solveset is perhaps oversimplifying

[smichr]

When computing a solution for a surd within a numerical expression, solveset appears to add in factoring of the surd. This can add a lot of time when the argument is large. solve does not do so and returns much more quickly with an unsimplified surd:

>>> solve(z,surds[0])
[-sqrt(494780809584713239924897123795467407048970073445360407198353838952892466)
, sqrt(494780809584713239924897123795467407048970073445360407198353838952892466)
]
>>> solveset(z,surds[0])
{-3253006644823572288469*sqrt(46756602478563333774770976706), 325300664482357228
8469*sqrt(46756602478563333774770976706)}

>>> nfloat(_)
{-7.03406574880213e+35, 7.03406574880213e+35}
>>> nfloat(surds[0])
7.03406574880213e+35
>>> surds[0].args[0]
494780809584713239924897123795467407048970073445360407198353838952892466
>>> factorint(_)
{2: 1, 19: 1, 445187: 1, 4274029139: 2, 761110076471: 2, 2763865313521315866601: 1}

So solveset factored out the squares:

>>> 4274029139*761110076471
3253006644823572288469

[smichr]

This may also be a symptom of the same problem. I suspect it is related to the use of roots (or similar):

>>> a = S("6506833320952669167898688709329/5070602400912917605986812821504")
>>> solve(Rational(Float(a,5))<(a.p-x)/a.q)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "s\solvers\solvers.py", line 985, in solve
    return reduce_inequalities(f, symbols=symbols)
  File "s\solvers\inequalities.py", line 986, in reduce_inequalities
    rv = _reduce_inequalities(inequalities, symbols)
  File "s\solvers\inequalities.py", line 923, in _reduce_inequalities
    poly_reduced.append(reduce_rational_inequalities([exprs], gen))
  File "s\solvers\inequalities.py", line 266, in reduce_rational_inequalities
    solution &= solve_rational_inequalities(eqs)
  File "s\solvers\inequalities.py", line 164, in solve_rational_inequalities
    numer_intervals = solve_poly_inequality(numer*denom, rel)
  File "s\solvers\inequalities.py", line 57, in solve_poly_inequality
    reals, intervals = poly.real_roots(multiple=False), []
  File "s\polys\polytools.py", line 3496, in real_roots
    reals = sympy.polys.rootoftools.CRootOf.real_roots(f, radicals=radicals)
  File "s\polys\rootoftools.py", line 400, in real_roots
    return cls._get_roots("_real_roots", poly, radicals)
  File "s\polys\rootoftools.py", line 732, in _get_roots
    coeff, poly = cls._preprocess_roots(poly)
  File "s\polys\rootoftools.py", line 706, in _preprocess_roots
    coeff, poly = preprocess_roots(poly)
  File "s\polys\polyroots.py", line 770, in preprocess_roots
    basis = _integer_basis(poly)
  File "s\polys\polyroots.py", line 693, in _integer_basis
    divs = reversed(divisors(gcd_list(coeffs))[1:])
  File "s\ntheory\factor_.py", line 1404, in divisors
    return sorted(rv)
  File "s\ntheory\factor_.py", line 1344, in _divisors

    factordict = factorint(n)
  File "s\ntheory\factor_.py", line 1217, in factorint

    seed=high_)
  File "s\ntheory\factor_.py", line 492, in pollard_rho
    g = igcd(U - V, n)
  File "s\core\numbers.py", line 180, in igcd
    args_temp = [abs(as_int(i)) for i in args]
  File "s\core\numbers.py", line 180, in <listcomp>
    args_temp = [abs(as_int(i)) for i in args]
  File "s\core\compatibility.py", line 416, in as_int
    from sympy.core.numbers import Integer
  File "<frozen importlib._bootstrap>", line 1019, in _handle_fromlist
KeyboardInterrupt -> it was going very slow

The following is very fast:

>>> solve(Rational(Float(a,5))-(a.p-x)/a.q)
[-1967882098648739254148399]