Incorrect result of simplify

[proy87]

simplify(180*acos(S.One*7823207/7823209)/pi) returns 0, but the value of the expression is approximately 0.04

[oscarbenjamin]

I don't get zero:

In [1]: simplify(180 * acos(S.One * 7823207 / 7823209) / pi)
Out[1]: 
        ⎛7823207⎞
180⋅acos⎜───────⎟
        ⎝7823209⎠
─────────────────
        π 

[oscarbenjamin]

I see, it only happens sometimes:

$ cat t.py
from sympy import *

print(simplify(180 * acos(S.One * 7823207 / 7823209) / pi))
$ python t.py 
0
$ python t.py 
0
$ python t.py 
0
$ python t.py 
0
$ python t.py 
0
$ python t.py 
180*acos(7823207/7823209)/pi
$ python t.py 
0
$ python t.py 
180*acos(7823207/7823209)/pi
$ python t.py 
180*acos(7823207/7823209)/pi

[oscarbenjamin]

It's a problem with assumptions. This sometimes gives True and sometimes False:

from sympy import *

expr = 180 * acos(S.One * 7823207 / 7823209) / pi

print(expr.is_zero)

[oscarbenjamin]

The bug is in evalf:

In [2]: expr = acos(S(7823207) / 7823209)

In [3]: expr.evalf(2)
Out[3]: 0

In [4]: expr.evalf(20)
Out[4]: 0.00071505185649204996777

[oscarbenjamin]

Here the rational number is evalfed to 1 when it is not quite equal to 1:

sympy/sympy/core/function.py

Lines 570 to 576 in 131caae

	# Convert all args to mpf or mpc
	# Convert the arguments to *higher* precision than requested for the
	# final result.
	# XXX + 5 is a guess, it is similar to what is used in evalf.py. Should
	# we be more intelligent about it?
	try:
	args = [arg._to_mpmath(prec + 5) for arg in args]

[proy87]

Also from time to time sin(acos(S(7823207)/7823209)) gives 0.