diff --git a/doc/advanced_tutorials.rst b/doc/advanced_tutorials.rst
index ad1d9a419..02833671f 100644
--- a/doc/advanced_tutorials.rst
+++ b/doc/advanced_tutorials.rst
@@ -5,7 +5,7 @@ Advanced tutorials
 
 .. important::
 
-  More :ref:`tutorials <hypy:adv_tutorials>` and :ref:`examples <hypy:examples>` are available in the documentation
+  More tutorials and examples are available in the documentation
   of heyoka's `Python bindings <https://bluescarni.github.io/heyoka.py>`__.
 
 In this section we will show some of heyoka's more advanced functionalities,
diff --git a/doc/basic_tutorials.rst b/doc/basic_tutorials.rst
index 5c69e1a2f..951a8d6ef 100644
--- a/doc/basic_tutorials.rst
+++ b/doc/basic_tutorials.rst
@@ -5,7 +5,7 @@ Basic tutorials
 
 .. important::
 
-   More :ref:`tutorials <hypy:basic_tutorials>` and :ref:`examples <hypy:examples>` are available in the documentation
+   More tutorials and examples are available in the documentation
    of heyoka's `Python bindings <https://bluescarni.github.io/heyoka.py>`__.
 
 The code snippets in these tutorials assume the inclusion of the
diff --git a/doc/changelog.rst b/doc/changelog.rst
index 7c605e168..9a8e42762 100644
--- a/doc/changelog.rst
+++ b/doc/changelog.rst
@@ -21,6 +21,9 @@ New
 Changes
 ~~~~~~~
 
+- Substantial speedups in the computation of first-order derivatives
+  with respect to many variables/parameters
+  (`#358 <https://github.com/bluescarni/heyoka/pull/358>`__).
 - Substantial performance improvements in the computation of
   derivative tensors of large expressions with a high degree
   of internal redundancy
diff --git a/src/expression_diff.cpp b/src/expression_diff.cpp
index 8c95ddc9f..80d3cfa3e 100644
--- a/src/expression_diff.cpp
+++ b/src/expression_diff.cpp
@@ -797,7 +797,10 @@ void diff_tensors_reverse_impl(
 
     // Helpers to ease the access to the active member of the local_diff variant.
     // NOTE: if used incorrectly, these will throw at runtime.
-    auto local_dmap = [&local_diff]() -> diff_map_t & { return std::get<diff_map_t>(local_diff); };
+    // NOTE: currently local_dmap is never used because the heuristic
+    // for deciding between forward and reverse mode prevents reverse mode
+    // from being used for order > 1.
+    auto local_dmap = [&local_diff]() -> diff_map_t & { return std::get<diff_map_t>(local_diff); }; // LCOV_EXCL_LINE
     auto local_dvec = [&local_diff]() -> diff_vec_t & { return std::get<diff_vec_t>(local_diff); };
 
     // Cache the number of diff arguments.
@@ -959,6 +962,7 @@ void diff_tensors_reverse_impl(
 
                 local_dvec().emplace_back(tmp_v_idx, std::move(cur_der));
             } else {
+                // LCOV_EXCL_START
                 // Check if we already computed this derivative.
                 if (const auto it = local_dmap().find(tmp_v_idx); it == local_dmap().end()) {
                     // The derivative is new. If the diff argument is present in the
@@ -973,6 +977,7 @@ void diff_tensors_reverse_impl(
                     [[maybe_unused]] const auto [_, flag] = local_dmap().try_emplace(tmp_v_idx, std::move(cur_der));
                     assert(flag);
                 }
+                // LCOV_EXCL_STOP
             }
         }