diff --git a/llvm/include/llvm/Analysis/InstructionSimplify.h b/llvm/include/llvm/Analysis/InstructionSimplify.h
--- a/llvm/include/llvm/Analysis/InstructionSimplify.h
+++ b/llvm/include/llvm/Analysis/InstructionSimplify.h
@@ -299,6 +299,10 @@
                      const SimplifyQuery &Q);
 
 /// Given a callsite, fold the result or return null.
+///
+/// \note A call with declared side effect may be simplified into a value
+/// without such. It happens if simplification code deduces that side effect
+/// is actually absent.
 Value *SimplifyCall(CallBase *Call, const SimplifyQuery &Q);
 
 /// Given an operand for a Freeze, see if we can fold the result.
diff --git a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
--- a/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
+++ b/llvm/lib/Transforms/InstCombine/InstCombineCalls.cpp
@@ -1187,6 +1187,16 @@
       return NewCall;
   }
 
+  // Unused constrained FP intrinsic calls may have declared side effect, which
+  // actually absent. If SimplifyCall returns a replacement for such call,
+  // assume side effect is absent and the call may be removed.
+  if (CI.use_empty() && isa<ConstrainedFPIntrinsic>(CI)) {
+    if (SimplifyCall(&CI, SQ.getWithInstruction(&CI))) {
+      eraseInstFromFunction(CI);
+      return nullptr;
+    }
+  }
+
   Intrinsic::ID IID = II->getIntrinsicID();
   switch (IID) {
   case Intrinsic::objectsize:
diff --git a/llvm/test/Transforms/InstCombine/constrained.ll b/llvm/test/Transforms/InstCombine/constrained.ll
new file mode 100644
--- /dev/null
+++ b/llvm/test/Transforms/InstCombine/constrained.ll
@@ -0,0 +1,125 @@
+; NOTE: Assertions have been autogenerated by utils/update_test_checks.py
+; RUN: opt -S -instcombine %s | FileCheck %s
+
+; Treatment of operation with unused result.
+
+; If operation does not raise exceptions, it may be removed even in strict mode.
+define float @f_unused_precise() #0 {
+; CHECK-LABEL: @f_unused_precise(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fadd.f32(float 1.0, float 1.0, metadata !"round.upward", metadata !"fpexcept.strict") #0
+  ret float 1.0
+}
+
+; If operation raises exceptions, it cannot be removed in strict mode.
+define float @f_unused_strict() #0 {
+; CHECK-LABEL: @f_unused_strict(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[RESULT:%.*]] = call float @llvm.experimental.constrained.fdiv.f32(float 1.000000e+00, float 3.000000e+00, metadata !"round.tonearest", metadata !"fpexcept.strict") #[[ATTR0:[0-9]+]]
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.tonearest", metadata !"fpexcept.strict") #0
+  ret float 1.0
+}
+
+; If operation raises exceptions, it can be removed in non-strict mode.
+define float @f_unused_ignore() #0 {
+; CHECK-LABEL: @f_unused_ignore(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.towardzero", metadata !"fpexcept.ignore") #0
+  ret float 1.0
+}
+
+; If operation raises exceptions, it can be removed in non-strict mode even if rounding mode is dynamic.
+define float @f_unused_dynamic_ignore() #0 {
+; CHECK-LABEL: @f_unused_dynamic_ignore(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.dynamic", metadata !"fpexcept.ignore") #0
+  ret float 1.0
+}
+
+; If operation raises exceptions, it can be removed in "maytrap" mode.
+define float @f_unused_maytrap() #0 {
+; CHECK-LABEL: @f_unused_maytrap(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 1.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.tonearest", metadata !"fpexcept.maytrap") #0
+  ret float 1.0
+}
+
+; Constant evaluation.
+
+; If operation does not raise exceptions, it may be folded even in strict mode.
+define float @f_eval_precise() #0 {
+; CHECK-LABEL: @f_eval_precise(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 2.000000e+00
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fadd.f32(float 1.0, float 1.0, metadata !"round.upward", metadata !"fpexcept.strict") #0
+  ret float %result
+}
+
+; If operation raises exceptions, it cannot be folded in strict mode.
+define float @f_eval_strict() #0 {
+; CHECK-LABEL: @f_eval_strict(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[RESULT:%.*]] = call float @llvm.experimental.constrained.fdiv.f32(float 1.000000e+00, float 3.000000e+00, metadata !"round.upward", metadata !"fpexcept.strict") #[[ATTR0]]
+; CHECK-NEXT:    ret float [[RESULT]]
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.upward", metadata !"fpexcept.strict") #0
+  ret float %result
+}
+
+; If operation raises exceptions, it can be folded in non-strict mode.
+define float @f_eval_ignore() #0 {
+; CHECK-LABEL: @f_eval_ignore(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 0x3FD5555540000000
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.downward", metadata !"fpexcept.ignore") #0
+  ret float %result
+}
+
+; if result is imprecise, it cannot be folded if rounding mode is dynamic.
+define float @f_eval_dynamic_ignore() #0 {
+; CHECK-LABEL: @f_eval_dynamic_ignore(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    [[RESULT:%.*]] = call float @llvm.experimental.constrained.fdiv.f32(float 1.000000e+00, float 3.000000e+00, metadata !"round.dynamic", metadata !"fpexcept.ignore") #[[ATTR0]]
+; CHECK-NEXT:    ret float [[RESULT]]
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.dynamic", metadata !"fpexcept.ignore") #0
+  ret float %result
+}
+
+; If result is imprecise and rounding mode is not dynamic, operation can be folded in "maytrap" mode.
+define float @f_eval_maytrap() #0 {
+; CHECK-LABEL: @f_eval_maytrap(
+; CHECK-NEXT:  entry:
+; CHECK-NEXT:    ret float 0x3FD5555560000000
+;
+entry:
+  %result = call float @llvm.experimental.constrained.fdiv.f32(float 1.0, float 3.0, metadata !"round.tonearest", metadata !"fpexcept.maytrap") #0
+  ret float %result
+}
+
+
+declare float @llvm.experimental.constrained.fadd.f32(float, float, metadata, metadata)
+declare float @llvm.experimental.constrained.fdiv.f32(float, float, metadata, metadata)
+
+attributes #0 = { strictfp }