try to optimize things unsuccessfully

Baseline
```
Database loaded:     598.40ms, 304minstr, 118mb (metadata 390.57ms, 21minstr, 841kb; build 111.31ms, 8764kinstr, -214kb)
  crates: 39, mods: 824, decls: 18647, fns: 13910
Item Collection:     9.70s, 75ginstr, 377mb
  exprs: 382426, ??ty: 387 (0%), ?ty: 285 (0%), !ty: 145
Inference:           43.16s, 342ginstr, 641mb
Total:               52.86s, 417ginstr, 1018mb
```

Eager
```
Database loaded:     625.86ms, 304minstr, 118mb (metadata 414.52ms, 21minstr, 841kb; build 113.81ms, 8764kinstr, -230kb)
  crates: 39, mods: 824, decls: 18647, fns: 13910
Item Collection:     10.09s, 75ginstr, 389mb
  exprs: 382426, ??ty: 387 (0%), ?ty: 285 (0%), !ty: 145
Inference:           43.27s, 341ginstr, 644mb
Total:               53.37s, 417ginstr, 1034mb
```

Lazy
```
Database loaded:     626.34ms, 304minstr, 118mb (metadata 416.26ms, 21minstr, 841kb; build 113.67ms, 8750kinstr, -209kb)
  crates: 39, mods: 824, decls: 18647, fns: 13910
Item Collection:     10.16s, 75ginstr, 389mb
  exprs: 382426, ??ty: 387 (0%), ?ty: 285 (0%), !ty: 145
Inference:           44.51s, 342ginstr, 644mb
Total:               54.67s, 417ginstr, 1034mb
```

Cargo.lock

@@ -529,6 +529,7 @@ dependencies = [
  "la-arena",
  "limit",
  "mbe",
+ "once_cell",
  "profile",
  "rustc-hash",
  "syntax",

crates/hir_expand/Cargo.toml

@@ -16,6 +16,7 @@ either = "1.5.3"
 rustc-hash = "1.0.0"
 la-arena = { version = "0.3.0", path = "../../lib/arena" }
 itertools = "0.10.0"
+once_cell = "1"
 
 base_db = { path = "../base_db", version = "0.0.0" }
 cfg = { path = "../cfg", version = "0.0.0" }

crates/hir_expand/src/ast_id_map.rs

@@ -61,13 +61,29 @@ impl<N: AstNode> FileAstId<N> {
 type ErasedFileAstId = Idx<SyntaxNodePtr>;
 
 /// Maps items' `SyntaxNode`s to `ErasedFileAstId`s and back.
-#[derive(Debug, PartialEq, Eq, Default)]
+#[derive(Default)]
 pub struct AstIdMap {
     arena: Arena<SyntaxNodePtr>,
-    map: FxHashMap<SyntaxNodePtr, ErasedFileAstId>,
+    /// Reversed mapping lazily derived from [`self.arena`].
+    ///
+    /// FIXE: Do not store `SyntaxNodePtr` twice.
+    map: once_cell::sync::OnceCell<FxHashMap<SyntaxNodePtr, ErasedFileAstId>>,
     _c: Count<Self>,
 }
 
+impl fmt::Debug for AstIdMap {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        f.debug_struct("AstIdMap").field("arena", &self.arena).finish()
+    }
+}
+
+impl PartialEq for AstIdMap {
+    fn eq(&self, other: &Self) -> bool {
+        self.arena == other.arena
+    }
+}
+impl Eq for AstIdMap {}
+
 impl AstIdMap {
     pub(crate) fn from_source(node: &SyntaxNode) -> AstIdMap {
         assert!(node.parent().is_none());
@@ -91,9 +107,11 @@ impl AstIdMap {
                 }
             }
         });
-        res.map.extend(res.arena.iter().map(|(idx, ptr)| (ptr.clone(), idx)));
         res
     }
+    fn map(&self) -> &FxHashMap<SyntaxNodePtr, ErasedFileAstId> {
+        self.map.get_or_init(|| self.arena.iter().map(|(idx, ptr)| (ptr.clone(), idx)).collect())
+    }
 
     pub fn ast_id<N: AstNode>(&self, item: &N) -> FileAstId<N> {
         let raw = self.erased_ast_id(item.syntax());
@@ -102,7 +120,7 @@ impl AstIdMap {
 
     fn erased_ast_id(&self, item: &SyntaxNode) -> ErasedFileAstId {
         let ptr = SyntaxNodePtr::new(item);
-        *self.map.get(&ptr).unwrap_or_else(|| {
+        *self.map().get(&ptr).unwrap_or_else(|| {
             panic!(
                 "Can't find {:?} in AstIdMap:\n{:?}",
                 item,