Now that I managed to installed pynormaliz, I could run the doctests 
including the below optional/external ones:

Using 
--optional=4ti2,bliss,cbc,ccache,cmake,cryptominisat,dot2tex,e_antic,external,glucose,latte_int,lidia,lrslib,memlimit,mpir,ninja_build,normaliz,notedown,pandoc_attributes,pycosat,pynormaliz,python2,qhull,rst2ipynb,sage,topcom
External software detected for doctesting: 
ffmpeg,graphviz,gurobi,imagemagick,internet,latex,pandoc

I get:

----------------------------------------------------------------------
sage -t --long src/sage/databases/oeis.py  # 1 doctest failed
sage -t --long src/sage/databases/findstat.py  # 8 doctests failed
sage -t --long src/sage/combinat/species/library.py  # 1 doctest failed
sage -t --long src/sage/combinat/designs/ext_rep.py  # 1 doctest failed
----------------------------------------------------------------------

The usual ext_rep.py one is not reproducible. I can reproduce the other 
three files failures with:

sage -tp --long --optional=sage,optional,external 
src/sage/databases/oeis.py  src/sage/databases/findstat.py  
src/sage/combinat/species/library.py  src/sage/combinat/designs/ext_rep.py  

find_stat.py failures are already tracked at 
https://trac.sagemath.org/ticket/25536

New failures are pasted below:

sage -t --long src/sage/databases/oeis.py
**********************************************************************
File "src/sage/databases/oeis.py", line 1747, in 
sage.databases.oeis.OEISSequence.programs
Failed example:
    ee.programs()[0]                      # optional -- internet
Expected:
    '(PARI) { default(realprecision, 50080); x=exp(1); for (n=1, 50000, 
d=floor(x); x=(x-d)*10; write("b001113.txt", n, " ", d)); } \\\\ _Harry J. 
Smith_, Apr 15 2009'
Got:
    '(PARI) default(realprecision, 50080); x=exp(1); for (n=1, 50000, 
d=floor(x); x=(x-d)*10; write("b001113.txt", n, " ", d)); \\\\ _Harry J. 
Smith_, Apr 15 2009'
**********************************************************************
1 item had failures:
   1 of   7 in sage.databases.oeis.OEISSequence.programs
    5 webbrowser tests not run
    0 tests not run because we ran out of time
    [266 tests, 1 failure, 65.86 s]



sage -t --long src/sage/combinat/species/library.py
**********************************************************************
File "src/sage/combinat/species/library.py", line 64, in 
sage.combinat.species.library.SimpleGraphSpecies
Failed example:
    oeis(seq)[0]                              # optional -- internet
Expected:
    A006125: a(n) = 2^(n(n-1)/2).
Got:
    A006125: a(n) = 2^(n*(n-1)/2).
**********************************************************************
1 item had failures:
   1 of   9 in sage.combinat.species.library.SimpleGraphSpecies
    0 tests not run because we ran out of time
    [23 tests, 1 failure, 5.82 s]

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