diff --git a/llvm/lib/Analysis/ValueTracking.cpp b/llvm/lib/Analysis/ValueTracking.cpp
index 6434de3e463c9..7660009b088d0 100644
--- a/llvm/lib/Analysis/ValueTracking.cpp
+++ b/llvm/lib/Analysis/ValueTracking.cpp
@@ -8857,20 +8857,20 @@ isImpliedCondMatchingOperands(CmpInst::Predicate LPred,
   return std::nullopt;
 }
 
-/// Return true if "icmp LPred X, LC" implies "icmp RPred X, RC" is true.
-/// Return false if "icmp LPred X, LC" implies "icmp RPred X, RC" is false.
+/// Return true if "icmp LPred X, LCR" implies "icmp RPred X, RCR" is true.
+/// Return false if "icmp LPred X, LCR" implies "icmp RPred X, RCR" is false.
 /// Otherwise, return std::nullopt if we can't infer anything.
-static std::optional<bool> isImpliedCondCommonOperandWithConstants(
-    CmpInst::Predicate LPred, const APInt &LC, CmpInst::Predicate RPred,
-    const APInt &RC) {
-  ConstantRange DomCR = ConstantRange::makeExactICmpRegion(LPred, LC);
-  ConstantRange CR = ConstantRange::makeExactICmpRegion(RPred, RC);
-  ConstantRange Intersection = DomCR.intersectWith(CR);
-  ConstantRange Difference = DomCR.difference(CR);
-  if (Intersection.isEmptySet())
-    return false;
-  if (Difference.isEmptySet())
+static std::optional<bool> isImpliedCondCommonOperandWithCR(
+    CmpInst::Predicate LPred, const ConstantRange &LCR,
+    CmpInst::Predicate RPred, const ConstantRange &RCR) {
+  ConstantRange DomCR = ConstantRange::makeAllowedICmpRegion(LPred, LCR);
+  // If all true values for lhs and true for rhs, lhs implies rhs
+  if (DomCR.icmp(RPred, RCR))
     return true;
+
+  // If there is no overlap, lhs implies not rhs
+  if (DomCR.icmp(CmpInst::getInversePredicate(RPred), RCR))
+    return false;
   return std::nullopt;
 }
 
@@ -8910,11 +8910,29 @@ static std::optional<bool> isImpliedCondICmps(const ICmpInst *LHS,
     }
   }
 
-  // Can we infer anything when the 0-operands match and the 1-operands are
-  // constants (not necessarily matching)?
-  const APInt *LC, *RC;
-  if (L0 == R0 && match(L1, m_APInt(LC)) && match(R1, m_APInt(RC)))
-    return isImpliedCondCommonOperandWithConstants(LPred, *LC, RPred, *RC);
+  // See if we can infer anything if operand-0 matches and we have at least one
+  // constant.
+  const APInt *Unused;
+  if (L0 == R0 && (match(L1, m_APInt(Unused)) || match(R1, m_APInt(Unused)))) {
+    // Potential TODO: We could also further use the constant range of L0/R0 to
+    // further constraint the constant ranges. At the moment this leads to
+    // several regressions related to not transforming `multi_use(A + C0) eq/ne
+    // C1` (see discussion: D58633).
+    ConstantRange LCR = computeConstantRange(
+        L1, ICmpInst::isSigned(LPred), /* UseInstrInfo=*/true, /*AC=*/nullptr,
+        /*CxtI=*/nullptr, /*DT=*/nullptr, MaxAnalysisRecursionDepth - 1);
+    ConstantRange RCR = computeConstantRange(
+        R1, ICmpInst::isSigned(RPred), /* UseInstrInfo=*/true, /*AC=*/nullptr,
+        /*CxtI=*/nullptr, /*DT=*/nullptr, MaxAnalysisRecursionDepth - 1);
+    // Even if L1/R1 are not both constant, we can still sometimes deduce
+    // relationship from a single constant. For example X u> Y implies X != 0.
+    if (auto R = isImpliedCondCommonOperandWithCR(LPred, LCR, RPred, RCR))
+      return R;
+    // If both L1/R1 were exact constant ranges and we didn't get anything
+    // here, we won't be able to deduce this.
+    if (match(L1, m_APInt(Unused)) && match(R1, m_APInt(Unused)))
+      return std::nullopt;
+  }
 
   // Can we infer anything when the two compares have matching operands?
   if (L0 == R0 && L1 == R1)
diff --git a/llvm/test/Transforms/InstCombine/icmp-select-implies-common-op.ll b/llvm/test/Transforms/InstCombine/icmp-select-implies-common-op.ll
index bacdb54f787d6..8d393a7ae28c9 100644
--- a/llvm/test/Transforms/InstCombine/icmp-select-implies-common-op.ll
+++ b/llvm/test/Transforms/InstCombine/icmp-select-implies-common-op.ll
@@ -29,10 +29,10 @@ define i1 @sgt_3_impliesT_sgt_2(i8 %x, i8 %y) {
 
 define i1 @sgt_x_impliesF_eq_smin_todo(i8 %x, i8 %y, i8 %z) {
 ; CHECK-LABEL: @sgt_x_impliesF_eq_smin_todo(
-; CHECK-NEXT:    [[CMP:%.*]] = icmp sgt i8 [[X:%.*]], [[Z:%.*]]
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 -128, i8 [[Y:%.*]]
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i8 [[SEL]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP2]]
+; CHECK-NEXT:    [[CMP:%.*]] = icmp sle i8 [[X:%.*]], [[Z:%.*]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp eq i8 [[SEL:%.*]], [[X]]
+; CHECK-NEXT:    [[CMP3:%.*]] = select i1 [[CMP]], i1 [[CMP2]], i1 false
+; CHECK-NEXT:    ret i1 [[CMP3]]
 ;
   %cmp = icmp sgt i8 %x, %z
   %sel = select i1 %cmp, i8 -128, i8 %y
@@ -43,9 +43,9 @@ define i1 @sgt_x_impliesF_eq_smin_todo(i8 %x, i8 %y, i8 %z) {
 define i1 @slt_x_impliesT_ne_smin_todo(i8 %x, i8 %y, i8 %z) {
 ; CHECK-LABEL: @slt_x_impliesT_ne_smin_todo(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp slt i8 [[X:%.*]], [[Z:%.*]]
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 127, i8 [[Y:%.*]]
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i8 [[SEL]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP2]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i8 [[SEL:%.*]], [[X]]
+; CHECK-NEXT:    [[CMP3:%.*]] = select i1 [[CMP]], i1 true, i1 [[CMP2]]
+; CHECK-NEXT:    ret i1 [[CMP3]]
 ;
   %cmp = icmp slt i8 %x, %z
   %sel = select i1 %cmp, i8 127, i8 %y
@@ -56,9 +56,9 @@ define i1 @slt_x_impliesT_ne_smin_todo(i8 %x, i8 %y, i8 %z) {
 define i1 @ult_x_impliesT_eq_umax_todo(i8 %x, i8 %y, i8 %z) {
 ; CHECK-LABEL: @ult_x_impliesT_eq_umax_todo(
 ; CHECK-NEXT:    [[CMP:%.*]] = icmp ugt i8 [[Z:%.*]], [[X:%.*]]
-; CHECK-NEXT:    [[SEL:%.*]] = select i1 [[CMP]], i8 -1, i8 [[Y:%.*]]
-; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i8 [[SEL]], [[X]]
-; CHECK-NEXT:    ret i1 [[CMP2]]
+; CHECK-NEXT:    [[CMP2:%.*]] = icmp ne i8 [[SEL:%.*]], [[X]]
+; CHECK-NEXT:    [[CMP3:%.*]] = select i1 [[CMP]], i1 true, i1 [[CMP2]]
+; CHECK-NEXT:    ret i1 [[CMP3]]
 ;
   %cmp = icmp ugt i8 %z, %x
   %sel = select i1 %cmp, i8 255, i8 %y
diff --git a/llvm/test/Transforms/InstCombine/range-check.ll b/llvm/test/Transforms/InstCombine/range-check.ll
index 0d138b6ba7e79..210e57c1d1fe4 100644
--- a/llvm/test/Transforms/InstCombine/range-check.ll
+++ b/llvm/test/Transforms/InstCombine/range-check.ll
@@ -340,11 +340,7 @@ define i1 @negative4_logical(i32 %x, i32 %n) {
 
 define i1 @negative5(i32 %x, i32 %n) {
 ; CHECK-LABEL: @negative5(
-; CHECK-NEXT:    [[NN:%.*]] = and i32 [[N:%.*]], 2147483647
-; CHECK-NEXT:    [[A:%.*]] = icmp sgt i32 [[NN]], [[X:%.*]]
-; CHECK-NEXT:    [[B:%.*]] = icmp sgt i32 [[X]], -1
-; CHECK-NEXT:    [[C:%.*]] = or i1 [[A]], [[B]]
-; CHECK-NEXT:    ret i1 [[C]]
+; CHECK-NEXT:    ret i1 true
 ;
   %nn = and i32 %n, 2147483647
   %a = icmp slt i32 %x, %nn
@@ -355,11 +351,7 @@ define i1 @negative5(i32 %x, i32 %n) {
 
 define i1 @negative5_logical(i32 %x, i32 %n) {
 ; CHECK-LABEL: @negative5_logical(
-; CHECK-NEXT:    [[NN:%.*]] = and i32 [[N:%.*]], 2147483647
-; CHECK-NEXT:    [[A:%.*]] = icmp sgt i32 [[NN]], [[X:%.*]]
-; CHECK-NEXT:    [[B:%.*]] = icmp sgt i32 [[X]], -1
-; CHECK-NEXT:    [[C:%.*]] = or i1 [[A]], [[B]]
-; CHECK-NEXT:    ret i1 [[C]]
+; CHECK-NEXT:    ret i1 true
 ;
   %nn = and i32 %n, 2147483647
   %a = icmp slt i32 %x, %nn
diff --git a/llvm/test/Transforms/LoopVectorize/X86/pr23997.ll b/llvm/test/Transforms/LoopVectorize/X86/pr23997.ll
index 3d7153e66fc66..8800fa26f067c 100644
--- a/llvm/test/Transforms/LoopVectorize/X86/pr23997.ll
+++ b/llvm/test/Transforms/LoopVectorize/X86/pr23997.ll
@@ -12,8 +12,7 @@ define void @foo(ptr addrspace(1) align 8 dereferenceable_or_null(16), ptr addrs
 ; CHECK:       preheader:
 ; CHECK-NEXT:    [[DOT10:%.*]] = getelementptr inbounds i8, ptr addrspace(1) [[TMP0:%.*]], i64 16
 ; CHECK-NEXT:    [[DOT12:%.*]] = getelementptr inbounds i8, ptr addrspace(1) [[TMP1:%.*]], i64 16
-; CHECK-NEXT:    [[UMAX2:%.*]] = call i64 @llvm.umax.i64(i64 [[TMP2:%.*]], i64 1)
-; CHECK-NEXT:    [[MIN_ITERS_CHECK:%.*]] = icmp ult i64 [[TMP2]], 16
+; CHECK-NEXT:    [[MIN_ITERS_CHECK:%.*]] = icmp ult i64 [[TMP2:%.*]], 16
 ; CHECK-NEXT:    br i1 [[MIN_ITERS_CHECK]], label [[SCALAR_PH:%.*]], label [[VECTOR_MEMCHECK:%.*]]
 ; CHECK:       vector.memcheck:
 ; CHECK-NEXT:    [[TMP3:%.*]] = shl i64 [[TMP2]], 3
@@ -25,7 +24,7 @@ define void @foo(ptr addrspace(1) align 8 dereferenceable_or_null(16), ptr addrs
 ; CHECK-NEXT:    [[FOUND_CONFLICT:%.*]] = and i1 [[BOUND0]], [[BOUND1]]
 ; CHECK-NEXT:    br i1 [[FOUND_CONFLICT]], label [[SCALAR_PH]], label [[VECTOR_PH:%.*]]
 ; CHECK:       vector.ph:
-; CHECK-NEXT:    [[N_VEC:%.*]] = and i64 [[UMAX2]], -16
+; CHECK-NEXT:    [[N_VEC:%.*]] = and i64 [[TMP2]], -16
 ; CHECK-NEXT:    br label [[VECTOR_BODY:%.*]]
 ; CHECK:       vector.body:
 ; CHECK-NEXT:    [[INDEX:%.*]] = phi i64 [ 0, [[VECTOR_PH]] ], [ [[INDEX_NEXT:%.*]], [[VECTOR_BODY]] ]
@@ -49,7 +48,7 @@ define void @foo(ptr addrspace(1) align 8 dereferenceable_or_null(16), ptr addrs
 ; CHECK-NEXT:    [[TMP13:%.*]] = icmp eq i64 [[INDEX_NEXT]], [[N_VEC]]
 ; CHECK-NEXT:    br i1 [[TMP13]], label [[MIDDLE_BLOCK:%.*]], label [[VECTOR_BODY]], !llvm.loop [[LOOP5:![0-9]+]]
 ; CHECK:       middle.block:
-; CHECK-NEXT:    [[CMP_N:%.*]] = icmp eq i64 [[UMAX2]], [[N_VEC]]
+; CHECK-NEXT:    [[CMP_N:%.*]] = icmp eq i64 [[N_VEC]], [[TMP2]]
 ; CHECK-NEXT:    br i1 [[CMP_N]], label [[LOOPEXIT:%.*]], label [[SCALAR_PH]]
 ; CHECK:       scalar.ph:
 ; CHECK-NEXT:    [[BC_RESUME_VAL:%.*]] = phi i64 [ [[N_VEC]], [[MIDDLE_BLOCK]] ], [ 0, [[PREHEADER]] ], [ 0, [[VECTOR_MEMCHECK]] ]
diff --git a/llvm/test/Transforms/NewGVN/pr35125.ll b/llvm/test/Transforms/NewGVN/pr35125.ll
index 9a96594e3446d..6724538a5a7f2 100644
--- a/llvm/test/Transforms/NewGVN/pr35125.ll
+++ b/llvm/test/Transforms/NewGVN/pr35125.ll
@@ -18,15 +18,12 @@ define i32 @main() #0 {
 ; CHECK-NEXT:    [[CMP2:%.*]] = icmp ult i32 [[STOREMERGE]], [[PHIOFOPS]]
 ; CHECK-NEXT:    br i1 [[CMP2]], label [[IF_THEN3:%.*]], label [[IF_END6:%.*]]
 ; CHECK:       if.then3:
-; CHECK-NEXT:    [[TOBOOL:%.*]] = icmp eq i32 [[STOREMERGE]], -1
-; CHECK-NEXT:    br i1 [[TOBOOL]], label [[LOR_RHS:%.*]], label [[LOR_END:%.*]]
+; CHECK-NEXT:    br i1 false, label [[LOR_RHS:%.*]], label [[LOR_END:%.*]]
 ; CHECK:       lor.rhs:
-; CHECK-NEXT:    [[TOBOOL5:%.*]] = icmp ne i32 [[TMP0]], 0
-; CHECK-NEXT:    [[PHITMP:%.*]] = zext i1 [[TOBOOL5]] to i32
+; CHECK-NEXT:    store i8 poison, ptr null, align 1
 ; CHECK-NEXT:    br label [[LOR_END]]
 ; CHECK:       lor.end:
-; CHECK-NEXT:    [[TMP1:%.*]] = phi i32 [ 1, [[IF_THEN3]] ], [ [[PHITMP]], [[LOR_RHS]] ]
-; CHECK-NEXT:    store i32 [[TMP1]], ptr @a, align 4
+; CHECK-NEXT:    store i32 1, ptr @a, align 4
 ; CHECK-NEXT:    br label [[IF_END6]]
 ; CHECK:       if.end6:
 ; CHECK-NEXT:    [[TMP2:%.*]] = load i32, ptr @a, align 4