# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [s, t, U, var_ket_u, phase]
sub_expr3 = Add(t, one)
sub_expr4 = Add(t, s)
sub_expr5 = InSet(phase, Real)
sub_expr6 = InSet(t, NaturalPos)
sub_expr7 = Interval(sub_expr3, sub_expr4)
sub_expr8 = Mult(two_pow_t, phase)
sub_expr9 = MultiQubitElem(element = Gate(operation = QPE(U, t), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr10 = InSet(sub_expr8, Interval(zero, subtract(two_pow_t, one)))
sub_expr11 = Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u))
sub_expr12 = Equals(Prob(Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = var_ket_u, part = sub_expr1), targets = sub_expr7), one, s)], [ExprRange(sub_expr1, sub_expr9, one, t), ExprRange(sub_expr1, sub_expr9, sub_expr3, sub_expr4)], [ExprRange(sub_expr1, Measure(basis = Z), one, t), ExprRange(sub_expr1, Gate(operation = I).with_implicit_representation(), one, s)], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(sub_expr8, t), part = sub_expr1), targets = Interval(one, t)), one, t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = var_ket_u, part = sub_expr1), targets = sub_expr7), one, s)]))), one)
expr = Equals(Lambda(sub_expr2, Conditional(Conditional(sub_expr12, And(sub_expr5, sub_expr10, sub_expr11, InSet(phase, IntervalCO(zero, one)))), sub_expr6)), Lambda(sub_expr2, Conditional(Conditional(sub_expr12, And(sub_expr5, sub_expr10, sub_expr11)), sub_expr6))).with_wrapping_at(2)