def exptrigsimp(expr, simplify=True):
    from sympy.simplify.fu import hyper_as_trig, TR2i
    from sympy.simplify.simplify import bottom_up

    def exp_trig(e):
        # select the better of e, and e rewritten in terms of exp or trig
        # functions
        choices = [e]
        if e.has(*_trigs):
            choices.append(e.rewrite(exp))
        choices.append(e.rewrite(cos))
        return min(*choices, key=count_ops)
    newexpr = bottom_up(expr, exp_trig)

    if simplify:
        newexpr = newexpr.simplify()

    # conversion from exp to hyperbolic
    ex = newexpr.atoms(exp, S.Exp1)
    ex = [ei for ei in ex if 1/ei not in ex]
    ## sinh and cosh
    for ei in ex:
        e2 = ei**-2
        if e2 in ex:
            a = e2.args[0]/2 if not e2 is S.Exp1 else S.Half
            newexpr = newexpr.subs((e2 + 1)*ei, 2*cosh(a))
            newexpr = newexpr.subs((e2 - 1)*ei, 2*sinh(a))
    ## exp ratios to tan and tanh
    for ei in ex:
        n, d = ei - 1, ei + 1
        et = n/d
        etinv = d/n  # not 1/et or else recursion errors arise
        a = ei.args[0] if ei.func is exp else S.One
        if a.is_Mul or a is S.ImaginaryUnit:
            c = a.as_coefficient(I)
            if c:
                t = S.ImaginaryUnit*tan(c/2)
                newexpr = newexpr.subs(etinv, 1/t)
                newexpr = newexpr.subs(et, t)
                continue
        t = tanh(a/2)
        newexpr = newexpr.subs(etinv, 1/t)
        newexpr = newexpr.subs(et, t)

    # sin/cos and sinh/cosh ratios to tan and tanh, respectively
    if newexpr.has(HyperbolicFunction):
        e, f = hyper_as_trig(newexpr)
        newexpr = f(TR2i(e))
    if newexpr.has(TrigonometricFunction):
        newexpr = TR2i(newexpr)

    # can we ever generate an I where there was none previously?
    if not (newexpr.has(I) and not expr.has(I)):
        expr = newexpr
    return expr

#-------------------- the old trigsimp routines ---------------------
Simplifies exponential / trigonometric / hyperbolic functions.
dataset/ETHPy150Open sympy/sympy/sympy/simplify/trigsimp.py/exptrigsimp