diff --git a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
--- a/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
+++ b/flang/lib/Optimizer/Builder/IntrinsicCall.cpp
@@ -733,8 +733,9 @@
                              mlir::FunctionType mathLibFuncType,
                              llvm::ArrayRef<mlir::Value> args) {
   mlir::Value result;
-  if (disableMlirComplex ||
-      (mathRuntimeVersion == preciseVersion && !mathLibFuncName.empty())) {
+  bool hasApproxFunc = mlir::arith::bitEnumContainsAny(
+      builder.getFastMathFlags(), mlir::arith::FastMathFlags::afn);
+  if ((disableMlirComplex || !hasApproxFunc) && !mathLibFuncName.empty()) {
     result = genLibCall(builder, loc, mathLibFuncName, mathLibFuncType, args);
     LLVM_DEBUG(result.dump(); llvm::dbgs() << "\n");
     return result;
@@ -1204,8 +1205,9 @@
   for (auto iter = range.first; iter != range.second && iter; ++iter) {
     const auto &impl = *iter;
     auto implType = impl.typeGenerator(builder.getContext(), builder);
-    if (funcType == implType)
+    if (funcType == implType) {
       return &impl; // exact match
+    }
 
     FunctionDistance distance(funcType, implType);
     if (distance.isSmallerThan(bestMatchDistance)) {
diff --git a/flang/test/Lower/HLFIR/binary-ops.f90 b/flang/test/Lower/HLFIR/binary-ops.f90
--- a/flang/test/Lower/HLFIR/binary-ops.f90
+++ b/flang/test/Lower/HLFIR/binary-ops.f90
@@ -168,10 +168,8 @@
 ! CHECK:  %[[VAL_5:.*]]:2 = hlfir.declare %{{.*}}z"} : (!fir.ref<!fir.complex<4>>) -> (!fir.ref<!fir.complex<4>>, !fir.ref<!fir.complex<4>>)
 ! CHECK:  %[[VAL_6:.*]] = fir.load %[[VAL_4]]#0 : !fir.ref<!fir.complex<4>>
 ! CHECK:  %[[VAL_7:.*]] = fir.load %[[VAL_5]]#0 : !fir.ref<!fir.complex<4>>
-! CHECK:  %[[VAL_8:.*]] = fir.convert %[[VAL_6]] : (!fir.complex<4>) -> complex<f32>
-! CHECK:  %[[VAL_9:.*]] = fir.convert %[[VAL_7]] : (!fir.complex<4>) -> complex<f32>
-! CHECK:  %[[VAL_10:.*]] = complex.pow %[[VAL_8]], %[[VAL_9]] : complex<f32>
-! CHECK:  %[[VAL_11:.*]] = fir.convert %[[VAL_10]] : (complex<f32>) -> !fir.complex<4>
+! CHECK:  %[[VAL_8:.*]] = fir.call @cpowf(%[[VAL_6]], %[[VAL_7]]) fastmath<contract> : (!fir.complex<4>, !fir.complex<4>) -> !fir.complex<4>
+
 
 subroutine real_to_int_power(x, y, z)
   real :: x, y
diff --git a/flang/test/Lower/Intrinsics/abs.f90 b/flang/test/Lower/Intrinsics/abs.f90
--- a/flang/test/Lower/Intrinsics/abs.f90
+++ b/flang/test/Lower/Intrinsics/abs.f90
@@ -1,9 +1,10 @@
-! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: bbc --disable-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -fapprox-func -emit-fir %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 
 ! Test abs intrinsic for various types (int, float, complex)
 
diff --git a/flang/test/Lower/Intrinsics/exp.f90 b/flang/test/Lower/Intrinsics/exp.f90
--- a/flang/test/Lower/Intrinsics/exp.f90
+++ b/flang/test/Lower/Intrinsics/exp.f90
@@ -1,7 +1,8 @@
-! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --disable-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 
@@ -55,7 +56,8 @@
 ! CHECK: %[[RESULT64_OUTLINE:.*]] = math.exp %[[ARG64_OUTLINE]] fastmath<contract> : f64
 ! CHECK: return %[[RESULT64_OUTLINE]] : f64
 
-! CMPLX-LABEL: private @fir.exp.contract.z4.z4
+! CMPLX-FAST-LABEL: private @fir.exp.contract_afn.z4.z4
+! CMPLX-PRECISE-LABEL: private @fir.exp.contract.z4.z4
 ! CMPLX-SAME: (%[[ARG32_OUTLINE:.*]]: !fir.complex<4>) -> !fir.complex<4>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG32_OUTLINE]] : (!fir.complex<4>) -> complex<f32>
 ! CMPLX-FAST: %[[E:.*]] = complex.exp %[[C]] : complex<f32>
@@ -63,7 +65,8 @@
 ! CMPLX-PRECISE: %[[RESULT32_OUTLINE:.*]] = fir.call @cexpf(%[[ARG32_OUTLINE]]) fastmath<contract> : (!fir.complex<4>) -> !fir.complex<4>
 ! CMPLX: return %[[RESULT32_OUTLINE]] : !fir.complex<4>
 
-! CMPLX-LABEL: private @fir.exp.contract.z8.z8
+! CMPLX-FAST-LABEL: private @fir.exp.contract_afn.z8.z8
+! CMPLX-PRECISE-LABEL: private @fir.exp.contract.z8.z8
 ! CMPLX-SAME: (%[[ARG64_OUTLINE:.*]]: !fir.complex<8>) -> !fir.complex<8>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG64_OUTLINE]] : (!fir.complex<8>) -> complex<f64>
 ! CMPLX-FAST: %[[E:.*]] = complex.exp %[[C]] : complex<f64>
diff --git a/flang/test/Lower/Intrinsics/log.f90 b/flang/test/Lower/Intrinsics/log.f90
--- a/flang/test/Lower/Intrinsics/log.f90
+++ b/flang/test/Lower/Intrinsics/log.f90
@@ -1,9 +1,10 @@
-! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --math-runtime=precise -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: bbc -emit-fir --disable-mlir-complex -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-FAST"
+! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-PRECISE"
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX,CMPLX-FAST"
 
 ! CHECK-LABEL: log_testr
 ! CHECK-SAME: (%[[AREF:.*]]: !fir.ref<f32> {{.*}}, %[[BREF:.*]]: !fir.ref<f32> {{.*}})
@@ -75,7 +76,8 @@
 ! CHECK: %[[RESULT64_OUTLINE:.*]] = math.log %[[ARG64_OUTLINE]] fastmath<contract> : f64
 ! CHECK: return %[[RESULT64_OUTLINE]] : f64
 
-! CMPLX-LABEL: private @fir.log.contract.z4.z4
+! CMPLX-FAST-LABEL: private @fir.log.contract_afn.z4.z4
+! CMPLX-PRECISE-LABEL: private @fir.log.contract.z4.z4
 ! CMPLX-SAME: (%[[ARG32_OUTLINE:.*]]: !fir.complex<4>) -> !fir.complex<4>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG32_OUTLINE]] : (!fir.complex<4>) -> complex<f32>
 ! CMPLX-FAST: %[[E:.*]] = complex.log %[[C]] : complex<f32>
@@ -83,7 +85,8 @@
 ! CMPLX-PRECISE: %[[RESULT32_OUTLINE:.*]] = fir.call @clogf(%[[ARG32_OUTLINE]]) fastmath<contract> : (!fir.complex<4>) -> !fir.complex<4>
 ! CMPLX: return %[[RESULT32_OUTLINE]] : !fir.complex<4>
 
-! CMPLX-LABEL: private @fir.log.contract.z8.z8
+! CMPLX-FAST-LABEL: private @fir.log.contract_afn.z8.z8
+! CMPLX-PRECISE-LABEL: private @fir.log.contract.z8.z8
 ! CMPLX-SAME: (%[[ARG64_OUTLINE:.*]]: !fir.complex<8>) -> !fir.complex<8>
 ! CMPLX-FAST: %[[C:.*]] = fir.convert %[[ARG64_OUTLINE]] : (!fir.complex<8>) -> complex<f64>
 ! CMPLX-FAST: %[[E:.*]] = complex.log %[[C]] : complex<f64>
diff --git a/flang/test/Lower/math-lowering.f90 b/flang/test/Lower/math-lowering.f90
--- a/flang/test/Lower/math-lowering.f90
+++ b/flang/test/Lower/math-lowering.f90
@@ -41,21 +41,15 @@
   complex(4) :: c, test_complex4
   test_complex4 = abs(c)
 end function
-
 ! ALL-LABEL: @_QPtest_complex4
-! FAST: {{%[A-Za-z0-9._]+}} = complex.abs {{%[A-Za-z0-9._]+}} : complex<f32>
-! RELAXED: {{%[A-Za-z0-9._]+}} = complex.abs {{%[A-Za-z0-9._]+}} : complex<f32>
-! PRECISE: {{%[A-Za-z0-9._]+}} = fir.call @cabsf({{%[A-Za-z0-9._]+}}) {{.*}}: (!fir.complex<4>) -> f32
+! ALL: {{%[A-Za-z0-9._]+}} = fir.call @cabsf({{%[A-Za-z0-9._]+}}) {{.*}}: (!fir.complex<4>) -> f32
 
 function test_complex8(c)
   complex(8) :: c, test_complex8
   test_complex8 = abs(c)
 end function
-
 ! ALL-LABEL: @_QPtest_complex8
-! FAST: {{%[A-Za-z0-9._]+}} = complex.abs {{%[A-Za-z0-9._]+}} : complex<f64>
-! RELAXED: {{%[A-Za-z0-9._]+}} = complex.abs {{%[A-Za-z0-9._]+}} : complex<f64>
-! PRECISE: {{%[A-Za-z0-9._]+}} = fir.call @cabs({{%[A-Za-z0-9._]+}}) {{.*}}: (!fir.complex<8>) -> f64
+! ALL: {{%[A-Za-z0-9._]+}} = fir.call @cabs({{%[A-Za-z0-9._]+}}) {{.*}}: (!fir.complex<8>) -> f64
 
 ! PRECISE-DAG: func.func private @fabsf(f32) -> f32 attributes {fir.bindc_name = "fabsf", fir.runtime}
 ! PRECISE-DAG: func.func private @fabs(f64) -> f64 attributes {fir.bindc_name = "fabs", fir.runtime}
diff --git a/flang/test/Lower/power-operator.f90 b/flang/test/Lower/power-operator.f90
--- a/flang/test/Lower/power-operator.f90
+++ b/flang/test/Lower/power-operator.f90
@@ -1,7 +1,8 @@
-! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,FAST"
+! RUN: bbc -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,PRECISE"
 ! RUN: bbc --math-runtime=precise -emit-fir %s -o - | FileCheck %s --check-prefixes="PRECISE"
 ! RUN: bbc --disable-mlir-complex -emit-fir %s -o - | FileCheck %s --check-prefixes="PRECISE"
-! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,FAST"
+! RUN: %flang_fc1 -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,PRECISE"
+! RUN: %flang_fc1 -fapprox-func -emit-fir %s -o - | FileCheck %s --check-prefixes="CHECK,FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise %s -o - | FileCheck %s --check-prefixes="PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex %s -o - | FileCheck %s --check-prefixes="PRECISE"
 
diff --git a/flang/test/Lower/sqrt.f90 b/flang/test/Lower/sqrt.f90
--- a/flang/test/Lower/sqrt.f90
+++ b/flang/test/Lower/sqrt.f90
@@ -1,7 +1,8 @@
-! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-FAST"
+! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-PRECISE"
 ! RUN: bbc --math-runtime=precise -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
 ! RUN: bbc --disable-mlir-complex -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
-! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-FAST"
+! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-PRECISE"
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-FAST"
 ! RUN: %flang_fc1 -emit-fir -mllvm --math-runtime=precise -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm --disable-mlir-complex -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
 
diff --git a/flang/test/Lower/trigonometric-intrinsics.f90 b/flang/test/Lower/trigonometric-intrinsics.f90
--- a/flang/test/Lower/trigonometric-intrinsics.f90
+++ b/flang/test/Lower/trigonometric-intrinsics.f90
@@ -1,6 +1,7 @@
-! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-FAST"
+! RUN: bbc -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CHECK,CMPLX-PRECISE"
 ! RUN: bbc --math-runtime=precise -emit-fir -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-PRECISE"
 ! RUN: %flang_fc1 -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s
+! RUN: %flang_fc1 -fapprox-func -emit-fir -mllvm -outline-intrinsics %s -o - | FileCheck %s --check-prefixes="CMPLX-FAST"
 
 ! CHECK-LABEL: tan_testr
 subroutine tan_testr(a, b)