find_root should call fast_float

[robertwb]

sage: f(x) = sin(x)-cos(x)
sage: g = f._fast_float_()

sage: timeit("find_root(f, 0, pi)")
625 loops, best of 3: 154 µs per loop

sage: timeit("find_root(g, 0, pi)")
625 loops, best of 3: 24 µs per loop

See also http://groups.google.com/group/sage-devel/browse_thread/thread/927319a4fa61ae3b/9fc80aa9c114e041

CC: @jasongrout

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/5091

[sagetrac-mabshoff]

comment:1

3.4 is for ReST tickets only.

Cheers,

Michael

[sagetrac-wcauchois]

comment:3

Incorporating the time it takes to call fast_float, the speedup is not that radical:

sage: var('x')
x
sage: from sage.ext.fast_eval import fast_float
sage: timeit("find_root(sin(x)-cos(x), 0, pi)")
625 loops, best of 3: 441 µs per loop
sage: timeit("find_root(fast_float(sin(x)-cos(x), x), 0, pi)")
625 loops, best of 3: 393 µs per loop

Its better for clients to call fast_float themselves, if they're using find_root inside a loop.

[jasongrout]

comment:4

There is a small speedup here, so why not call it?

[robertwb]

comment:5

The point is that there should be a big speedup--I'm going to try and track down why construction is so expensive.