Method->{"ParallelBestQuality",Method->{"Automatic"}}]
In[]:=
ProductLog[-x]
In[]:=
Timing[​​MKB-Quiet[NIntegrate[​​Exp[PiIx](
1/x
x
-1),{x,1,​​InfinityI},WorkingPrecision1000,Method"Trapezoidal"]]]
Out[]=
{1.75,0.×
-1002
10
+0.×
-1002
10
}
In[]:=
ClearSystemCache[];Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision1000,Method"Trapezoidal"])&[x]]]
Out[]=
{1.82813,0.×
-1001
10
+0.×
-1001
10
}
In[]:=
Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision1000,Method"Trapezoidal"])&[x]]]
Out[]=
{1.64063,0.×
-1001
10
+0.×
-1001
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision2000,Method"Trapezoidal",​​MaxRecursion10]]]
Out[]=
{11.4688,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
ClearSystemCache[];Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision2000,Method"Trapezoidal",MaxRecursion10])&[x]]]
Out[]=
{11.5469,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision2000,Method"Trapezoidal",MaxRecursion10])&[x]]]
Out[]=
{11.1094,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision2000,Method"Trapezoidal",​​MaxRecursion10]]]
Out[]=
{11.0313,0.×
-2001
10
+0.×
-2001
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision3000,Method"Trapezoidal",​​MaxRecursion11]]]
Out[]=
{48.2344,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision3000,Method"Trapezoidal",​​MaxRecursion11]]]
Out[]=
{47.2969,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
ClearSystemCache[];Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision3000,Method"Trapezoidal",MaxRecursion11])&[x]]]
Out[]=
{48.4844,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision3000,Method"Trapezoidal",MaxRecursion11])&[x]]]
Out[]=
{47.3125,0.×
-3001
10
+0.×
-3001
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision4000,Method"Trapezoidal",​​MaxRecursion11]]]
Out[]=
{84.4688,0.×
-4001
10
+0.×
-4001
10
}
In[]:=
Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision4000,Method"Trapezoidal",​​MaxRecursion11]]]
{95.421875`,0``4001.220221114951+0``4001.220221114951}
In[]:=
ClearSystemCache[];Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision4000,Method"Trapezoidal",MaxRecursion11])&[x]]]
Out[]=
{84.4219,0.×
-4001
10
+0.×
-4001
10
}
In[]:=
Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision4000,Method"Trapezoidal",MaxRecursion11])&[x]]]
Out[]=
{83.4688,0.×
-4001
10
+0.×
-4001
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision5000,Method"Trapezoidal",​​MaxRecursion12]]]
Out[]=
{254.375,0.×
-5001
10
+0.×
-5001
10
}
In[]:=
Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision5000,Method"Trapezoidal",​​MaxRecursion12]]]
Out[]=
{252.234,0.×
-5001
10
+0.×
-5001
10
}
{253.265625`,0``5000.579416043584+0``5000.579416043584}
{289.9375`,0``5001.2202211149515+0``5001.2202211149515}
In[]:=
ClearSystemCache[];Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision5000,Method"Trapezoidal",MaxRecursion12])&[x]]]​​
Out[]=
{253.703,0.×
-5001
10
+0.×
-5001
10
}
In[]:=
Timing[MKB-Quiet[I/Pi+(NIntegrate[Exp[PiI#+Log[#]/#],{#,1,InfinityI},WorkingPrecision5000,Method"Trapezoidal",MaxRecursion12])&[x]]]
Out[]=
{251.844,0.×
-5001
10
+0.×
-5001
10
}
In[]:=
ClearSystemCache[];Timing[​​MKB-Quiet[I/Pi+NIntegrate[​​Exp[PiIx+Log[x]/x],{x,1,​​InfinityI},WorkingPrecision10000,Method"Trapezoidal",​​MaxRecursion13]]]
Out[]=
{1926.03,0.×
-10001
10
+0.×
-10001
10
}
{2130.171875`,0``10001.22022111495+0``10001.22022111495}
{2204.640625`,0``10001.22022111495+0``10001.22022111495}