2. Stochastic Calculus We begin by recalling the definition of an...

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      • Illuminate\Cache\Events\CacheHit (677μs)
      • Illuminate\Cache\Events\CacheHit (408μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (533μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (667μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • creating: site.layouts.app (628μs)
      • composing: site.layouts.app (32μs)
      • creating: components.canonical (1.15ms)
      • composing: components.canonical (175μs)
      • creating: components.open-graph (595μs)
      • composing: components.open-graph (107μs)
      • creating: site.headers.header (375μs)
      • composing: site.headers.header (94μs)
      • Illuminate\Cache\Events\CacheHit (1.92ms)
      • creating: components.footer (88μs)
      • composing: components.footer (105μs)
      • Illuminate\Cache\Events\CacheHit (1.09ms)
      • Illuminate\Cache\Events\CacheHit (444μs)
      • Illuminate\Cache\Events\CacheHit (478μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (374μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (324μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (246μs)
      • creating: components.forms.contact-us (518μs)
      • composing: components.forms.contact-us (169μs)
      • creating: components.forms.get-started (146μs)
      • composing: components.forms.get-started (62μs)
      • creating: components.forms.free-tool-download (90μs)
      • composing: components.forms.free-tool-download (57μs)
      • creating: components.forms.claim-free-worksheet (88μs)
      • composing: components.forms.claim-free-worksheet (56μs)
      • creating: components.forms.tutor-subscription-waitlist (86μs)
      • composing: components.forms.tutor-subscription-waitlist (137μs)
      • creating: components.forms.tutor-subscription-join (112μs)
      • composing: components.forms.tutor-subscription-join (61μs)
      • creating: components.forms.tutor-support (207μs)
      • composing: components.forms.tutor-support (165μs)
      • 312 x Illuminate\Cache\Events\CacheHit (24.31%)
        164ms
        19 x Illuminate\Database\Events\QueryExecuted (7.15%)
        48.34ms
        19 x Illuminate\Database\Events\StatementPrepared (6.33%)
        42.78ms
        10 x Illuminate\Cache\Events\CacheMissed (1.71%)
        11.58ms
        10 x Illuminate\Cache\Events\KeyWritten (0.71%)
        4.82ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.3%)
        2.05ms
        1 x creating: components.canonical (0.17%)
        1.15ms
        11 x eloquent.retrieved: App\Models\SubjectCat (0.17%)
        1.15ms
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        870μs
        1 x Illuminate\Routing\Events\Routing (0.11%)
        745μs
        1 x creating: site.layouts.app (0.09%)
        628μs
        1 x creating: components.open-graph (0.09%)
        595μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        534μs
        1 x creating: components.forms.contact-us (0.08%)
        518μs
        15 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.07%)
        459μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        458μs
        1 x creating: site.headers.header (0.06%)
        375μs
        1 x Illuminate\Routing\Events\RouteMatched (0.06%)
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        1 x creating: homework.show (0.04%)
        289μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
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        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        251μs
        1 x creating: components.breadcrumbs (0.04%)
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        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        225μs
        1 x creating: components.forms.tutor-support (0.03%)
        207μs
        1 x composing: components.breadcrumbs (0.03%)
        189μs
        1 x composing: components.canonical (0.03%)
        175μs
        1 x composing: components.forms.contact-us (0.03%)
        169μs
        1 x composing: components.forms.tutor-support (0.02%)
        165μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        159μs
        1 x creating: components.forms.get-started (0.02%)
        146μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        137μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        112μs
        1 x composing: components.open-graph (0.02%)
        107μs
        1 x composing: components.footer (0.02%)
        105μs
        1 x composing: site.headers.header (0.01%)
        94μs
        1 x creating: components.forms.free-tool-download (0.01%)
        90μs
        1 x creating: components.footer (0.01%)
        88μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        88μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        86μs
        1 x composing: homework.show (0.01%)
        81μs
        1 x eloquent.booting: App\Models\Subject (0.01%)
        72μs
        1 x composing: components.forms.get-started (0.01%)
        62μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        60μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        58μs
        1 x composing: components.forms.free-tool-download (0.01%)
        57μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        56μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        56μs
        1 x composing: site.layouts.app (0%)
        32μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      19 statements were executed, 5 of which were duplicates, 14 unique. Show only duplicated70.66ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '62885' limit 1
        11.92mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 62885
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (6)
        3.33mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (62885)
        4.58mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.08mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 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
      • select * from `solutionslibrary` where `id` <> 62885 and `subject` = 6 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        22.63mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 62885
        • 1: 6
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (6)
        1.03mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62885 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.23mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62885
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62885 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        3.2mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62885
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 62885 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        4.22mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 62885
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.5mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        4.4mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        990μstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        3.66mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.21mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.15mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      15HomeworkLibraryFile.php
      App\Models\SubjectCat
      11SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
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          utm_source
          direct
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Cal...
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          PHPDEBUGBAR_STACK_DATA
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          status_text
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          request_request
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          request_headers
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          request_cookies
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