diff --git a/src/ast/simplifiers/CMakeLists.txt b/src/ast/simplifiers/CMakeLists.txt
index d43bbe203..784e18314 100644
--- a/src/ast/simplifiers/CMakeLists.txt
+++ b/src/ast/simplifiers/CMakeLists.txt
@@ -38,6 +38,7 @@ z3_add_component(simplifiers
     blast_term_ite_simplifier.h
     elim_bounds.h
     elim_term_ite.h
+    normalize_bounds.h
     pull_nested_quantifiers.h
     push_ite.h
     randomizer.h
diff --git a/src/ast/simplifiers/normalize_bounds.h b/src/ast/simplifiers/normalize_bounds.h
new file mode 100644
index 000000000..361910c29
--- /dev/null
+++ b/src/ast/simplifiers/normalize_bounds.h
@@ -0,0 +1,109 @@
+/*++
+Copyright (c) 2011 Microsoft Corporation
+
+Module Name:
+
+    normalize_bounds.h
+
+Abstract:
+
+    Replace x with x' + l, when l <= x
+    where x' is a fresh variable.
+    Note that, after the transformation 0 <= x'.
+
+Author:
+
+    Leonardo de Moura (leonardo) 2011-10-21.
+    Ported to simplifier by Nikolaj Bjorner (nbjorner) 2024.
+
+--*/
+
+#pragma once
+
+#include "ast/simplifiers/dependent_expr_state.h"
+#include "ast/simplifiers/bound_manager.h"
+#include "ast/rewriter/th_rewriter.h"
+#include "ast/expr_substitution.h"
+#include "ast/arith_decl_plugin.h"
+
+class normalize_bounds_simplifier : public dependent_expr_simplifier {
+    arith_util  m_util;
+    th_rewriter m_rw;
+    bool        m_normalize_int_only;
+    params_ref  m_params;
+
+    bool is_target(expr* var, bound_manager& bm, rational& val) const {
+        bool strict;
+        return is_uninterp_const(var) &&
+               (!m_normalize_int_only || m_util.is_int(var)) &&
+               bm.has_lower(var, val, strict) &&
+               !val.is_zero();
+    }
+
+public:
+    normalize_bounds_simplifier(ast_manager& m, params_ref const& p, dependent_expr_state& s) :
+        dependent_expr_simplifier(m, s),
+        m_util(m),
+        m_rw(m, p),
+        m_normalize_int_only(true),
+        m_params(p) {
+        updt_params(p);
+    }
+
+    char const* name() const override { return "normalize-bounds"; }
+
+    bool supports_proofs() const override { return true; }
+
+    void updt_params(params_ref const& p) override {
+        m_params.append(p);
+        m_rw.updt_params(m_params);
+        m_normalize_int_only = m_params.get_bool("norm_int_only", true);
+    }
+
+    void collect_param_descrs(param_descrs& r) override {
+        r.insert("norm_int_only", CPK_BOOL,
+                 "normalize only the bounds of integer constants.", "true");
+    }
+
+    void reduce() override {
+        // pass 1: collect bounds over indices()
+        bound_manager bm(m);
+        for (unsigned idx : indices())
+            bm(m_fmls[idx].fml(), m_fmls[idx].dep(), nullptr);
+
+        // check whether there is anything to do
+        bool has_lower = false;
+        rational val;
+        for (expr* e : bm) {
+            if (is_target(e, bm, val)) {
+                has_lower = true;
+                break;
+            }
+        }
+        if (!has_lower)
+            return;
+
+        // pass 2: build substitution and apply
+        expr_substitution subst(m);
+        for (expr* x : bm) {
+            if (!is_target(x, bm, val))
+                continue;
+            sort* s = x->get_sort();
+            app* x_prime = m.mk_fresh_const(nullptr, s);
+            expr* def = m_util.mk_add(x_prime, m_util.mk_numeral(val, s));
+            subst.insert(x, def);
+            m_fmls.model_trail().hide(x_prime->get_decl());
+            m_fmls.model_trail().push(to_app(x)->get_decl(), def, nullptr, {});
+        }
+
+        m_rw.set_substitution(&subst);
+        expr_ref new_curr(m);
+        proof_ref new_pr(m);
+        for (unsigned idx : indices()) {
+            auto const& d = m_fmls[idx];
+            m_rw(d.fml(), new_curr, new_pr);
+            m_fmls.update(idx, dependent_expr(m, new_curr, mp(d.pr(), new_pr), d.dep()));
+        }
+        m_rw.set_substitution(nullptr);
+    }
+};
diff --git a/src/tactic/arith/normalize_bounds_tactic.h b/src/tactic/arith/normalize_bounds_tactic.h
index 4d456c38a..f597b556e 100644
--- a/src/tactic/arith/normalize_bounds_tactic.h
+++ b/src/tactic/arith/normalize_bounds_tactic.h
@@ -38,12 +38,23 @@ Note that, after the transformation $0 \leq x'$.
 #pragma once
 
 #include "util/params.h"
+#include "tactic/dependent_expr_state_tactic.h"
+#include "ast/simplifiers/normalize_bounds.h"
 class ast_manager;
 class tactic;
 
 tactic * mk_normalize_bounds_tactic(ast_manager & m, params_ref const & p = params_ref());
 
+inline tactic* mk_normalize_bounds2_tactic(ast_manager& m, params_ref const& p = params_ref()) {
+    return alloc(dependent_expr_state_tactic, m, p,
+        [](auto& m, auto& p, auto& s) -> dependent_expr_simplifier* {
+            return alloc(normalize_bounds_simplifier, m, p, s);
+        });
+}
+
 /*
   ADD_TACTIC("normalize-bounds", "replace a variable x with lower bound k <= x with x' = x - k.", "mk_normalize_bounds_tactic(m, p)")
+  ADD_TACTIC("normalize-bounds2", "replace a variable x with lower bound k <= x with x' = x - k.", "mk_normalize_bounds2_tactic(m, p)")
+  ADD_SIMPLIFIER("normalize-bounds", "replace a variable x with lower bound k <= x with x' = x - k.", "alloc(normalize_bounds_simplifier, m, p, s)")
 */