import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple, e, l
from proveit.numbers import Add, Exp, Interval, Mult, Sum, four, frac, one, subtract, two
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _neg_domain, _pos_domain, _two_pow__t_minus_one
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, four)
sub_expr3 = frac(one, Exp(l, two))
sub_expr4 = frac(one, Exp(_diff_l_scaled_delta_floor, two))
expr = ExprTuple(Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr4, domain = _pos_domain))), Mult(sub_expr2, Add(Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr3, domain = Interval(e, subtract(_two_pow__t_minus_one, one))))))
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
stored_expr.style_options()
# display the expression information
stored_expr.expr_info()