SDExpandAsy returning nans when pushing the expansion to 2nd order.
*Created by: vshtabov*
Hi,
I’m using FIESTA with the following options
```
SetOptions[FIESTA, "NumberOfSubkernels" -> 4, "NumberOfLinks" -> 4,
"ComplexMode" -> True, "ReturnErrorWithBrackets" -> True,
"Integrator" -> "quasiMonteCarlo", "Precision" -> 14];
```
When doing asymptotic expansion of one 2-loop on-shell SE-type integral, the expansion up to 1st order
\(expand\_degree\) works fine. However, if I set expand\_degree to 2, I get a weird output full of nans.
This works:
```
SDExpandAsy[
UF[{p1, p3}, {m2^2 - (p1)^2, m2^2 - (p1 + q)^2, m1^2 - (q + p3)^2,
m2^2 - (p1 - p3)^2}, {q^2 -> m1^2, m1 -> 2.76}], {1, 1, 1,
1}, 1, 1 ExpandVar -> m2, RegVar -> la, ExpandResult -> True]
(*(-7.22160487162011 - 3.33298684862356I) + ep((14.89916567208156 + 4.45428944363231I) + 1.45242586^-6pm[19]) + 2.1915646^-7pm[20] + ((0.46953864577542 + 3.1415926392249I) + 1.856227*^-8pm[21])/ep +
((0.5 - 1.^-14I) + 1.^-14*pm[22])/ep^2*)
```
This doesn’t:
```
SDExpandAsy[
UF[{p1, p3}, {m2^2 - (p1)^2, m2^2 - (p1 + q)^2, m1^2 - (q + p3)^2,
m2^2 - (p1 - p3)^2}, {q^2 -> m1^2, m1 -> 2.76}], {1, 1, 1,
1}, 1, 2, ExpandVar -> m2, RegVar -> la, ExpandResult -> True]
(*
(-7.22160487162011 - 3.33298684862356I) + ep((14.89916567208155 + 4.45428944363231I) + m2^2((1.95541078990744 - 0.5461110192169399I) + Log[m2]^3((-0.35006651263764 - 1.2*^-13I) + 2.^-13pm[127]) +
Log[m2]^2((0.55764842398982 - 0.82482703173078I) + Sqrt[8.000000000144174 + Abs[(2. + 0.I)Sqrt[(6.^-14 + 0.99999999999994nan)^2] + (0. + 2.I)Sqrt[(5.^-14 + 0.99999999999995nan)^2]]^2]pm[128]) +
Log[m2]((-3.11411370288696 + 0.7997191341749998I) + Sqrt[0.1907924073499643 + 7.999999999999998Abs[3.^-14 + 1.52732173926478nan]^2]pm[129]) +
Sqrt[17.714956785674243 + 5.553483621764343Abs[nan]^2 + 1.9999999999999996Abs[1.^-14 + 1.66635584761543nan]^2]pm[130]) + 1.45242586^-6pm[131]) +
m2^2((1.3821052006307695 - 0.39985956708749987I) + Log[m2]^2((0.52509976895646 + 1.8*^-13I) + 3.^-13pm[132]) +
Log[m2]((-0.5576484239898195 + 0.8248270317307794I) +
Sqrt[8.000000000144178 + Abs[(-1.9999999999999993 - 2.220446049250313^-16I)Sqrt[(6.^-14 + 0.99999999999994nan)^2] + (2.220446049250313*^-16 - 1.9999999999999993I)Sqrt[(5.^-14 + 0.99999999999995nan)^2]]^2]pm[133]) +
Sqrt[0.19079231558595824 + 4.665423390461767Abs[nan]^2 + 2.0000000000000004Abs[3.^-14 + 1.52732173926478nan]^2]pm[134]) + 2.1915646^-7pm[135] +
((0.46953864577542 + 3.1415926392249I) + m2^2((-0.024271600282729927 - 0.41241351586539005I) + Log[m2]((-0.52509976895646 - 1.8*^-13I) + 3.^-13pm[136]) +
Sqrt[8.00000000003604 + Abs[(1. + 5.551115123125783^-17I)Sqrt[(6.^-14 + 0.99999999999994nan)^2] - (5.551115123125783*^-17 - 1.I)Sqrt[(5.^-14 + 0.99999999999995nan)^2]]^2 + 1.9999999999999991Abs[nan]^2]pm[137]) +
1.856227^-8pm[138])/ep + ((0.5 - 1.^-14I) + 1.^-14pm[140])/ep^2
*)
```
Am I doing something wrong here or is it just a bug?
I’m running the latest version from the dev branch with Mma 13.0 on Fedora 35 \(gcc 11.3.1\)
issue