.: 0.0)
176: 2.846e-321 ± NaN (prob.: 1.1306024406498487e-133)
177: NaN ± 1.291898561994434e-307 (prob.: -4.0894643205415667e-94)
178: 0.0 ± 2.65836685e-316 (prob.: 4.1614342915116655e142)
179: 0.0 ± 2.3740797e-316 (prob.: 6.96112474630513e-310)
180: 1.616e-321 ± 2.65514243e-316 (prob.: 2.0879786376472108e39)
181: 1.0e-323 ± 0.0 (prob.: 1.6299224908552438e235)
182: 6.9225739581143e-310 ± 3.26e-322 (prob.: 1.060144534993504e39)
183: 7.94e-321 ± 0.0 (prob.: 1.636583307986998e-294)
184: 1.0e-323 ± 2.1219957944e-314 (prob.: -1.5988411582915197e288)
185: 6.9225739581682e-310 ± 1.347525408457114e-307 (prob.: -2.417853081665927e24)
186: 7.95e-322 ± 2.65837e-316 (prob.: 3.5679823376e-312)
187: 2.5e-323 ± 2.3740797e-316 (prob.: 1.7285349093580439e22)
188: 9.24e-322 ± 5.736e-321 (prob.: 3.9929561232407936e116)
189: 3.325e-321 ± 0.0 (prob.: -1.7864798705873357e305)
190: 2.5e-323 ± 3.26e-322 (prob.: -2.0448303690536636e-53)
191: 0.0 ± 0.0 (prob.: 7.395038019294464e-132)
192: 2.505e-321 ± 2.1219957944e-314 (prob.: 7.316416488079428e42)
193: 1.0e-323 ± 1.403152254919794e-307 (prob.: 8.792267425114694e-77)
194: 6.9225739581205e-310 ± 2.65837317e-316 (prob.: 2.1579965703514174e176)
195: NaN ± 2.3740797e-316 (prob.: 1.5275188223e-314)
196: 2.65397915e-316 ± 5.736e-321 (prob.: 9.34760365878112e-309)
197: 0.0 ± 0.0 (prob.: -2.9836762966860265e-254)
198: 2.915e-321 ± 3.7e-322 (prob.: -1.516142028411315e82)
199: 4.4e-323 ± 0.0 (prob.: 6.8112788132495e305)
200: 0.0 ± 2.121995795e-314 (prob.: -7.187538103692136e-264)
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202: 0.0 ± 2.121995791e-314 (prob.: 5.4799352033703446e60)
203: 2.6539349e-316 ± 2.65837633e-316 (prob.: -5.97027772696097e-264)
204: 8.65e-322 ± 2.3740797e-316 (prob.: -4.993549841827051e-264)
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209: 2.8e-322 ± 2.121995795e-314 (prob.: 3.549551881245e-311)
210: 8.043e-321 ± 9.164982120504031e-72 (prob.: 8.507659131956943e291)
211: 4.4e-323 ± 0.0 (prob.: 5.922912193176821e42)
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213: NaN ± 2.3740797e-316 (prob.: -8.678833657648909e157)
214: 2.6606194e-316 ± 5.736e-321 (prob.: 6.80647443059542e38)
215: 7.6458160843e-313 ± 4.243991582e-314 (prob.: 2.197090375666735e40)
216: 6.813e-321 ± 4.15e-322 (prob.: 9.14e-322)
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219: 3.873e-321 ± 6.006362682493522e-67 (prob.: 1.1019418637607654e49)
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221: 1.344e-321 ± 2.65838345e-316 (prob.: -5.486790798926835e303)
222: 7.26e-321 ± 2.3740797e-316 (prob.: 3.910443950237e-312)
223: 2.5e-323 ± 2.65514243e-316 (prob.: 2.032383823322372e-112)
224: 2.233e-321 ± 0.0 (prob.: 6.806474430550349e38)
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226: 2.65396176e-316 ± 0.0 (prob.: 2.1189700036546345e-255)
227: 5.0e-324 ± 2.121995795e-314 (prob.: 2.3308e-319)
228: 7.702e-321 ± 3.9363298475989545e-62 (prob.: 9.887594027016889e-269)
229: 1.0e-323 ± 2.121995791e-314 (prob.: 1.5475141611856865e-272)
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231: 3.5e-321 ± 2.3740797e-316 (prob.: 3.457788812530143e-305)
232: 2.5e-323 ± 5.736e-321 (prob.: 6.80564733841877e38)
233: 5.8e-322 ± 0.0 (prob.: 2.7976939670950618e-306)
234: 6.71e-321 ± 4.55e-322 (prob.: 7.25033052569437e226)
235: 9.0e-323 ± 0.0 (prob.: -1.5152156910774689e82)
236: 3.61e-321 ± 2.121995795e-314 (prob.: 3.70056122383997e-310)
237: 1.5e-322 ± 2.579713128922451e-57 (prob.: 8.534660437284818e-269)
238: 1.0e-323 ± 2.121995791e-314 (prob.: -2.967195795247298e25)
239: 6.9225739581046e-310 ± 2.65839056e-316 (prob.: -7.336838652606284e24)
240: 3.943e-321 ± 2.3740797e-316 (prob.: 5.108168163857755e58)
241: 2.5e-323 ± 5.736e-321 (prob.: -2.574214514677823e-254)
242: 1.487e-321 ± 0.0 (prob.: 1.0830033332924273e-262)
243: 6.88e-321 ± 4.55e-322 (prob.: 1.2981149782259936e58)
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245: 1.813e-321 ± 2.121995795e-314 (prob.: 1.326791589791763e41)
246: 2.71e-321 ± 1.6906407961706174e-52 (prob.: 4.037845895926e-312)
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249: 6.507e-321 ± 2.3740797e-316 (prob.: 7.11963405132079e6)
250: 1.0e-323 ± 5.736e-321 (prob.: 3.70056122617112e-310)
251: 6.92257395815233e-310 ± 3.60739284464e-313 (prob.: -5.193148633571995e214)
252: 9.24e-321 ± 4.94e-322 (prob.: 2.0109186636539e-310)
253: 4.4e-323 ± 0.0 (prob.: 3.30187624705234e-310)
254: 3.557e-321 ± 2.121995795e-314 (prob.: 8.5896857680344925e9)
255: 7.77e-321 ± 1.1079783521783758e-47 (prob.: 1.938930828983819e-269)
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257: 3.473e-321 ± 2.6583977e-316 (prob.: -1.4550375291559e-37)
258: 7.327e-321 ± 2.3740797e-316 (prob.: 0.0)
259: 2.5e-323 ± 5.736e-321 (prob.: -1.5672779566706535e32)
260: 2.39e-321 ± 0.0 (prob.: 1.5836748933447107e-214)
261: 9.516e-321 ± 4.94e-322 (prob.: 5.076633583331442e-235)
262: 1.0e-323 ± 0.0 (prob.: 4.7281415051728747e24)
263: 6.9225739581797e-310 ± 2.121995795e-314 (prob.: 5.9669667e-317)
264: 9.41e-321 ± 7.261246928836204e-43 (prob.: 3.910523259e-312)
265: 1.0e-323 ± 5.06e-321 (prob.: 7.2138658831220605e19)
266: 6.92257395818133e-310 ± 2.65840123e-316 (prob.: -4.200627699928472e-255)
267: NaN ± 2.3740797e-316 (prob.: -2.2839062067981644e307)
268: 2.6539665e-316 ± 5.736e-321 (prob.: 6.764857844117446e-228)
269: 2.65397283e-316 ± 0.0 (prob.: 3.6617106243476414e-85)
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272: 6.77e-322 ± 4.4e-323 (prob.: -1.5261292110010404e176)
273: 8.285e-321 ± 2.65840756e-316 (prob.: 3.414797275436e-312)
274: 1.0e-323 ± 3.518913817613768e150 (prob.: 8.295220625127514e19)
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279: 2.406e-321 ± 1.09313506e-316 (prob.: -2.557436824896256e-254)
280: 1.0e-323 ± 5.736e-321 (prob.: 5.0789599388022244e60)
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283: 2.6539665e-316 ± 0.0 (prob.: 3.4583210425696284e-305)
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288: 7.66e-322 ± 5.0e-324 (prob.: 3.54936952253e-313)
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311: 2.9e-322 ± 1.0990424095911335e248 (prob.: 2.9710123175433205e41)
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313: 2.5e-323 ± 0.0 (prob.: 6.805699031678199e38)
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315: 7.16e-321 ± 2.65842416e-316 (prob.: 6.934476568595418e38)
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329: 6.3e-322 ± 2.65842416e-316 (prob.: 3.910503372496e-312)
330: 5.143e-321 ± 8.544604122911922e-306 (prob.: 6.514860628703381e-152)
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333: 7.673e-321 ± 1.1392890965547699e-304 (prob.: 3.4986602011362645e28)
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402: 9.18e-321 ± 2.36276915e-316 (prob.: 5.040432065936094e180)
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411: 3.95e-322 ± 1.5717498880000003e11 (prob.: 7.201718609367876e256)
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413: 0.0 ± 2.65845953e-316 (prob.: 1.959073646639458e166)
414: 4.19e-321 ± 1.09313506e-316 (prob.: 5.6114261634438495e45)
415: 2.5e-323 ± 2.65514243e-316 (prob.: 5.6114255658010783e45)
416: 3.32e-321 ± 0.0 (prob.: 2.769909939905081e276)
417: 7.574e-321 ± 2.357e-321 (prob.: 1.4187372606331283e-22)
418: 2.5e-323 ± 0.0 (prob.: 8.42961547227883e252)
419: 2.89e-321 ± 1.0e-323 (prob.: 8.42961547227883e252)
420: 7.846e-321 ± 0.0 (prob.: 1.4830141166287497e185)
421: 1.0e-323 ± 0.0 (prob.: 6.650347296484395e-48)
422: 6.9225739581682e-310 ± 2.6584609e-316 (prob.: 1.483014116628748e185)
423: NaN ± 5.0e-324 (prob.: 6.650347296484395e-48)
424: 2.6540329e-316 ± 0.0 (prob.: 1.4830141159407832e185)
425: 0.0 ± NaN (prob.: 3.856749093434569e255)
426: 5.934e-321 ± 6.8385555700151894e246 (prob.: 2.4935857192996842e243)
427: 1.0e-323 ± 0.0 (prob.: 1.0647842856834288e248)
428: 6.92257395814546e-310 ± 1.2644989894328385e-306 (prob.: 2.1669592932615893e233)
429: 4.64e-322 ± 2.6584629e-316 (prob.: 1.0647842856245993e248)
430: 2.5e-323 ± 2.65846447e-316 (prob.: 2.1669592932615893e233)
431: 2.8e-322 ± 4.330298393201253e-294 (prob.: 1.2224593665383673e224)
432: 9.32e-321 ± 1.7950456676585938e-52 (prob.: 2.596196531554721e161)
433: 1.0e-323 ± 2.65844946e-316 (prob.: 1.4830141166287657e185)
434: 6.92257395818133e-310 ± 2.65846764e-316 (prob.: 1.5263443127830439e-307)
435: NaN ± 1.09313506e-316 (prob.: 9.041152200436188e271)
436: 2.6495286e-316 ± 2.6486666e-316 (prob.: 2.6493744805659334e180)
437: 2.6540811e-316 ± 0.0 (prob.: 1.1949010660918068e190)
438: NaN ± 0.0 (prob.: 6.9673097154140004e252)
439: 8.28578224657e-313 ± 0.0 (prob.: 1.5237477823033522e-307)
440: 2.6495286e-316 ± 2.121995795e-314 (prob.: 9.041152200436206e271)
441: 9.0e-323 ± 1.176401128756736e-47 (prob.: 6.017436343505729e175)
442: 2.5e-323 ± 2.6584621e-316 (prob.: 1.6264335779813884e-307)
443: 3.0e-323 ± 2.6584712e-316 (prob.: 1.14448344427235e243)
444: 9.44e-322 ± 1.09313506e-316 (prob.: 1.1444834447966714e243)
445: 2.5e-323 ± 6.6312942e-316 (prob.: 1.6262162864929016e-307)
446: 1.344e-321 ± 0.0 (prob.: 4.72623718341189e-10)
447: NaN ± 0.0 (prob.: 6.967697761092746e252)
448: 2.6495286e-316 ± 0.0 (prob.: 5.069131515291451e173)
449: 2.6495444e-316 ± 6.8992449151658e-310 (prob.: 2.587422588006458e161)
450: 6.413e-321 ± 7.709662437420145e-43 (prob.: 6.46336673856702e170)
451: 1.0e-323 ± 0.0 (prob.: 1.240409630014435e224)
452: 6.92257395815233e-310 ± 2.65847475e-316 (prob.: 7.762479214023661e168)
453: NaN ± 1.09313506e-316 (prob.: 3.5961496524931415e252)
454: 2.67087224e-316 ± 2.65514243e-316 (prob.: 7.35980127980769e223)
455: 5.0944477081e-313 ± 0.0 (prob.: 6.9390590756718125e252)
456: 5.7e-322 ± 4.0e-323 (prob.: 6.939059075669884e252)
457: 2.5e-323 ± 0.0 (prob.: 9.076817706933106e223)
458: 5.8e-322 ± 2.121995795e-314 (prob.: 3.674101853686185e228)
459: 9.01e-321 ± 5.052604374987666e-38 (prob.: 5.018409772638668e173)
460: 4.4e-323 ± 0.0 (prob.: 2.587422588006458e161)
461: 2.61e-321 ± 2.6584783e-316 (prob.: 7.355303208489294e223)
462: 1.013e-321 ± 1.09313506e-316 (prob.: 8.389436687858174e-148)
463: 2.5e-323 ± 2.65514243e-316 (prob.: 1.2480553473853193e243)
464: 1.487e-321 ± 0.0 (prob.: 6.040989884666085e151)
465: 8.19e-321 ± 4.0e-323 (prob.: 6.9673097012821825e252)
466: 1.0e-323 ± 0.0 (prob.: 1.9494851243466997e233)
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468: NaN ± 3.311274803191917e-33 (prob.: 1.2146041393540103e224)
469: 2.65409377e-316 ± 1.7627890677572205e214 (prob.: 9.076801800631216e223)
470: 2.67087857e-316 ± 2.65848187e-316 (prob.: 1.0647658574058744e248)
471: 2.31e-321 ± 1.09313506e-316 (prob.: 2.994891665351643e262)
472: 1.0e-323 ± 2.939330637272588e203 (prob.: 4.903518142212659e252)
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474: 3.577e-321 ± 6.0e-323 (prob.: 3.9057664459552914e233)
475: 2.5e-323 ± 0.0 (prob.: 3.904045013584429e257)
476: 6.77e-322 ± 1.53e-322 (prob.: 1.3047195848448898e243)
477: 4.02e-321 ± 2.65849017e-316 (prob.: 1.2353522837293071e-307)
478: 2.5e-323 ± 8.747240985390595e189 (prob.: 3.9041411772348863e257)
479: 1.645e-321 ± 3.7540955791448835e199 (prob.: 3.9415351821638107e180)
480: 6.14e-321 ± 6.011247068092252e175 (prob.: 5.298748636390525e180)
481: 1.0e-323 ± 1.4022328231173338e-307 (prob.: 7.047681563092273e-71)
482: 6.92257395814586e-310 ± 2.1219958063e-314 (prob.: 6.189109960726547e223)
483: 6.96e-321 ± 8.747240985390595e189 (prob.: 6.967641817690062e252)
484: 2.5e-323 ± 3.7540955791448835e199 (prob.: 4.837396588382759e-308)
485: 1.833e-321 ± 6.011247068092252e175 (prob.: 3.030777661262795e180)
486: NaN ± 1.4022328231173338e-307 (prob.: 7.337226921908853e223)
487: 2.6607348e-316 ± 2.6584878e-316 (prob.: 7.989240024239726e-148)
488: 5.0e-324 ± 2.6602923e-316 (prob.: 3.965236284216975e202)
489: 3.646e-321 ± 8.7129147185374e-311 (prob.: 2.8736032887466733e257)
490: 2.5e-323 ± 1.1e-322 (prob.: 1.188629769322206e-47)
491: 7.16e-322 ± 0.0 (prob.: 1.5612491354795672e195)
492: 7.03e-321 ± 2.3768518e-316 (prob.: 1.549719707907355e-303)
493: 2.5e-323 ± 2.0316e-320 (prob.: 1.342350584179393e-197)
494: 6.47e-322 ± 2.0316e-320 (prob.: 5.901808209480216e-222)
495: 4.09e-321 ± 6.9225868688661e-310 (prob.: 1.549427410893787e-303)
496: 2.5e-323 ± 0.0 (prob.: 3.5723466865654266e-241)
497: 1.72e-321 ± 2.65508507e-316 (prob.: 1.3714551888301e-310)
498: 7.406e-321 ± 2.65849017e-316 (prob.: 5.724323068542413e-5)
499: 2.5e-323 ± 2.121995795e-314 (prob.: 5.4711896096783476e-303)
500: 2.46e-321 ± 1.5711886604854386e-76 (prob.: 3.610637286676916e-239)
501: 7.475e-321 ± 1.09328743e-316 (prob.: 4.459216490394366e-187)
502: 2.5e-323 ± 2.6584945e-316 (prob.: 2.0253050827473594e-226)
503: 2.663e-321 ± 1.09313506e-316 (prob.: 1.578109901411359e-308)
504: NaN ± 2.37020647e-316 (prob.: 1.5561958026206985e-303)
505: 9.5547833916e-313 ± 0.0 (prob.: 2.9051062674655e-311)
506: 2.6495808e-316 ± 6.0e-323 (prob.: 5.901776185059399e-222)
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508: 0.0 ± 1.53e-322 (prob.: 1.983704872889255e-279)
509: 5.52299138875e-313 ± 2.6585028e-316 (prob.: 8.280421829307663e-169)
510: NaN ± 8.747240985390595e189 (prob.: 8.826164305539649e120)
511: 0.0 ± 3.7540955791448835e199 (prob.: 3.0822180750329423e-216)
512: 0.0 ± 6.011247068092252e175 (prob.: 6.1644918045714e-311)
513: 3.66e-322 ± 9.574353437848884e-308 (prob.: 2.298350945717234e116)
514: 3.0e-323 ± 2.1219958063e-314 (prob.: 4.0394651397873055e-308)
515: 0.0 ± 8.747240985390595e189 (prob.: 6.736793044213476e-283)
516: 6.69e-321 ± 3.7540955791448835e199 (prob.: 2.052268889948104e-289)
517: 2.5e-323 ± 6.011247068092252e175 (prob.: 1.43412963536597e-309)
518: 3.0e-323 ± 9.574353437848884e-308 (prob.: 8.289046e-317)
519: NaN ± 2.65850044e-316 (prob.: 0.0)
520: 0.0 ± 2.6602789e-316 (prob.: 0.0)
521: 1.082383634313e-312 ± 8.712940880839e-311 (prob.: 1.086461857496e-311)
522: 5.46e-321 ± 1.14e-322 (prob.: 8.455280662327365e-307)
523: 1.0e-323 ± 0.0 (prob.: 7.21179386e-315)
524: 6.92257395814546e-310 ± 2.65947237e-316 (prob.: 8.412328508072983e62)
525: 5.05e-321 ± 1.0e-323 (prob.: 3.3156185e-316)
526: 1.0e-323 ± 0.0 (prob.: 7.291122019665813e-304)
527: 6.92257395814097e-310 ± 2.65508507e-316 (prob.: 0.0)
528: 8.45e-322 ± 2.6585028e-316 (prob.: 0.0)
529: 2.5e-323 ± 2.121995795e-314 (prob.: 2.297866802120474e-309)
530: 1.047e-321 ± 1.029694200535737e-71 (prob.: 3.794e-321)
531: 3.374e-321 ± 0.0 (prob.: 2.48995173e-316)
532: 9.0e-323 ± 2.65850637e-316 (prob.: 1.6318147632523e-311)
533: 2.065e-321 ± 1.09313506e-316 (prob.: 3.327232628921146e-294)
534: NaN ± 2.17593195e-316 (prob.: 0.0)
535: 2.6542076e-316 ± 0.0 (prob.: 3.8e-321)
536: 2.6540424e-316 ± 2.03e-322 (prob.: 2.48995173e-316)
537: NaN ± 0.0 (prob.: 1.6318147632523e-311)
538: 2.65407796e-316 ± 2.121995795e-314 (prob.: 3.327232628921146e-294)
539: 2.51272025e-316 ± 6.748203912631006e-67 (prob.: 0.0)
540: 4.264e-321 ± 0.0 (prob.: 3.8e-321)
541: 1.0e-323 ± 2.65850993e-316 (prob.: 2.48995173e-316)
542: 6.92257395813845e-310 ± 1.09313506e-316 (prob.: 1.6318147632523e-311)
543: 6.0e-323 ± 2.32487575e-316 (prob.: 3.327232628921146e-294)
544: 2.5e-323 ± 0.0 (prob.: 0.0)
545: 0.0 ± 2.03e-322 (prob.: 3.8e-321)
546: 9.14e-322 ± 0.0 (prob.: 3.31885633e-316)
547: 2.5e-323 ± 2.121995795e-314 (prob.: 8.976042195783e-312)
548: 1.275e-321 ± 4.422502916181856e-62 (prob.: 1.0878e-319)
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550: 2.6540843e-316 ± 2.6585135e-316 (prob.: 0.0)
551: 0.0 ± 1.09313506e-316 (prob.: 8.609939084820409e-283)
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553: 6.922572414842e-310 ± 0.0 (prob.: 2.673714696616e-312)
554: 2.6540843e-316 ± 2.6e-322 (prob.: 5.969848494e-315)
555: 3.48e-321 ± 0.0 (prob.: 5.075883674631299e-116)
556: 2.5e-323 ± 2.121995795e-314 (prob.: 1.6701872474863329e-307)
557: 5.4e-322 ± 2.898331511148941e-57 (prob.: 0.0)
558: 4.743e-321 ± 0.0 (prob.: 3.001640056494754e-53)
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560: 6.92257395813845e-310 ± 1.09313506e-316 (prob.: 6.675221575521604e-308)
561: 1.3e-322 ± 5.736e-321 (prob.: 2.28306109973505e-310)
562: 2.5e-323 ± 0.0 (prob.: 0.0)
563: 2.8e-322 ± 2.6e-322 (prob.: 2.6920997000477834e-295)
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574: 2.5e-323 ± 2.121995795e-314 (prob.: 5.969848494e-315)
575: 6.47e-322 ± 1.2448239053350962e-47 (prob.: 3.785766995733679e-270)
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577: 2.5e-323 ± 2.65852416e-316 (prob.: 0.0)
578: 6.47e-322 ± 1.09313506e-316 (prob.: 3.001640055522408e-53)
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580: 2.5e-323 ± 0.0 (prob.: 1.1125369292536007e-308)
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590: 2.6541001e-316 ± 8.45e-322 (prob.: 1.1709557299830196e-258)
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601: 2.6606447e-316 ± 2.121995795e-314 (prob.: 5.0e-324)
602: 7.29114287962383e-304 ± 3.5038677976306406e-33 (prob.: 0.0)
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604: 0.0 ± 2.65853483e-316 (prob.: 9.71373e-319)
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615: 6.66e-321 ± 1.657550346036383e-76 (prob.: 6.374276419e-314)
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626: 2.6495539e-316 ± 2.65854353e-316 (prob.: 1.0374e-319)
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633: 6.73e-321 ± 7.119124527699748e-67 (prob.: 5.14115283e-315)
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652: 2.5e-323 ± 2.49966545e-316 (prob.: 5.340177260417283e-307)
653: 6.77e-322 ± 2.6619435e-316 (prob.: 1.3449746192255995e-284)
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656: 1.21e-321 ± 2.358184e-316 (prob.: 6.79876953e-315)
657: 7.653e-321 ± 2.6585558e-316 (prob.: 9.526820527087379e139)
658: 2.5e-323 ± 1.09313506e-316 (prob.: 2.6724177526825157e-307)
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661: 2.5e-323 ± 1.43e-321 (prob.: 7.845e-320)
662: 1.78e-321 ± 0.0 (prob.: 4.345847379897e-311)
663: 3.893e-321 ± 2.121995795e-314 (prob.: 2.82586279543075e-310)
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665: 1.39e-321 ± 2.2746308e-316 (prob.: 8.315176593829998e-275)
666: 2.22e-321 ± 2.65855934e-316 (prob.: 2.08e-322)
667: 1.0e-323 ± 1.09313506e-316 (prob.: 1.69759663277e-313)
668: 6.9225739581205e-310 ± 5.736e-321 (prob.: 4.075359992414678e231)
669: 1.81e-321 ± 0.0 (prob.: 0.0)
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675: 6.047e-321 ± 1.69759663277e-313 (prob.: 1.0116008175e-314)
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682: 2.6709513e-316 ± 0.0 (prob.: 3.232436188377434e-309)
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712: 2.6541317e-316 ± 2.121995806e-314 (prob.: 1.9494738465000217e106)
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921: 1.44283413e-316 ± 2.46e-321 (prob.: 6.011247068092252e175)
922: 0.0 ± 0.0 (prob.: 3.600811008269014e228)
923: NaN ± 2.1219957984e-314 (prob.: 3.232432393236579e-58)
924: 1.2989658e-316 ± 5.4948024486170185e247 (prob.: 1.4187372606270233e-22)
925: 2.65401393e-316 ± 1.068297078288979e-307 (prob.: 1.314618832418806e-309)
926: 2.6541728e-316 ± 2.6586621e-316 (prob.: -3.051757812500347e-5)
927: 6.9226076492734e-310 ± 2.5245626e-316 (prob.: 1.392347375773323e188)
928: 2.63937773e-316 ± 2.66161824e-316 (prob.: 1.1436551893983212e243)
929: 2.6607364e-316 ± 0.0 (prob.: 3.649852017736e-312)
930: 5.0e-324 ± 2.554e-321 (prob.: 7.547927717726013e168)
931: 0.0 ± 0.0 (prob.: 3.5961496524931415e252)
932: 0.0 ± 2.1219957984e-314 (prob.: 7.35980127980769e223)
933: 7.8522133312e-313 ± 5.4948024486170185e247 (prob.: 5.727783173530722e250)
934: 2.65401393e-316 ± 1.123923924751659e-307 (prob.: 1.5128331476963709e-307)
935: 1.0927325e-316 ± 2.65866566e-316 (prob.: 1.5612491345412894e195)
936: 2.6607285e-316 ± 2.5245626e-316 (prob.: 3.91130337284277e-310)
937: 9.54898105934e-313 ± 5.736e-321 (prob.: 1.194901067533223e190)
938: 2.65401393e-316 ± 0.0 (prob.: 5.340338589970714e-306)
939: 2.66073164e-316 ± 2.653e-321 (prob.: 5.298748883756438e180)
940: 1.09271353e-316 ± 0.0 (prob.: 1.5091816171729793e-307)
941: 2.65402974e-316 ± 2.1219957984e-314 (prob.: 9.757629699716533e199)
942: 2.65403923e-316 ± 5.4948024486170185e247 (prob.: 7.231742431588773e-308)
943: 6.9226076977029e-310 ± 1.179550771214339e-307 (prob.: 8.544605422302781e-306)
944: 2.63937773e-316 ± 2.6586692e-316 (prob.: 1.112587211397041e-307)
945: 1.09274515e-316 ± 2.5245626e-316 (prob.: 1.2817069036603297e-305)
946: 8.487983172e-314 ± 2.66161824e-316 (prob.: 1.248055347385308e243)
947: 0.0 ± 9.54898105934e-313 (prob.: 6.040989884666085e151)
948: 0.0 ± 2.663e-321 (prob.: 2.3141574667050853e-306)
949: 2.6421342e-316 ± 0.0 (prob.: 1.1449046184321006e243)
950: 2.67068173e-316 ± NaN (prob.: 3.75376095947388e255)
951: 0.0 ± 5.4948024486170185e247 (prob.: 3.6714325723525816e228)
952: 6.92260599319223e-310 ± 1.235177617677019e-307 (prob.: -4.333983267504073e96)
953: 2.64950963e-316 ± 2.65867277e-316 (prob.: 1.4187372606270233e-22)
954: 2.6539254e-316 ± 2.5245626e-316 (prob.: 3.6741005383186974e228)
955: 0.0 ± NaN (prob.: 3.2297724175009e-310)
956: 0.0 ± NaN (prob.: 4.778309975944753e-299)
957: -5.7293886356e-313 ± 2.68e-321 (prob.: 3.69397027291235e-310)
958: 2.6539254e-316 ± 0.0 (prob.: 7.6052329148195e-311)
959: 0.0 ± 2.1219957984e-314 (prob.: 1.5177100720515234e82)
960: 0.0 ± 5.4948024486170185e247 (prob.: 2.999393627791263e-241)
961: 2.6540329e-316 ± 1.290804464139699e-307 (prob.: 1.6578092e-316)
962: 2.6538748e-316 ± 2.65867633e-316 (prob.: 8.53745e-319)
963: 6.9226076492734e-310 ± 2.5245626e-316 (prob.: 1.086461846745e-311)
964: 2.63937773e-316 ± 5.736e-321 (prob.: 5.827199379e-314)
965: 1.0927309e-316 ± 0.0 (prob.: 0.0)
966: 5.0e-324 ± 2.75e-321 (prob.: 1.0e-322)
967: 0.0 ± 0.0 (prob.: 1.500947214415929e-303)
968: 0.0 ± 2.1219957984e-314 (prob.: 8.4886485694e-312)
969: 2.6605372e-316 ± 5.4948024486170185e247 (prob.: 5.9415882169e-313)
970: 2.6542503e-316 ± 1.3464313106023791e-307 (prob.: 0.0)
971: 0.0 ± 2.6586799e-316 (prob.: 4.9e-322)
972: 0.0 ± 2.5245626e-316 (prob.: 1.436826840724502e-298)
973: 5.0927898983e-313 ± 2.65514243e-316 (prob.: 5.445839311591111e-240)
974: 2.6542503e-316 ± 0.0 (prob.: 1.33087048e-315)
975: 0.0 ± 2.83e-321 (prob.: 1.61271680127e-312)
976: 0.0 ± 0.0 (prob.: 0.0)
977: 2.65403923e-316 ± 2.1219957984e-314 (prob.: 1.43e-322)
978: 2.6706659e-316 ± 5.4948024486170185e247 (prob.: 1.330862654e-315)
979: 6.9226076549935e-310 ± 1.4020581570650592e-307 (prob.: 2.29175545446e-312)
980: 2.63937773e-316 ± 2.65868344e-316 (prob.: 0.0)
981: 2.6542598e-316 ± 2.5245626e-316 (prob.: 2.09e-321)
982: 2.121995792e-314 ± 2.65514243e-316 (prob.: 8.700263573382166e-245)
983: 0.0 ± 8.70018274296e-313 (prob.: 6.246185691699477e-282)
984: 0.0 ± 2.89e-321 (prob.: 2.94979236e-316)
985: 2.48281796589e-312 ± 0.0 (prob.: 3.310313434044e-312)
986: 2.6542566e-316 ± 2.1219957984e-314 (prob.: 0.0)
987: 2.6606779e-316 ± 3.839447023354114e151 (prob.: 2.9e-322)
988: 2.6607095e-316 ± 1.2488653161816302e-307 (prob.: 1.330862654e-315)
989: 7.63918484747e-313 ± 2.658687e-316 (prob.: 3.98935208723e-312)
990: 2.6542566e-316 ± 2.666697e-316 (prob.: 0.0)
991: 2.6541934e-316 ± 5.736e-321 (prob.: 2.19e-321)
992: 2.67072126e-316 ± 8.487983164e-314 (prob.: 8.700263573382166e-245)
993: 2.670824e-316 ± 2.055e-321 (prob.: 6.246185691700064e-282)
994: 2.6708691e-316 ± 0.0 (prob.: 2.94979236e-316)
995: 6.9226076549334e-310 ± 2.1219957984e-314 (prob.: 5.007910066816e-312)
996: 2.63937773e-316 ± 3.839447023354114e151 (prob.: 0.0)
997: 2.6606613e-316 ± 1.3044921626443102e-307 (prob.: 3.26e-322)
998: 7.29114287962383e-304 ± 2.65869056e-316 (prob.: 1.330862654e-315)
999: 2.6606775e-316 ± 2.666697e-316 (prob.: 5.686948720004e-312)
1000: 0.0 ± 5.736e-321 (prob.: 0.0)
1001: NaN ± 0.0 (prob.: 4.24e-321)
1002: 1.2949417e-316 ± 2.29e-321 (prob.: 8.700263573382166e-245)
1003: 0.0 ± 0.0 (prob.: 6.246185691699477e-282)
1004: 2.66987067e-316 ± 2.1219957984e-314 (prob.: 2.94979236e-316)
1005: 4.063e-320 ± 3.839447023354114e151 (prob.: 6.705506699707e-312)
1006: 7.1e-322 ± 1.3601190091069903e-307 (prob.: 0.0)
1007: 1.594384779444706e-72 ± 9.54898105934e-313 (prob.: 5.24e-322)
1008: 2.523405350389384e136 ± 1.2574e-320 (prob.: 394128.26567938924)
1009: -3.3070034733856004e16 ± 6.9226078207703e-310 (prob.: 1.1689144969860864e34)
1010: 2.2924425029194104e43 ± 6.9226078207703e-310 (prob.: 1.1115234256981195e-38)
1011: -5.956198370821044e-264 ± 2.6586953e-316 (prob.: 1.74136880569965e-310)
1012: -9.317083048487885e-33 ± 2.6586953e-316 (prob.: 7.89382434261e-312)
1013: 0.0 ± 2.66193163e-316 (prob.: 0.0)
1014: -4.2005681585549365e36 ± 1.95521855e-316 (prob.: 7.4e-322)
1015: 1.4548796656779105e234 ± 2.66193163e-316 (prob.: 394128.51567938924)
1016: -5.209771597732987e232 ± 1.95521855e-316 (prob.: -3.8453073678603535e-241)
1017: 1.00107273434578e-309 ± 2.66193163e-316 (prob.: 8.28464e-319)
1018: 2.426485408108369e-300 ± 1.95521855e-316 (prob.: 8.91238232227e-312)
1019: -1.5176241665335837e82 ± 2.66193163e-316 (prob.: 0.0)
1020: 6.9225937398089e-310 ± 1.95521855e-316 (prob.: 2.02e-321)
1021: 0.0 ± 2.66193163e-316 (prob.: 8.700263573382166e-245)
1022: 0.0 ± 1.95521855e-316 (prob.: 6.246185691699477e-282)
1023: 7.1e-322 ± 2.66193163e-316 (prob.: 2.94979236e-316)
1024: 7.95e-322 ± 1.95521855e-316 (prob.: 9.930940301935e-312)
1025: 1.09318625e-316 ± 2.66193795e-316 (prob.: 0.0)
Integrand evaluations: 2
Number of subregions: 124
Note: Dimension out of range
jzhan039
commented
4 years ago @giordano Yeah, that's what I got. Any suggestions? Thanks.
giordano
commented
4 years ago I managed to reproduce the issue with the C library (there are a lot of useless macros here, I just used the benchmark.c file):
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "cuba.h"
#define NDIM 2
#define NCOMP 1025
#define USERDATA NULL
#define NVEC 1
#define EPSREL 1e-8
#define EPSABS 1e-8
#define VERBOSE 0
#define LAST 4
#define SEED 0
#define MINEVAL 0
#define MAXEVAL 1000000
#define NSTART 1000
#define NINCREASE 500
#define NBATCH 1000
#define GRIDNO 0
#define STATEFILE NULL
#define SPIN NULL
#define NNEW 1000
#define NMIN 2
#define FLATNESS 25.0
#define KEY1 47
#define KEY2 1
#define KEY3 1
#define MAXPASS 5
#define BORDER 0.
#define MAXCHISQ 10.
#define MINDEVIATION .25
#define NGIVEN 0
#define LDXGIVEN NDIM
#define NEXTRA 0
#define KEY 0
static int Integrand(const int *ndim, const double xx[],
const int *ncomp, double ff[], void *userdata) {
#define x xx[0]
#define y xx[1]
for (int i =0; i < NCOMP; i++)
{
ff[i] = x;
}
return 0;
}
int main() {
int comp, nregions, fail;
long long int neval;
double integral[NCOMP], error[NCOMP], prob[NCOMP];
llCuhre(NDIM, NCOMP, Integrand, USERDATA, NVEC,
EPSREL, EPSABS, VERBOSE | LAST,
MINEVAL, MAXEVAL, KEY,
STATEFILE, SPIN,
&nregions, &neval, &fail, integral, error, prob);
for (int i = 0; i < NCOMP; i++)
{
printf("integral[%04d] = %g\n", i, integral[i]);
}
return 0;
}It prints just a bunch of zeros:
integral[0000] = 0
integral[0001] = 0
integral[0002] = 0
integral[0003] = 0
integral[0004] = 0
integral[0005] = 0
integral[0006] = 0
integral[0007] = 0
integral[0008] = 0
integral[0009] = 0
integral[0010] = 0
integral[0011] = 0
integral[0012] = 0
integral[0013] = 0
integral[0014] = 0
integral[0015] = 0
integral[0016] = 0
integral[0017] = 0
integral[0018] = 0
integral[0019] = 0
integral[0020] = 0
[...]I'd suggest you to write to the author of the C library, you can find his contact here: http://wwwth.mpp.mpg.de/members/hahn/. With a quick look at the documentation I didn't find any reference to this issue, but maybe I'm missing something.
jzhan039
commented
4 years ago OK, I just wrote to him. I'm recently using Cubature.jl library, and it doesn't have this issue.
giordano
commented
4 years ago I've just found that configure script of Cuba has the following option:
--with-maxcomp=N the maximum number of components of the integrand,
if variable-size array are not supportedOk, I had the time to look into the issue. The configure option I pointed out above is only for when variable-size arrays are not supported, but that's not the case for our builds, which show in the build logs
checking for variable-size arrays... yesSo I think this is truly an upstream bug, where variable-size arrays are supported but the library returns bogus results when ncomp is "too large".
If anything, Cuba is correctly reporting that it failed to solve the integral
Note: Dimension out of rangeOne can check that the fail field is non-zero when ncomp is larger than 1024:
julia> using Cuba
julia> function integrand(x, f)
for i in eachindex(f)
f[i] = x[1]
end
end
integrand (generic function with 1 method)
julia> cuhre(integrand, 2, 1025).fail
-2
julia> cuhre(integrand, 2, 1024).fail
0
Hi Giordano,
I found that when the number of components of f is greater than 1024, cuhre fails to give the correct answer. Is this the limitation of the algorithm? Or is there some keyword to tune the maximum number of components? Thanks.
Jin