diff --git a/src/main/java/org/mobilitydb/spark/catalyst/MobilitySparkExtensions.java b/src/main/java/org/mobilitydb/spark/catalyst/MobilitySparkExtensions.java
new file mode 100644
index 00000000..ad3ac775
--- /dev/null
+++ b/src/main/java/org/mobilitydb/spark/catalyst/MobilitySparkExtensions.java
@@ -0,0 +1,67 @@
+/*****************************************************************************
+ *
+ * This MobilityDB code is provided under The PostgreSQL License.
+ * Copyright (c) 2020-2026, Université libre de Bruxelles and MobilityDB
+ * contributors
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose, without fee, and without a written
+ * agreement is hereby retained provided that the above copyright notice and
+ * this paragraph and the following two paragraphs appear in all copies.
+ *
+ * IN NO EVENT SHALL UNIVERSITE LIBRE DE BRUXELLES BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
+ * DOCUMENTATION, EVEN IF UNIVERSITE LIBRE DE BRUXELLES HAS BEEN ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * UNIVERSITE LIBRE DE BRUXELLES SPECIFICALLY DISCLAIMS ANY WARRANTIES,
+ * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
+ * AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND UNIVERSITE LIBRE DE BRUXELLES HAS NO OBLIGATIONS
+ * TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ *****************************************************************************/
+
+package org.mobilitydb.spark.catalyst;
+
+import org.apache.spark.sql.SparkSession;
+import org.apache.spark.sql.SparkSessionExtensions;
+import org.apache.spark.sql.catalyst.plans.logical.LogicalPlan;
+import org.apache.spark.sql.catalyst.rules.Rule;
+
+import scala.Function1;
+import scala.runtime.AbstractFunction1;
+import scala.runtime.BoxedUnit;
+
+/**
+ * The Catalyst rules MobilitySpark adds to a Spark session, named in `spark.sql.extensions`:
+ *
+ * <pre>
+ *   SparkSession.builder().config("spark.sql.extensions",
+ *       "org.mobilitydb.spark.catalyst.MobilitySparkExtensions")
+ * </pre>
+ *
+ * Spark applies the named class to the session's extensions, as a Scala function of one argument,
+ * which this class provides through scala.runtime.AbstractFunction1.
+ *
+ * It injects {@link OrderConjunctsByCost}, which moves a MobilitySpark function behind the
+ * comparisons beside it in one conjunction. Spark holds no cost for a user-defined function, so
+ * its optimizer never sinks one: in a proximity join over trajectories the distance is evaluated
+ * on every pair the join enumerates, while the box and time comparisons that reject almost all of
+ * them run afterwards.
+ */
+public final class MobilitySparkExtensions
+        extends AbstractFunction1<SparkSessionExtensions, BoxedUnit> {
+
+    @Override
+    public BoxedUnit apply(SparkSessionExtensions extensions) {
+        extensions.injectOptimizerRule(new AbstractFunction1<SparkSession, Rule<LogicalPlan>>() {
+            @Override
+            public Rule<LogicalPlan> apply(SparkSession session) {
+                return new OrderConjunctsByCost();
+            }
+        });
+        return BoxedUnit.UNIT;
+    }
+}
diff --git a/src/main/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCost.java b/src/main/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCost.java
new file mode 100644
index 00000000..b62cc93f
--- /dev/null
+++ b/src/main/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCost.java
@@ -0,0 +1,139 @@
+/*****************************************************************************
+ *
+ * This MobilityDB code is provided under The PostgreSQL License.
+ * Copyright (c) 2020-2026, Université libre de Bruxelles and MobilityDB
+ * contributors
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose, without fee, and without a written
+ * agreement is hereby retained provided that the above copyright notice and
+ * this paragraph and the following two paragraphs appear in all copies.
+ *
+ * IN NO EVENT SHALL UNIVERSITE LIBRE DE BRUXELLES BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
+ * DOCUMENTATION, EVEN IF UNIVERSITE LIBRE DE BRUXELLES HAS BEEN ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * UNIVERSITE LIBRE DE BRUXELLES SPECIFICALLY DISCLAIMS ANY WARRANTIES,
+ * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
+ * AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND UNIVERSITE LIBRE DE BRUXELLES HAS NO OBLIGATIONS
+ * TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ *****************************************************************************/
+
+package org.mobilitydb.spark.catalyst;
+
+import java.util.ArrayList;
+import java.util.List;
+
+import org.apache.spark.sql.catalyst.expressions.And;
+import org.apache.spark.sql.catalyst.expressions.Expression;
+import org.apache.spark.sql.catalyst.expressions.ScalaUDF;
+import org.apache.spark.sql.catalyst.plans.logical.Filter;
+import org.apache.spark.sql.catalyst.plans.logical.Join;
+import org.apache.spark.sql.catalyst.plans.logical.LogicalPlan;
+import org.apache.spark.sql.catalyst.rules.Rule;
+
+import scala.Option;
+import scala.runtime.AbstractPartialFunction;
+
+/**
+ * Moves every conjunct that calls a user-defined function behind the conjuncts that do not, in a
+ * join condition and in a filter.
+ *
+ * `AND` evaluates its operands in order and stops at the first false one, so a conjunct placed
+ * later is evaluated on fewer rows: the reordering can only reduce the number of evaluations, and
+ * it never introduces one, which is why it preserves both the answer and the exceptions a
+ * user-defined function can raise. The relative order inside each of the two groups is kept, so a
+ * condition already in this shape is returned unchanged.
+ *
+ * Spark attaches no cost to a user-defined function, so its optimizer leaves the order the query
+ * produced. A proximity join over trajectories shows what that costs: the plan evaluates the
+ * distance between two trajectories on every pair the join enumerates, while the box and time
+ * comparisons in the same conjunction, which reject almost all of those pairs, run after it.
+ */
+public final class OrderConjunctsByCost extends Rule<LogicalPlan> {
+
+    @Override
+    public LogicalPlan apply(LogicalPlan plan) {
+        return plan.transformUp(new AbstractPartialFunction<LogicalPlan, LogicalPlan>() {
+            @Override
+            public boolean isDefinedAt(LogicalPlan node) {
+                return node instanceof Join || node instanceof Filter;
+            }
+
+            @Override
+            public LogicalPlan apply(LogicalPlan node) {
+                if (node instanceof Filter) {
+                    Filter filter = (Filter) node;
+                    Expression ordered = order(filter.condition());
+                    return ordered == filter.condition() ? filter
+                            : new Filter(ordered, filter.child());
+                }
+                Join join = (Join) node;
+                if (join.condition().isEmpty()) {
+                    return join;
+                }
+                Expression condition = join.condition().get();
+                Expression ordered = order(condition);
+                return ordered == condition ? join
+                        : new Join(join.left(), join.right(), join.joinType(),
+                                Option.apply(ordered), join.hint());
+            }
+        });
+    }
+
+    /** The same conjunction with the calls to a user-defined function last, or it unchanged */
+    private static Expression order(Expression condition) {
+        List<Expression> conjuncts = new ArrayList<>();
+        split(condition, conjuncts);
+        if (conjuncts.size() < 2) {
+            return condition;
+        }
+        List<Expression> plain = new ArrayList<>();
+        List<Expression> calls = new ArrayList<>();
+        for (Expression conjunct : conjuncts) {
+            // A conjunct that is not deterministic keeps its place: its position is observable
+            if (!conjunct.deterministic()) {
+                return condition;
+            }
+            (callsUdf(conjunct) ? calls : plain).add(conjunct);
+        }
+        if (calls.isEmpty() || plain.isEmpty()) {
+            return condition;
+        }
+        plain.addAll(calls);
+        Expression ordered = plain.get(0);
+        for (int i = 1; i < plain.size(); i++) {
+            ordered = new And(ordered, plain.get(i));
+        }
+        return ordered;
+    }
+
+    /** The conjuncts of an `AND` tree, left to right */
+    private static void split(Expression condition, List<Expression> into) {
+        if (condition instanceof And) {
+            And and = (And) condition;
+            split(and.left(), into);
+            split(and.right(), into);
+        } else {
+            into.add(condition);
+        }
+    }
+
+    /** Whether the expression calls a user-defined function anywhere inside it */
+    private static boolean callsUdf(Expression expression) {
+        if (expression instanceof ScalaUDF) {
+            return true;
+        }
+        scala.collection.Iterator<Expression> children = expression.children().iterator();
+        while (children.hasNext()) {
+            if (callsUdf(children.next())) {
+                return true;
+            }
+        }
+        return false;
+    }
+}
diff --git a/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostControlTest.java b/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostControlTest.java
new file mode 100644
index 00000000..694c6898
--- /dev/null
+++ b/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostControlTest.java
@@ -0,0 +1,91 @@
+/*****************************************************************************
+ *
+ * This MobilityDB code is provided under The PostgreSQL License.
+ * Copyright (c) 2020-2026, Université libre de Bruxelles and MobilityDB
+ * contributors
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose, without fee, and without a written
+ * agreement is hereby retained provided that the above copyright notice and
+ * this paragraph and the following two paragraphs appear in all copies.
+ *
+ * IN NO EVENT SHALL UNIVERSITE LIBRE DE BRUXELLES BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
+ * DOCUMENTATION, EVEN IF UNIVERSITE LIBRE DE BRUXELLES HAS BEEN ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * UNIVERSITE LIBRE DE BRUXELLES SPECIFICALLY DISCLAIMS ANY WARRANTIES,
+ * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
+ * AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND UNIVERSITE LIBRE DE BRUXELLES HAS NO OBLIGATIONS
+ * TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ *****************************************************************************/
+
+package org.mobilitydb.spark.catalyst;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.apache.spark.sql.Dataset;
+import org.apache.spark.sql.Row;
+import org.apache.spark.sql.SparkSession;
+import org.apache.spark.sql.api.java.UDF2;
+import org.apache.spark.sql.types.DataTypes;
+import org.junit.jupiter.api.AfterAll;
+import org.junit.jupiter.api.BeforeAll;
+import org.junit.jupiter.api.Test;
+
+/**
+ * The control for {@link OrderConjunctsByCostTest}: the same query in a session WITHOUT the
+ * extension keeps the call to the user-defined function ahead of the comparison, which is what
+ * makes the other class's assertion a statement about the rule rather than about Spark's own
+ * optimizer. A session carries its extensions from the builder and a JVM holds one Spark context,
+ * so the control needs its own class: surefire forks per class and does not reuse a fork.
+ */
+public class OrderConjunctsByCostControlTest {
+
+    private static SparkSession spark;
+
+    @BeforeAll
+    static void session() {
+        spark = SparkSession.builder().appName("order-conjuncts-control").master("local[1]")
+                .config("spark.ui.enabled", "false")
+                .getOrCreate();
+        spark.sparkContext().setLogLevel("WARN");
+        spark.udf().register("near", (UDF2<Long, Long, Boolean>) (a, b) -> Math.abs(a - b) <= 1,
+                DataTypes.BooleanType);
+        spark.range(0, 8).createOrReplaceTempView("t");
+    }
+
+    @AfterAll
+    static void stop() {
+        if (spark != null) {
+            spark.stop();
+        }
+    }
+
+    /** The condition of a join, as the optimized plan prints it */
+    private static String joinCondition(Dataset<Row> query) {
+        for (String line : query.queryExecution().optimizedPlan().toString().split("\n")) {
+            if (line.contains("Join ")) {
+                return line;
+            }
+        }
+        throw new AssertionError("no join in the optimized plan");
+    }
+
+    @Test
+    void withoutTheRuleTheCallStaysFirst() {
+        Dataset<Row> query = spark.sql(
+                "SELECT count(*) AS n FROM t a JOIN t b ON near(a.id, b.id) AND a.id < b.id");
+        String condition = joinCondition(query);
+        assertTrue(condition.indexOf("near(") < condition.indexOf(" < "),
+                "Spark orders the conjunction by itself, so the other test proves nothing: "
+                        + condition);
+        // b - a <= 1 and a < b hold for b = a + 1 alone, so seven pairs of the eight ids
+        assertEquals(7L, query.collectAsList().get(0).getLong(0),
+                "the query answers seven pairs either way");
+    }
+}
diff --git a/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostTest.java b/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostTest.java
new file mode 100644
index 00000000..778bb29c
--- /dev/null
+++ b/src/test/java/org/mobilitydb/spark/catalyst/OrderConjunctsByCostTest.java
@@ -0,0 +1,99 @@
+/*****************************************************************************
+ *
+ * This MobilityDB code is provided under The PostgreSQL License.
+ * Copyright (c) 2020-2026, Université libre de Bruxelles and MobilityDB
+ * contributors
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose, without fee, and without a written
+ * agreement is hereby retained provided that the above copyright notice and
+ * this paragraph and the following two paragraphs appear in all copies.
+ *
+ * IN NO EVENT SHALL UNIVERSITE LIBRE DE BRUXELLES BE LIABLE TO ANY PARTY FOR
+ * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+ * INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS
+ * DOCUMENTATION, EVEN IF UNIVERSITE LIBRE DE BRUXELLES HAS BEEN ADVISED OF
+ * THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * UNIVERSITE LIBRE DE BRUXELLES SPECIFICALLY DISCLAIMS ANY WARRANTIES,
+ * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
+ * AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE PROVIDED HEREUNDER IS
+ * ON AN "AS IS" BASIS, AND UNIVERSITE LIBRE DE BRUXELLES HAS NO OBLIGATIONS
+ * TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
+ *
+ *****************************************************************************/
+
+package org.mobilitydb.spark.catalyst;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.apache.spark.sql.Dataset;
+import org.apache.spark.sql.Row;
+import org.apache.spark.sql.SparkSession;
+import org.apache.spark.sql.api.java.UDF2;
+import org.apache.spark.sql.types.DataTypes;
+import org.junit.jupiter.api.AfterAll;
+import org.junit.jupiter.api.BeforeAll;
+import org.junit.jupiter.api.Test;
+
+/**
+ * The rule in a session: a join condition naming a user-defined function first is optimized into
+ * one naming it last, and the query answers what it answered before.
+ */
+public class OrderConjunctsByCostTest {
+
+    private static SparkSession spark;
+
+    @BeforeAll
+    static void session() {
+        spark = SparkSession.builder().appName("order-conjuncts").master("local[1]")
+                .config("spark.ui.enabled", "false")
+                .config("spark.sql.extensions", MobilitySparkExtensions.class.getName())
+                .getOrCreate();
+        spark.sparkContext().setLogLevel("WARN");
+        spark.udf().register("near", (UDF2<Long, Long, Boolean>) (a, b) -> Math.abs(a - b) <= 1,
+                DataTypes.BooleanType);
+        spark.range(0, 8).createOrReplaceTempView("t");
+    }
+
+    @AfterAll
+    static void stop() {
+        if (spark != null) {
+            spark.stop();
+        }
+    }
+
+    /** The condition of a join, as the optimized plan prints it */
+    private static String joinCondition(Dataset<Row> query) {
+        for (String line : query.queryExecution().optimizedPlan().toString().split("\n")) {
+            if (line.contains("Join ")) {
+                return line;
+            }
+        }
+        throw new AssertionError("no join in the optimized plan");
+    }
+
+    @Test
+    void theCallGoesBehindTheComparisons() {
+        Dataset<Row> query = spark.sql(
+                "SELECT count(*) AS n FROM t a JOIN t b ON near(a.id, b.id) AND a.id < b.id");
+        String condition = joinCondition(query);
+        assertTrue(condition.indexOf("near(") > condition.indexOf(" < "),
+                "the call to near stays ahead of the comparison: " + condition);
+        // b - a <= 1 and a < b hold for b = a + 1 alone, so seven pairs of the eight ids
+        assertEquals(7L, query.collectAsList().get(0).getLong(0),
+                "the reordering answers what the query answered");
+    }
+
+    @Test
+    void aConditionAlreadyOrderedIsLeftAlone() {
+        Dataset<Row> query = spark.sql(
+                "SELECT count(*) AS n FROM t a JOIN t b ON a.id < b.id AND near(a.id, b.id)");
+        String condition = joinCondition(query);
+        assertTrue(condition.indexOf("near(") > condition.indexOf(" < "),
+                "the call to near moved ahead of the comparison: " + condition);
+        assertEquals(7L, query.collectAsList().get(0).getLong(0),
+                "the query answers what it answered");
+    }
+}