answer.txt

I think the best way to answer this definitively without just handwaving
and talking about the C preprocessor is to actually write two small 
example programs and compare the generated code from both. When I was
first learning C I did this constantly trying to understand how the
compiler worked. You don't need to understand assembly in great detail
to be able to spot differences in the output:

$ cat a.c
int main() {
    char *line = "HTTP/1.0 500 Internal Server Error";
    int line_len = sizeof("HTTP/1.0 500 Internal Server Error") - 1;
}

$ cat b.c
#include <string.h>
int main() {
    char *line = "HTTP/1.0 500 Internal Server Error";
    int line_len = strlen(line) - 1;
}

$ gcc -S a.c

$ gcc -S b.c

$ diff a.s b.s
1c1
<	.file	"a.c"
---
>	.file	"b.c"
16a17
>	subq	$16, %rsp
18c19,23
<	movl	$34, -12(%rbp)
---
>	movq	-8(%rbp), %rax
>	movq	%rax, %rdi
>	call	strlen
>	subl	$1, %eax
>	movl	%eax, -12(%rbp)
20c25
<	popq	%rbp
---
>	leave

So in a.c we see "movl    $34, -12(%rbp)" where the $34 is the number of characters in the string.
In b.c we end up with a runtime call to strlen() in order to find the length of the string.
It is obviously way more efficient to have the preprocessor pre-compute the length of the string
and just hardcode it like that.

Perhaps easier to see in a side-by-side diff. Look for the movl $34 on the left:

$ diff -y a.s b.s
	.file	"a.c"					      |		.file	"b.c"
	.section	.rodata						.section	.rodata
	.align 8							.align 8
.LC0:								.LC0:
	.string	"HTTP/1.0 500 Internal Server Error"			.string	"HTTP/1.0 500 Internal Server Error"
	.text								.text
	.globl	main							.globl	main
	.type	main, @function						.type	main, @function
main:								main:
.LFB0:								.LFB0:
	.cfi_startproc							.cfi_startproc
	pushq	%rbp							pushq	%rbp
	.cfi_def_cfa_offset 16						.cfi_def_cfa_offset 16
	.cfi_offset 6, -16						.cfi_offset 6, -16
	movq	%rsp, %rbp						movq	%rsp, %rbp
	.cfi_def_cfa_register 6						.cfi_def_cfa_register 6
							      >		subq	$16, %rsp
	movq	$.LC0, -8(%rbp)						movq	$.LC0, -8(%rbp)
	movl	$34, -12(%rbp)				      |		movq	-8(%rbp), %rax
							      >		movq	%rax, %rdi
							      >		call	strlen
							      >		subl	$1, %eax
							      >		movl	%eax, -12(%rbp)
	movl	$0, %eax						movl	$0, %eax
	popq	%rbp					      |		leave
	.cfi_def_cfa 7, 8						.cfi_def_cfa 7, 8
	ret								ret
	.cfi_endproc							.cfi_endproc
.LFE0:								.LFE0:
	.size	main, .-main						.size	main, .-main
	.ident	"GCC: (Debian 6.1.1-11) 6.1.1 20160802"			.ident	"GCC: (Debian 6.1.1-11) 6.1.1 20160802"
	.section	.note.GNU-stack,"",@progbits			.section	.note.GNU-stack,"",@progbits