diff --git a/milli/src/search/new/ranking_rule_graph/cheapest_paths.rs b/milli/src/search/new/ranking_rule_graph/cheapest_paths.rs
index c09f6e5e0..443ab0ec4 100644
--- a/milli/src/search/new/ranking_rule_graph/cheapest_paths.rs
+++ b/milli/src/search/new/ranking_rule_graph/cheapest_paths.rs
@@ -9,141 +9,202 @@ use crate::search::new::query_graph::QueryNode;
 use crate::search::new::small_bitmap::SmallBitmap;
 use crate::Result;
 
-impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
-    pub fn visit_paths_of_cost(
-        &mut self,
-        from: Interned<QueryNode>,
-        cost: u16,
-        all_distances: &MappedInterner<QueryNode, Vec<u16>>,
-        dead_ends_cache: &mut DeadEndsCache<G::Condition>,
-        mut visit: impl FnMut(
-            &[Interned<G::Condition>],
-            &mut Self,
-            &mut DeadEndsCache<G::Condition>,
-        ) -> Result<ControlFlow<()>>,
-    ) -> Result<()> {
-        let _ = self.visit_paths_of_cost_rec(
-            from,
-            cost,
-            all_distances,
-            dead_ends_cache,
-            &mut visit,
-            &mut vec![],
-            &mut SmallBitmap::for_interned_values_in(&self.conditions_interner),
-            dead_ends_cache.forbidden.clone(),
-        )?;
+type VisitFn<'f, G> = &'f mut dyn FnMut(
+    &[Interned<<G as RankingRuleGraphTrait>::Condition>],
+    &mut RankingRuleGraph<G>,
+    &mut DeadEndsCache<<G as RankingRuleGraphTrait>::Condition>,
+) -> Result<ControlFlow<()>>;
+
+struct VisitorContext<'a, G: RankingRuleGraphTrait> {
+    graph: &'a mut RankingRuleGraph<G>,
+    all_costs_from_node: &'a MappedInterner<QueryNode, Vec<u64>>,
+    dead_ends_cache: &'a mut DeadEndsCache<G::Condition>,
+}
+
+struct VisitorState<G: RankingRuleGraphTrait> {
+    remaining_cost: u64,
+
+    path: Vec<Interned<G::Condition>>,
+
+    visited_conditions: SmallBitmap<G::Condition>,
+    visited_nodes: SmallBitmap<QueryNode>,
+
+    forbidden_conditions: SmallBitmap<G::Condition>,
+    forbidden_conditions_to_nodes: SmallBitmap<QueryNode>,
+}
+
+pub struct PathVisitor<'a, G: RankingRuleGraphTrait> {
+    state: VisitorState<G>,
+    ctx: VisitorContext<'a, G>,
+}
+impl<'a, G: RankingRuleGraphTrait> PathVisitor<'a, G> {
+    pub fn new(
+        cost: u64,
+        graph: &'a mut RankingRuleGraph<G>,
+        all_costs_from_node: &'a MappedInterner<QueryNode, Vec<u64>>,
+        dead_ends_cache: &'a mut DeadEndsCache<G::Condition>,
+    ) -> Self {
+        Self {
+            state: VisitorState {
+                remaining_cost: cost,
+                path: vec![],
+                visited_conditions: SmallBitmap::for_interned_values_in(&graph.conditions_interner),
+                visited_nodes: SmallBitmap::for_interned_values_in(&graph.query_graph.nodes),
+                forbidden_conditions: SmallBitmap::for_interned_values_in(
+                    &graph.conditions_interner,
+                ),
+                forbidden_conditions_to_nodes: SmallBitmap::for_interned_values_in(
+                    &graph.query_graph.nodes,
+                ),
+            },
+            ctx: VisitorContext { graph, all_costs_from_node, dead_ends_cache },
+        }
+    }
+
+    pub fn visit_paths(mut self, visit: VisitFn<G>) -> Result<()> {
+        let _ =
+            self.state.visit_node(self.ctx.graph.query_graph.root_node, visit, &mut self.ctx)?;
         Ok(())
     }
-    pub fn visit_paths_of_cost_rec(
+}
+
+impl<G: RankingRuleGraphTrait> VisitorState<G> {
+    fn visit_node(
         &mut self,
-        from: Interned<QueryNode>,
-        cost: u16,
-        all_distances: &MappedInterner<QueryNode, Vec<u16>>,
-        dead_ends_cache: &mut DeadEndsCache<G::Condition>,
-        visit: &mut impl FnMut(
-            &[Interned<G::Condition>],
-            &mut Self,
-            &mut DeadEndsCache<G::Condition>,
-        ) -> Result<ControlFlow<()>>,
-        prev_conditions: &mut Vec<Interned<G::Condition>>,
-        cur_path: &mut SmallBitmap<G::Condition>,
-        mut forbidden_conditions: SmallBitmap<G::Condition>,
-    ) -> Result<bool> {
+        from_node: Interned<QueryNode>,
+        visit: VisitFn<G>,
+        ctx: &mut VisitorContext<G>,
+    ) -> Result<ControlFlow<(), bool>> {
         let mut any_valid = false;
 
-        let edges = self.edges_of_node.get(from).clone();
-        'edges_loop: for edge_idx in edges.iter() {
-            let Some(edge) = self.edges_store.get(edge_idx).as_ref() else { continue };
-            if cost < edge.cost as u16 {
+        let edges = ctx.graph.edges_of_node.get(from_node).clone();
+        for edge_idx in edges.iter() {
+            let Some(edge) = ctx.graph.edges_store.get(edge_idx).clone() else { continue };
+
+            if self.remaining_cost < edge.cost as u64 {
                 continue;
             }
-            let next_any_valid = match edge.condition {
-                None => {
-                    if edge.dest_node == self.query_graph.end_node {
-                        any_valid = true;
-                        let control_flow = visit(prev_conditions, self, dead_ends_cache)?;
-                        match control_flow {
-                            ControlFlow::Continue(_) => {}
-                            ControlFlow::Break(_) => return Ok(true),
-                        }
-                        true
-                    } else {
-                        self.visit_paths_of_cost_rec(
-                            edge.dest_node,
-                            cost - edge.cost as u16,
-                            all_distances,
-                            dead_ends_cache,
-                            visit,
-                            prev_conditions,
-                            cur_path,
-                            forbidden_conditions.clone(),
-                        )?
-                    }
-                }
-                Some(condition) => {
-                    if forbidden_conditions.contains(condition)
-                        || all_distances
-                            .get(edge.dest_node)
-                            .iter()
-                            .all(|next_cost| *next_cost != cost - edge.cost as u16)
-                    {
-                        continue;
-                    }
-                    cur_path.insert(condition);
-                    prev_conditions.push(condition);
-                    let mut new_forbidden_conditions = forbidden_conditions.clone();
-                    if let Some(next_forbidden) =
-                        dead_ends_cache.forbidden_conditions_after_prefix(prev_conditions)
-                    {
-                        new_forbidden_conditions.union(&next_forbidden);
-                    }
-
-                    let next_any_valid = if edge.dest_node == self.query_graph.end_node {
-                        any_valid = true;
-                        let control_flow = visit(prev_conditions, self, dead_ends_cache)?;
-                        match control_flow {
-                            ControlFlow::Continue(_) => {}
-                            ControlFlow::Break(_) => return Ok(true),
-                        }
-                        true
-                    } else {
-                        self.visit_paths_of_cost_rec(
-                            edge.dest_node,
-                            cost - edge.cost as u16,
-                            all_distances,
-                            dead_ends_cache,
-                            visit,
-                            prev_conditions,
-                            cur_path,
-                            new_forbidden_conditions,
-                        )?
-                    };
-                    cur_path.remove(condition);
-                    prev_conditions.pop();
-                    next_any_valid
-                }
+            self.remaining_cost -= edge.cost as u64;
+            let cf = match edge.condition {
+                Some(condition) => self.visit_condition(
+                    condition,
+                    edge.dest_node,
+                    &edge.nodes_to_skip,
+                    visit,
+                    ctx,
+                )?,
+                None => self.visit_no_condition(edge.dest_node, &edge.nodes_to_skip, visit, ctx)?,
             };
-            any_valid |= next_any_valid;
+            self.remaining_cost += edge.cost as u64;
 
+            let ControlFlow::Continue(next_any_valid) = cf else {
+                return Ok(ControlFlow::Break(()));
+            };
             if next_any_valid {
-                forbidden_conditions =
-                    dead_ends_cache.forbidden_conditions_for_all_prefixes_up_to(prev_conditions);
-                if cur_path.intersects(&forbidden_conditions) {
-                    break 'edges_loop;
+                self.forbidden_conditions = ctx
+                    .dead_ends_cache
+                    .forbidden_conditions_for_all_prefixes_up_to(self.path.iter().copied());
+                if self.visited_conditions.intersects(&self.forbidden_conditions) {
+                    break;
                 }
             }
+            any_valid |= next_any_valid;
         }
 
-        Ok(any_valid)
+        Ok(ControlFlow::Continue(any_valid))
     }
 
-    pub fn initialize_distances_with_necessary_edges(&self) -> MappedInterner<QueryNode, Vec<u16>> {
-        let mut distances_to_end = self.query_graph.nodes.map(|_| vec![]);
+    fn visit_no_condition(
+        &mut self,
+        dest_node: Interned<QueryNode>,
+        edge_forbidden_nodes: &SmallBitmap<QueryNode>,
+        visit: VisitFn<G>,
+        ctx: &mut VisitorContext<G>,
+    ) -> Result<ControlFlow<(), bool>> {
+        if ctx
+            .all_costs_from_node
+            .get(dest_node)
+            .iter()
+            .all(|next_cost| *next_cost != self.remaining_cost)
+        {
+            return Ok(ControlFlow::Continue(false));
+        }
+        if dest_node == ctx.graph.query_graph.end_node {
+            let control_flow = visit(&self.path, ctx.graph, ctx.dead_ends_cache)?;
+            match control_flow {
+                ControlFlow::Continue(_) => Ok(ControlFlow::Continue(true)),
+                ControlFlow::Break(_) => Ok(ControlFlow::Break(())),
+            }
+        } else {
+            let old_fbct = self.forbidden_conditions_to_nodes.clone();
+            self.forbidden_conditions_to_nodes.union(edge_forbidden_nodes);
+            let cf = self.visit_node(dest_node, visit, ctx)?;
+            self.forbidden_conditions_to_nodes = old_fbct;
+            Ok(cf)
+        }
+    }
+    fn visit_condition(
+        &mut self,
+        condition: Interned<G::Condition>,
+        dest_node: Interned<QueryNode>,
+        edge_forbidden_nodes: &SmallBitmap<QueryNode>,
+        visit: VisitFn<G>,
+        ctx: &mut VisitorContext<G>,
+    ) -> Result<ControlFlow<(), bool>> {
+        assert!(dest_node != ctx.graph.query_graph.end_node);
+
+        if self.forbidden_conditions_to_nodes.contains(dest_node)
+            || edge_forbidden_nodes.intersects(&self.visited_nodes)
+        {
+            return Ok(ControlFlow::Continue(false));
+        }
+        if self.forbidden_conditions.contains(condition) {
+            return Ok(ControlFlow::Continue(false));
+        }
+
+        if ctx
+            .all_costs_from_node
+            .get(dest_node)
+            .iter()
+            .all(|next_cost| *next_cost != self.remaining_cost)
+        {
+            return Ok(ControlFlow::Continue(false));
+        }
+
+        self.path.push(condition);
+        self.visited_nodes.insert(dest_node);
+        self.visited_conditions.insert(condition);
+
+        let old_fc = self.forbidden_conditions.clone();
+        if let Some(next_forbidden) =
+            ctx.dead_ends_cache.forbidden_conditions_after_prefix(self.path.iter().copied())
+        {
+            self.forbidden_conditions.union(&next_forbidden);
+        }
+        let old_fctn = self.forbidden_conditions_to_nodes.clone();
+        self.forbidden_conditions_to_nodes.union(edge_forbidden_nodes);
+
+        let cf = self.visit_node(dest_node, visit, ctx)?;
+
+        self.forbidden_conditions_to_nodes = old_fctn;
+        self.forbidden_conditions = old_fc;
+
+        self.visited_conditions.remove(condition);
+        self.visited_nodes.remove(dest_node);
+        self.path.pop();
+
+        Ok(cf)
+    }
+}
+
+impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
+    pub fn find_all_costs_to_end(&self) -> MappedInterner<QueryNode, Vec<u64>> {
+        let mut costs_to_end = self.query_graph.nodes.map(|_| vec![]);
         let mut enqueued = SmallBitmap::new(self.query_graph.nodes.len());
 
         let mut node_stack = VecDeque::new();
 
-        *distances_to_end.get_mut(self.query_graph.end_node) = vec![0];
+        *costs_to_end.get_mut(self.query_graph.end_node) = vec![0];
 
         for prev_node in self.query_graph.nodes.get(self.query_graph.end_node).predecessors.iter() {
             node_stack.push_back(prev_node);
@@ -151,22 +212,22 @@ impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
         }
 
         while let Some(cur_node) = node_stack.pop_front() {
-            let mut self_distances = BTreeSet::<u16>::new();
+            let mut self_costs = BTreeSet::<u64>::new();
 
             let cur_node_edges = &self.edges_of_node.get(cur_node);
             for edge_idx in cur_node_edges.iter() {
                 let edge = self.edges_store.get(edge_idx).as_ref().unwrap();
                 let succ_node = edge.dest_node;
-                let succ_distances = distances_to_end.get(succ_node);
-                for succ_distance in succ_distances {
-                    self_distances.insert(edge.cost as u16 + succ_distance);
+                let succ_costs = costs_to_end.get(succ_node);
+                for succ_distance in succ_costs {
+                    self_costs.insert(edge.cost as u64 + succ_distance);
                 }
             }
-            let distances_to_end_cur_node = distances_to_end.get_mut(cur_node);
-            for cost in self_distances.iter() {
-                distances_to_end_cur_node.push(*cost);
+            let costs_to_end_cur_node = costs_to_end.get_mut(cur_node);
+            for cost in self_costs.iter() {
+                costs_to_end_cur_node.push(*cost);
             }
-            *distances_to_end.get_mut(cur_node) = self_distances.into_iter().collect();
+            *costs_to_end.get_mut(cur_node) = self_costs.into_iter().collect();
             for prev_node in self.query_graph.nodes.get(cur_node).predecessors.iter() {
                 if !enqueued.contains(prev_node) {
                     node_stack.push_back(prev_node);
@@ -174,6 +235,6 @@ impl<G: RankingRuleGraphTrait> RankingRuleGraph<G> {
                 }
             }
         }
-        distances_to_end
+        costs_to_end
     }
 }
diff --git a/milli/src/search/new/ranking_rule_graph/dead_ends_cache.rs b/milli/src/search/new/ranking_rule_graph/dead_ends_cache.rs
index d25c69c23..f3bb25d56 100644
--- a/milli/src/search/new/ranking_rule_graph/dead_ends_cache.rs
+++ b/milli/src/search/new/ranking_rule_graph/dead_ends_cache.rs
@@ -36,12 +36,12 @@ impl<T> DeadEndsCache<T> {
     }
     pub fn forbidden_conditions_for_all_prefixes_up_to(
         &mut self,
-        prefix: &[Interned<T>],
+        prefix: impl Iterator<Item = Interned<T>>,
     ) -> SmallBitmap<T> {
         let mut forbidden = self.forbidden.clone();
         let mut cursor = self;
-        for c in prefix.iter() {
-            if let Some(next) = cursor.advance(*c) {
+        for c in prefix {
+            if let Some(next) = cursor.advance(c) {
                 cursor = next;
                 forbidden.union(&cursor.forbidden);
             } else {
@@ -52,11 +52,11 @@ impl<T> DeadEndsCache<T> {
     }
     pub fn forbidden_conditions_after_prefix(
         &mut self,
-        prefix: &[Interned<T>],
+        prefix: impl Iterator<Item = Interned<T>>,
     ) -> Option<SmallBitmap<T>> {
         let mut cursor = self;
-        for c in prefix.iter() {
-            if let Some(next) = cursor.advance(*c) {
+        for c in prefix {
+            if let Some(next) = cursor.advance(c) {
                 cursor = next;
             } else {
                 return None;