The problem is just the expansion of (1+x)^10000.
(1) -> )set message time on
(1) -> g(x) == (1+x)^10000
Type: Void
Time: 0 sec
(2) -> eval(D(g(x),x), x=0.1)
Compiling function g with type Variable x -> Polynomial Integer
Type: Polynomial Float
Time: 3.09 (IN) + 6.74 (EV) + 0.06 (OT) = 9.89 sec
In FriCAS and OpenAxiom (probably Axiom too) the correct way to avoid
this is to treat (1+x) as a kernel via the identity operator 'paren'.
(3) -> g(x) == paren(1+x)^10000
Compiled code for g has been cleared.
1 old definition(s) deleted for function or rule g
Type: Void
Time: 0 sec
(4) -> eval(D(g(x),x), x=0.1)
Compiling function g with type Variable x -> Expression Integer
9999 ,
(4) 10000.0 (1.1) %paren (1.1)
Type: Expression Float
Time: 0.09 (IN) + 0.05 (OT) = 0.14 sec
The only trouble here is that neither FriCAS nor OpenAxiom know how to
differentiate this operator. This can be fixed with the following
patch:
https://github.com/billpage/fricas/commit/04c1f9b2d5eb4ece95c6f5dded46a72181cecb06
https://github.com/billpage/fricas/commit/04c1f9b2d5eb4ece95c6f5dded46a72181cecb06.patch
(1) -> g(x) == paren(1+x)^10000
Type: Void
Time: 0 sec
(2) -> eval(D(g(x),x), x=0.1)
Compiling function g with type Variable(x) -> Expression(Integer)
9999
(2) 10000.0 (1.1)
Type: Expression(Float)
Time: 0.04 (IN) + 0.00 (EV) + 0.12 (OT) = 0.16 sec
On 9 March 2017 at 16:58, Mark Clements <mark.cleme...@ki.se> wrote:
> [Apologies for cross-posting]
>
> For the algorithmic differentiation: I have started an implementation
> (attached) of the jet machinery using a domain rather than the
> domain+package used in Smith et al.
>
> This provides considerably faster differentiation than symbolic
> differentiation. For example:
>
> g(x) == (1+x)^10000
> eval(D(g(x),x), x=0.1) -- slow
> g(jet(0.1)) -- fast!
>
> I was not certain how to get x=jet(1.0) or eval(x^x, x=jet(2.0)) to work:
> any suggestions?
>
> Sincerely, Mark,
>
>
> On 02/19/2017 12:21 PM, Gabriel Dos Reis wrote:
>
> It was available in a branch of OpenAxiom. Jacob wanted to rewrite for
> merging in the main trunk. He graduated and got a job, so did not get to
> rewrite it. I added the AST part of the work to the trunk, but the jet
> machinery remained in Jacob's branch.
>
> Jacob: do you still have that?
>
> -- Gaby
>
>
> On Feb 19, 2017 3:15 AM, "Mark Clements" <mark.cleme...@ki.se> wrote:
>
> Is the Axiom code for Smith's work on algorithmic differentiation
> available?
>
> http://www.axiomatics.org/~gdr/ad/issac07.pdf
> http://oaktrust.library.tamu.edu/bitstream/handle/1969.1/ETD-TAMU-2010-05-7823/SMITH-DISSERTATION.pdf
>
> Sincerely, Mark Clements.
>
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