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function [x,Emaxs] = crude (f, xL, xU, Edes, display)
% CUDE Finds a minimum by performing a bisection like search
% Inputs: f = a function of one variable
%         xL = lower bound of region containing minimum
%         xU = upper bound of region containing minimum
%         Edes = function stops when x is guaranteed within Edes of minimum
%         display = display option (0 = no display (default), 1 = display)
% Outputs: x - estimate of minimum
%          Emaxs - value of Emax as a function of iteration number k;
if nargin < 5; display = 0; end

if display
fprintf ...
('    N       xL          xA          xB          xU          Emax\n');
end

functionCount = 0;

for k = 0 : 1000

    Emax = (xU - xL) / 2;
    Emaxs(k+1)=Emax;   

    xA = xL + 0.49 * (xU - xL); fxA = f(xA);
    xB = xL + 0.51 * (xU - xL); fxB = f(xB);
    functionCount = functionCount + 2;
   
    if display
      fprintf ('%5d %12.6f %12.6f %12.6f %12.6f %12.6f\n', ...
               k, xL, xA, xB, xU, Emax);
    end
   
    if Emax <= Edes
       x = (xL + xU) / 2; % take midpoint as final answer
       if display
            % the last two function evaluations weren't actually needed
            % (the results weren't used) and could be eliminated
            fprintf ('Tolerance achieved after %d function evaluations.\n', ...
                     functionCount - 2);
       end
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      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (389μs)
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        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        22.1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
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      • select * from `subjects` where `subjects`.`id` in (60)
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        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 11685 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.28mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
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