Test Deriv

Jan Burse, erstellt 15. Sep 2018
/**
* Prolog code for the symbolic derivation benchmark.
*
* This is the benchmark of page 222 of:
* Warren, D.H.D. (1983): Applied Logic - Its Use and
* Implementation as a Programming Tool,
* Technical Note 290, SRI International, 1983
*
* Warranty & Liability
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* otherwise agreed upon, XLOG Technologies GmbH makes no warranties
* regarding the provided information. XLOG Technologies GmbH assumes
* no liability that any problems might be solved with the information
* provided by XLOG Technologies GmbH.
*
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* and patent rights in particular - are the sole property of XLOG
* Technologies GmbH. If the company was not the originator of some
* excerpts, XLOG Technologies GmbH has at least obtained the right to
* reproduce, change and translate the information.
*
* Reproduction is restricted to the whole unaltered document. Reproduction
* of the information is only allowed for non-commercial uses. Selling,
* giving away or letting of the execution of the library is prohibited.
* The library can be distributed as part of your applications and libraries
* for execution provided this comment remains unchanged.
*
* Restrictions
* Only to be distributed with programs that add significant and primary
* functionality to the library. Not to be distributed with additional
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*
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*/
/*****************************************************************/
/* Normal Test Cases */
/*****************************************************************/
% ops8(-Expr)
ops8(E) :-
d((x+1)*((x^2+2)*(x^3+3)), x, E).
% divide10(-Expr)
d(x/x/x/x/x/x/x/x/x/x, x, E).
% log10(-Expr)
d(log(log(log(log(log(log(log(log(log(log(x)))))))))), x, E).
% times10(-Expr)
d(x*x*x*x*x*x*x*x*x*x, x, E).
% deriv
ops8(_),
log10(_),
times10(_).
/*****************************************************************/
/* Reduced Test Cases */
/*****************************************************************/
% ops4(-Expr)
ops4(E) :-
d((x+1)*(x^2+2), x, E).
% divide5(-Expr)
d(x/x/x/x/x, x, E).
% log5(-Expr)
log5(E) :-
d(log(log(log(log(log(x))))), x, E).
% times5(-Expr)
d(x*x*x*x*x, x, E).
% rderiv
ops4(_),
log5(_),
times5(_).
/*****************************************************************/
/* The Derivator */
/*****************************************************************/
% d(+Expr, +Var, -Expr)
d(U+V, X, DU+DV) :- !,
d(U, X, DU),
d(V, X, DV).
d(U-V, X, DU-DV) :- !,
d(U, X, DU),
d(V, X, DV).
d(U*V, X, DU*V+U*DV) :- !,
d(U, X, DU),
d(V, X, DV).
d(U/V, X, (DU*V-U*DV)/V^2) :- !,
d(U, X, DU),
d(V, X, DV).
d(U^N, X, DU*N*U^N1) :- !,
N1 is N-1,
d(U, X, DU).
d(-U, X, -DU) :- !,
d(U, X, DU).
d(exp(U), X, exp(U)*DU) :- !,
d(U, X, DU).
d(log(U), X, DU/U) :- !,
d(U, X, DU).
d(X, X, 1) :- !.
d(_, _, 0).

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