diff --git a/src/Interpreters/ExtractExpressionInfoVisitor.cpp b/src/Interpreters/ExtractExpressionInfoVisitor.cpp
index c730f49fe90..75e94de0db5 100644
--- a/src/Interpreters/ExtractExpressionInfoVisitor.cpp
+++ b/src/Interpreters/ExtractExpressionInfoVisitor.cpp
@@ -27,8 +27,14 @@ void ExpressionInfoMatcher::visit(const ASTFunction & ast_function, const ASTPtr
         const auto & function = FunctionFactory::instance().tryGet(ast_function.name, data.context);
 
         /// Skip lambda, tuple and other special functions
-        if (function && function->isStateful())
-            data.is_stateful_function = true;
+        if (function)
+        {
+            if (function->isStateful())
+                data.is_stateful_function = true;
+
+            if (!function->isDeterministicInScopeOfQuery())
+                data.is_deterministic_function = false;
+        }
     }
 }
 
diff --git a/src/Interpreters/ExtractExpressionInfoVisitor.h b/src/Interpreters/ExtractExpressionInfoVisitor.h
index a412704edcc..0cb43e5b00a 100644
--- a/src/Interpreters/ExtractExpressionInfoVisitor.h
+++ b/src/Interpreters/ExtractExpressionInfoVisitor.h
@@ -21,6 +21,7 @@ struct ExpressionInfoMatcher
         bool is_array_join = false;
         bool is_stateful_function = false;
         bool is_aggregate_function = false;
+        bool is_deterministic_function = true;
         std::unordered_set<size_t> unique_reference_tables_pos = {};
     };
 
diff --git a/src/Interpreters/PredicateExpressionsOptimizer.cpp b/src/Interpreters/PredicateExpressionsOptimizer.cpp
index 86bdec628cd..d401e51a392 100644
--- a/src/Interpreters/PredicateExpressionsOptimizer.cpp
+++ b/src/Interpreters/PredicateExpressionsOptimizer.cpp
@@ -90,8 +90,8 @@ std::vector<ASTs> PredicateExpressionsOptimizer::extractTablesPredicates(const A
         ExpressionInfoVisitor::Data expression_info{.context = context, .tables = tables_with_columns};
         ExpressionInfoVisitor(expression_info).visit(predicate_expression);
 
-        if (expression_info.is_stateful_function)
-            return {};   /// give up the optimization when the predicate contains stateful function
+        if (expression_info.is_stateful_function || !expression_info.is_deterministic_function)
+            return {};   /// Not optimized when predicate contains state function or indeterministic function
 
         if (!expression_info.is_array_join)
         {
diff --git a/tests/queries/0_stateless/01582_deterministic_function_with_predicate.reference b/tests/queries/0_stateless/01582_deterministic_function_with_predicate.reference
new file mode 100644
index 00000000000..a1b4bfdcc03
--- /dev/null
+++ b/tests/queries/0_stateless/01582_deterministic_function_with_predicate.reference
@@ -0,0 +1,11 @@
+SELECT count()
+FROM 
+(
+    SELECT number
+    FROM 
+    (
+        SELECT number
+        FROM numbers(1000000)
+    )
+    WHERE rand64() < (0.01 * 18446744073709552000.)
+)
diff --git a/tests/queries/0_stateless/01582_deterministic_function_with_predicate.sql b/tests/queries/0_stateless/01582_deterministic_function_with_predicate.sql
new file mode 100644
index 00000000000..9f64c292a65
--- /dev/null
+++ b/tests/queries/0_stateless/01582_deterministic_function_with_predicate.sql
@@ -0,0 +1 @@
+EXPLAIN SYNTAX SELECT count(*) FROM ( SELECT number FROM ( SELECT number FROM numbers(1000000) ) WHERE rand64() < (0.01 * 18446744073709552000.));