`\\` is translated inconsitently

I have try to prase markdown with the pulldown-cmark crate and to convert it back, using this crate. But \\ is translated back inconsistent. At some point \\ is converted to \ and at other points it is still \\. For Example This line occurs in my markdown files multiple times \\( \int x dx = \frac{x^2}{2} + C \\). The first time it stay the same, all other time it result in \( \int x dx = \frac{x^2}{2} + C \), so the mathjax expression are not render by the mdbook.

code:

        let markdown_copy = markdown.clone();
        eprintln!("{markdown_copy}");
        let parser = pulldown_cmark::Parser::new(&markdown_copy);
        let mut in_code_block = false;
        let iter = parser.into_iter().map(|f| {
            eprintln!("in  {f:?}");
            let f =match f {
                Event::Text(text) => Event::Text(CowStr::from(text.replace("=>", "⇒"))),
                Event::Start(Tag::CodeBlock(value)) => {in_code_block = true; Event::Start(Tag::CodeBlock(value))},
                Event::End(Tag::CodeBlock(value)) => {in_code_block = false; Event::Start(Tag::CodeBlock(value))}
                f => f 
            };
            eprintln!("out {f:?}");
            f
        });
        let mut output = String::new();
        pulldown_cmark_to_cmark::cmark(iter, &mut output).unwrap();
        eprintln!("{output}");

output: input.md

in  Start(Heading(H1, None, []))
out Start(Heading(H1, None, []))
in  Text(Borrowed("Chapter 1"))
out Text(Boxed("Chapter 1"))
in  End(Heading(H1, None, []))
out End(Heading(H1, None, []))
in  Start(Paragraph)
out Start(Paragraph)
in  Text(Borrowed("hello world."))
out Text(Boxed("hello world."))
in  SoftBreak
out SoftBreak
in  Text(Borrowed("This is a "))
out Text(Boxed("This is a "))
in  Start(Link(Inline, Borrowed("https://duckduckgo.com"), Borrowed("")))
out Start(Link(Inline, Borrowed("https://duckduckgo.com"), Borrowed("")))
in  Text(Borrowed("duck"))
out Text(Boxed("duck"))
in  End(Link(Inline, Borrowed("https://duckduckgo.com"), Borrowed("")))
out End(Link(Inline, Borrowed("https://duckduckgo.com"), Borrowed("")))
in  SoftBreak
out SoftBreak
in  Text(Borrowed("arrows: -> = >"))
out Text(Boxed("arrows: -> = >"))
in  SoftBreak
out SoftBreak
in  Text(Borrowed("ee"))
out Text(Boxed("ee"))
in  End(Paragraph)
out End(Paragraph)
in  Start(Paragraph)
out Start(Paragraph)
in  Text(Borrowed("\\( \\int x dx = \\frac{x^2}{2} + C "))
out Text(Boxed("\\( \\int x dx = \\frac{x^2}{2} + C "))
in  Text(Borrowed("\\)"))
out Text(Boxed("\\)"))
in  End(Paragraph)
out End(Paragraph)
in  Start(CodeBlock(Fenced(Borrowed(""))))
out Start(CodeBlock(Fenced(Borrowed(""))))
in  Text(Borrowed("this arrows should not be replaced:\n-> =>\n"))
out Text(Boxed("this arrows should not be replaced:\n-> ⇒\n"))
in  End(CodeBlock(Fenced(Borrowed(""))))
out Start(CodeBlock(Fenced(Borrowed(""))))
in  Start(Paragraph)
out Start(Paragraph)
in  Text(Borrowed("\\( \\int x dx = \\frac{x^2}{2} + C "))
out Text(Boxed("\\( \\int x dx = \\frac{x^2}{2} + C "))
in  Text(Borrowed("\\)"))
out Text(Boxed("\\)"))
in  End(Paragraph)
out End(Paragraph)
in  Start(Paragraph)
out Start(Paragraph)
in  Text(Borrowed("this should also not be replaced "))
out Text(Boxed("this should also not be replaced "))
in  Code(Borrowed("->"))
out Code(Borrowed("->"))
in  Text(Borrowed(" "))
out Text(Boxed(" "))
in  Code(Borrowed("=>"))
out Code(Borrowed("=>"))
in  Text(Borrowed(". "))
out Text(Boxed(". "))
in  End(Paragraph)
out End(Paragraph)
in  Start(Paragraph)
out Start(Paragraph)
in  Text(Borrowed("\\"))
out Text(Boxed("\\"))
in  Text(Borrowed("["))
out Text(Boxed("["))
in  Text(Borrowed(" \\mu = \\frac{1}{N} \\sum"))
out Text(Boxed(" \\mu = \\frac{1}{N} \\sum"))
in  Text(Borrowed("_"))
out Text(Boxed("_"))
in  Text(Borrowed("{i=0} x_i \\Rightarrow"))
out Text(Boxed("{i=0} x_i \\Rightarrow"))
in  Text(Borrowed("\\"))
out Text(Boxed("\\"))
in  Text(Borrowed("]"))
out Text(Boxed("]"))
in  End(Paragraph)
out End(Paragraph)

output.md

I war forced to upload the markdowns as file, because otherwise github has try to interpret it.