diff --git a/src/AssociativeOpsTable.cpp b/src/AssociativeOpsTable.cpp
index 63b4add503e9..34fb40d93ab5 100644
--- a/src/AssociativeOpsTable.cpp
+++ b/src/AssociativeOpsTable.cpp
@@ -2,6 +2,7 @@
 #include "IRPrinter.h"
 
 #include <mutex>
+#include <tuple>
 
 namespace Halide {
 namespace Internal {
@@ -93,17 +94,8 @@ struct TableKey {
         return (types == other.types) && (root == other.root) && (dim == other.dim);
     }
     bool operator<(const TableKey &other) const {
-        if (types < other.types) {
-            return true;
-        } else if (types > other.types) {
-            return false;
-        }
-        if (root < other.root) {
-            return true;
-        } else if (root > other.root) {
-            return false;
-        }
-        return (dim < other.dim);
+        return std::tie(types, root, dim) <
+               std::tie(other.types, other.root, other.dim);
     }
 };
 
diff --git a/src/Schedule.h b/src/Schedule.h
index a72c52bbd59f..fe7eb70b23d2 100644
--- a/src/Schedule.h
+++ b/src/Schedule.h
@@ -7,6 +7,7 @@
 
 #include <map>
 #include <string>
+#include <tuple>
 #include <utility>
 #include <vector>
 
@@ -552,19 +553,9 @@ struct FusedPair {
                (var_name == other.var_name);
     }
     bool operator<(const FusedPair &other) const {
-        if (func_1 != other.func_1) {
-            return func_1 < other.func_1;
-        }
-        if (func_2 != other.func_2) {
-            return func_2 < other.func_2;
-        }
-        if (var_name != other.var_name) {
-            return var_name < other.var_name;
-        }
-        if (stage_1 != other.stage_1) {
-            return stage_1 < other.stage_1;
-        }
-        return stage_2 < other.stage_2;
+        return std::tie(func_1, func_2, var_name, stage_1, stage_2) <
+               std::tie(other.func_1, other.func_2, other.var_name,
+                        other.stage_1, other.stage_2);
     }
 };
 
diff --git a/src/StageStridedLoads.cpp b/src/StageStridedLoads.cpp
index 896a33b5193e..2912bbd2c726 100644
--- a/src/StageStridedLoads.cpp
+++ b/src/StageStridedLoads.cpp
@@ -1,4 +1,5 @@
-#include "StageStridedLoads.h"
+#include <tuple>
+
 #include "CSE.h"
 #include "ExprUsesVar.h"
 #include "IREquality.h"
@@ -7,6 +8,7 @@
 #include "IRVisitor.h"
 #include "Scope.h"
 #include "Simplify.h"
+#include "StageStridedLoads.h"
 #include "Substitute.h"
 
 namespace Halide {
@@ -39,31 +41,15 @@ class FindStridedLoads : public IRVisitor {
 
         bool operator<(const Key &other) const {
             // Check fields in order of cost to compare
-            if (stride < other.stride) {
-                return true;
-            } else if (stride > other.stride) {
-                return false;
-            } else if (lanes < other.lanes) {
-                return true;
-            } else if (lanes > other.lanes) {
-                return false;
-            } else if (scope < other.scope) {
-                return true;
-            } else if (scope > other.scope) {
-                return false;
-            } else if (allocation < other.allocation) {
-                return true;
-            } else if (allocation > other.allocation) {
-                return false;
-            } else if (type < other.type) {
-                return true;
-            } else if (other.type < type) {
-                return false;
-            } else if (buf < other.buf) {
+            auto lhs = std::tie(stride, lanes, scope, allocation, type, buf);
+            auto rhs = std::tie(other.stride, other.lanes, other.scope,
+                                other.allocation, other.type, other.buf);
+            if (lhs < rhs) {
                 return true;
-            } else if (buf > other.buf) {
+            } else if (rhs < lhs) {
                 return false;
             } else {
+                // base compares by graph equivalence, so it can't go in the tuple.
                 return graph_less_than(base, other.base);
             }
         }
diff --git a/src/autoschedulers/mullapudi2016/AutoSchedule.cpp b/src/autoschedulers/mullapudi2016/AutoSchedule.cpp
index 9005999bf1a8..fa98b49e19ee 100644
--- a/src/autoschedulers/mullapudi2016/AutoSchedule.cpp
+++ b/src/autoschedulers/mullapudi2016/AutoSchedule.cpp
@@ -6,6 +6,7 @@
 #include <map>
 #include <regex>
 #include <set>
+#include <tuple>
 #include <utility>
 
 namespace Halide {
@@ -203,22 +204,8 @@ struct DependenceAnalysis {
                    (only_regions_computed == other.only_regions_computed);
         }
         bool operator<(const RegionsRequiredQuery &other) const {
-            if (f < other.f) {
-                return true;
-            } else if (f > other.f) {
-                return false;
-            }
-            if (stage < other.stage) {
-                return true;
-            } else if (stage > other.stage) {
-                return false;
-            }
-            if (only_regions_computed < other.only_regions_computed) {
-                return true;
-            } else if (only_regions_computed > other.only_regions_computed) {
-                return false;
-            }
-            return prods < other.prods;
+            return std::tie(f, stage, only_regions_computed, prods) <
+                   std::tie(other.f, other.stage, other.only_regions_computed, other.prods);
         }
     };
     struct RegionsRequired {