tolerance keyword of nsimplify is ignored

[asmeurer]

In [39]: print nsimplify(0.5*x**2 - 3.333333*x, tolerance=0.001, rational=True)
x**2/2 - 3333333*x/1000000

I would have expected a smaller fraction on the x term (no more than 1000 in the denominator).

Original issue for #6527: http://code.google.com/p/sympy/issues/detail?id=3428
Original author: https://code.google.com/u/asmeurer@gmail.com/

[eacousineau]

I confirm this behavior, running Ubuntu 12.04 amd64, Python 2.7.3.

[ From this discussion: http://stackoverflow.com/a/12792656/170413 ]

I think tolerance isn't used because sympy.simplify.nsimplify() calls sympy.simplify._real_to_rational() if the rational flag is true, but does not pass any tolerance parameters.

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c1
Original author: https://code.google.com/u/108550831992238876765/

[asmeurer]

So it should be straightforward to fix if you understand what's going on in _real_to_rational.

**Labels:** EasyToFix  

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c2
Original author: https://code.google.com/u/asmeurer@gmail.com/

[prasoon2211]

I think we can modify _real_to_rational to add a tolerance argument to it. Based on that, we can round the real number to given number of digits if the tolerance is provided.
Does that sounds okay? Or is there something else we can do?

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c3
Original author: https://code.google.com/u/102594231986105975028/

[asmeurer]

That sounds basically correct.

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c4
Original author: https://code.google.com/u/asmeurer@gmail.com/

[smichr]

**Status:** Fixed  

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c5
Original author: https://code.google.com/u/117933771799683895267/

[smichr]

>>> nsimplify(0.5*x**2 - 3.333333*x, tolerance=0.001, rational=True)
x**2/2 - 10*x/3

Original comment: http://code.google.com/p/sympy/issues/detail?id=3428#c6
Original author: https://code.google.com/u/117933771799683895267/