I tried to show the search box in a custom front page, which is a regular HTML page.
How can I achieve it?
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I'm not sure if this is exactly what you're asking, but if you want to output a block directly in code you can use module_invoke().
$block = module_invoke('block', 'block_view', 'current_search');
$block = module_invoke('block', 'block', 'view', 'current_search');
Then render the contents of $block.