Coverage for sympy/simplify/cse_opts.py : 71%

""" Optimizations of the expression tree representation for better CSE 

opportunities. 

""" 

from __future__ import print_function, division 

from sympy.core import Add, Basic, Mul 

from sympy.core.basic import preorder_traversal 

from sympy.core.singleton import S 

from sympy.utilities.iterables import default_sort_key 

def sub_pre(e): 

""" Replace y - x with -(x - y) if -1 can be extracted from y - x. 

""" 

reps = [a for a in e.atoms(Add) if a.could_extract_minus_sign()] 

# make it canonical 

reps.sort(key=default_sort_key) 

e = e.xreplace(dict((a, Mul._from_args([S.NegativeOne, -a])) for a in reps)) 

# repeat again for persisting Adds but mark these with a leading 1, -1 

# e.g. y - x -> 1*-1*(x - y) 

if isinstance(e, Basic): 

negs = {} 

for a in sorted(e.atoms(Add), key=default_sort_key): 

if a in reps or a.could_extract_minus_sign(): 

negs[a] = Mul._from_args([S.One, S.NegativeOne, -a]) 

e = e.xreplace(negs) 

return e 

def sub_post(e): 

""" Replace 1*-1*x with -x. 

""" 

replacements = [] 

for node in preorder_traversal(e): 

if isinstance(node, Mul) and \ 

node.args[0] is S.One and node.args[1] is S.NegativeOne: 

replacements.append((node, -Mul._from_args(node.args[2:]))) 

for node, replacement in replacements: 

e = e.xreplace({node: replacement}) 

return e