diff --git a/libcxx/include/__algorithm/is_permutation.h b/libcxx/include/__algorithm/is_permutation.h
index 1afb11596bc6b..5a8672663753a 100644
--- a/libcxx/include/__algorithm/is_permutation.h
+++ b/libcxx/include/__algorithm/is_permutation.h
@@ -11,9 +11,13 @@
 #define _LIBCPP___ALGORITHM_IS_PERMUTATION_H
 
 #include <__algorithm/comp.h>
+#include <__algorithm/count_if.h>
+#include <__algorithm/find_if.h>
 #include <__algorithm/iterator_operations.h>
+#include <__algorithm/mismatch.h>
 #include <__config>
 #include <__functional/identity.h>
+#include <__functional/reference_wrapper.h>
 #include <__iterator/concepts.h>
 #include <__iterator/distance.h>
 #include <__iterator/iterator_traits.h>
@@ -79,31 +83,30 @@ _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool __is_permutation_impl(
     _Proj1&& __proj1,
     _Proj2&& __proj2) {
   using _D1 = __iter_diff_t<_Iter1>;
+  using _Ref1 = typename iterator_traits<_Iter1>::reference;
+  using _Ref2 = typename iterator_traits<_Iter2>::reference;
+  __identity __ident;
 
   for (auto __i = __first1; __i != __last1; ++__i) {
     //  Have we already counted the number of *__i in [f1, l1)?
-    auto __match = __first1;
-    for (; __match != __i; ++__match) {
-      if (std::__invoke(__pred, std::__invoke(__proj1, *__match), std::__invoke(__proj1, *__i)))
-        break;
-    }
+    auto __match = std::find_if(__first1, __i, [&](_Ref1 __x) -> bool {
+      return std::__invoke(__pred, std::__invoke(__proj1, __x), std::__invoke(__proj1, *__i));
+    });
 
     if (__match == __i) {
       // Count number of *__i in [f2, l2)
-      _D1 __c2 = 0;
-      for (auto __j = __first2; __j != __last2; ++__j) {
-        if (std::__invoke(__pred, std::__invoke(__proj1, *__i), std::__invoke(__proj2, *__j)))
-          ++__c2;
-      }
+      auto __predicate2 = [&](_Ref2 __x) -> bool {
+        return std::__invoke(__pred, std::__invoke(__proj1, *__i), std::__invoke(__proj2, __x));
+      };
+      _D1 __c2 = std::__count_if<_AlgPolicy>(__first2, __last2, __predicate2, __ident);
       if (__c2 == 0)
         return false;
 
-      // Count number of *__i in [__i, l1) (we can start with 1)
-      _D1 __c1 = 1;
-      for (auto __j = _IterOps<_AlgPolicy>::next(__i); __j != __last1; ++__j) {
-        if (std::__invoke(__pred, std::__invoke(__proj1, *__i), std::__invoke(__proj1, *__j)))
-          ++__c1;
-      }
+      // Count number of *__i in [__i, l1)
+      auto __predicate1 = [&](_Ref1 __x) -> bool {
+        return std::__invoke(__pred, std::__invoke(__proj1, *__i), std::__invoke(__proj1, __x));
+      };
+      _D1 __c1 = std::__count_if<_AlgPolicy>(__i, __last1, __predicate1, __ident);
       if (__c1 != __c2)
         return false;
     }
@@ -116,11 +119,10 @@ _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool __is_permutation_impl(
 template <class _AlgPolicy, class _ForwardIterator1, class _Sentinel1, class _ForwardIterator2, class _BinaryPredicate>
 [[__nodiscard__]] _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool __is_permutation(
     _ForwardIterator1 __first1, _Sentinel1 __last1, _ForwardIterator2 __first2, _BinaryPredicate&& __pred) {
-  // Shorten sequences as much as possible by lopping of any equal prefix.
-  for (; __first1 != __last1; ++__first1, (void)++__first2) {
-    if (!__pred(*__first1, *__first2))
-      break;
-  }
+  // Shorten sequences as much as possible by lopping off any equal prefix.
+  auto __result = std::mismatch(__first1, __last1, __first2, std::ref(__pred));
+  __first1      = __result.first;
+  __first2      = __result.second;
 
   if (__first1 == __last1)
     return true;
@@ -160,13 +162,11 @@ _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20 bool __is_permutation(
     _Proj1&& __proj1,
     _Proj2&& __proj2,
     /*_ConstTimeDistance=*/false_type) {
-  // Shorten sequences as much as possible by lopping of any equal prefix.
-  while (__first1 != __last1 && __first2 != __last2) {
-    if (!std::__invoke(__pred, std::__invoke(__proj1, *__first1), std::__invoke(__proj2, *__first2)))
-      break;
-    ++__first1;
-    ++__first2;
-  }
+  // Shorten sequences as much as possible by lopping off any equal prefix.
+  auto __result = std::__mismatch(__first1, __last1, __first2, __last2, __pred, __proj1, __proj2);
+
+  __first1 = __result.first;
+  __first2 = __result.second;
 
   if (__first1 == __last1)
     return __first2 == __last2;