/* 

  Derive benchmark in Picat v3.
  
  From bench/derive.pl (for Picat v3)
  https://github.com/SWI-Prolog/bench

  Had to add "$" in ops8/0, log10/0, and divide10/0.

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

main => go.


go =>
  top,
  
  nl.

go => true.

% """"
% generated: 25 October 1989
% option(s): 
%
%   (deriv) ops8
%
%   David H. D. Warren
%
%   symbolic derivative of (x+1)*((^(x,2)+2)*(^(x,3)+3))
% """

top:-ops8,log10,divide10.

ops8 :- d($(x+1)*((^(x,2)+2)*(^(x,3)+3)),x,_), println(ops8_ok).
log10 :- d($log(log(log(log(log(log(log(log(log(log(x)))))))))),x,_),println(log10_ok).
divide10 :- d($((((((((x/x)/x)/x)/x)/x)/x)/x)/x)/x,x,_),println(divide10_ok).

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))) :- !, 
    integer(N),
    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).