def nsimplify(expr, constants=[], tolerance=None, full=False, rational=None):
    try:
        return sympify(as_int(expr))
    except (TypeError, ValueError):
        pass
    expr = sympify(expr).xreplace({
        Float('inf'): S.Infinity,
        Float('-inf'): S.NegativeInfinity,
        })
    if expr is S.Infinity or expr is S.NegativeInfinity:
        return expr
    if rational or expr.free_symbols:
        return _real_to_rational(expr, tolerance)

    # SymPy's default tolerance for Rationals is 15; other numbers may have
    # lower tolerances set, so use them to pick the largest tolerance if None
    # was given
    if tolerance is None:
        tolerance = 10**-min([15] +
             [mpmath.libmp.libmpf.prec_to_dps(n._prec)
             for n in expr.atoms(Float)])
    # XXX should prec be set independent of tolerance or should it be computed
    # from tolerance?
    prec = 30
    bprec = int(prec*3.33)

    constants_dict = {}
    for constant in constants:
        constant = sympify(constant)
        v = constant.evalf(prec)
        if not v.is_Float:
            raise ValueError("constants must be real-valued")
        constants_dict[str(constant)] = v._to_mpmath(bprec)

    exprval = expr.evalf(prec, chop=True)
    re, im = exprval.as_real_imag()

    # safety check to make sure that this evaluated to a number
    if not (re.is_Number and im.is_Number):
        return expr

    def nsimplify_real(x):
        orig = mpmath.mp.dps
        xv = x._to_mpmath(bprec)
        try:
            # We'll be happy with low precision if a simple fraction
            if not (tolerance or full):
                mpmath.mp.dps = 15
                rat = mpmath.pslq([xv, 1])
                if rat is not None:
                    return Rational(-int(rat[1]), int(rat[0]))
            mpmath.mp.dps = prec
            newexpr = mpmath.identify(xv, constants=constants_dict,
                tol=tolerance, full=full)
            if not newexpr:
                raise ValueError
            if full:
                newexpr = newexpr[0]
            expr = sympify(newexpr)
            if x and not expr:  # don't let x become 0
                raise ValueError
            if expr.is_finite is False and not xv in [mpmath.inf, mpmath.ninf]:
                raise ValueError
            return expr
        finally:
            # even though there are returns above, this is executed
            # before leaving
            mpmath.mp.dps = orig
    try:
        if re:
            re = nsimplify_real(re)
        if im:
            im = nsimplify_real(im)
    except ValueError:
        if rational is None:
            return _real_to_rational(expr)
        return expr

    rv = re + im*S.ImaginaryUnit
    # if there was a change or rational is explicitly not wanted
    # return the value, else return the Rational representation
    if rv != expr or rational is False:
        return rv
    return _real_to_rational(expr)
Find a simple representation for a number or, if there are free symbols or
dataset/ETHPy150Open sympy/sympy/sympy/simplify/simplify.py/nsimplify