#15030: Switch standard 2D plotting from `fast_float` to `fast_callable`
-------------------------------+----------------------------
       Reporter:  eviatarbach  |        Owner:
           Type:  defect       |       Status:  needs_review
       Priority:  major        |    Milestone:  sage-5.12
      Component:  graphics     |   Resolution:
       Keywords:               |    Merged in:
        Authors:               |    Reviewers:
Report Upstream:  N/A          |  Work issues:
         Branch:               |       Commit:
   Dependencies:               |     Stopgaps:
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Comment (by ppurka):

 Hmm.. so, you are changing only the plots for symbolic expressions. This
 patch makes the symbolic expression plots about five times slower.
 {{{
 sage: timeit('plot(abs(log(x)), (x, -20, 20))') # with patch
 25 loops, best of 3: 18.5 ms per loop

 sage: timeit('plot(abs(log(x)), (x, -20, 20))') # without patch
 125 loops, best of 3: 3.58 ms per loop
 }}}

 What do you think of the following change which introduces only a factor
 of two slowdown? The main problem seems to be that the fast float stuff
 does not handle complex numbers, and so we can explicitly specify the
 domain as CDF. I am not sure what is the default domain.
 {{{
 +        from sage.ext.fast_callable import fast_callable
 +        from sage.rings.all import CDF
 +        return fast_callable(self, vars=vars, expect_one_var=True,
 +                             domain=CDF)
 }}}

 The timeit results are as follows:
 {{{
 sage: timeit('plot(abs(log(x)), (x, -20, 20))')
 125 loops, best of 3: 6 ms per loop
 }}}
 A few doctests in `expression.pyx` fail, but they can be fixed (by
 changing their output).

--
Ticket URL: <http://trac.sagemath.org/ticket/15030#comment:6>
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