diff --git a/enzyme/Enzyme/InstructionDerivatives.td b/enzyme/Enzyme/InstructionDerivatives.td
index 6491fa032798..e309055c34d2 100644
--- a/enzyme/Enzyme/InstructionDerivatives.td
+++ b/enzyme/Enzyme/InstructionDerivatives.td
@@ -655,30 +655,30 @@ def ToStruct2 : SubRoutine<(Op (Op $re, $im):$z),
 def : CallPattern<(Op $x, $tbd),
                   ["Faddeeva_erf"],
                   [
-                    (ToStruct2 (CFMul (DiffeRet), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x)))))),
+                    (ToStruct2 (Conj (CFMul (Conj (DiffeRet)), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x))))))),
                     (InactiveArg) // relerr
                   ],
-                  (ForwardFromSummedReverse),
+                  (ToStruct2 (CFMul (Shadow $x), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x)))))),
                   [ReadNone, NoUnwind]
                   >;
 
 def : CallPattern<(Op $x, $tbd),
                   ["Faddeeva_erfi"],
                   [
-                    (ToStruct2 (CFMul (DiffeRet), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFMul $x, $x))))),
+                    (ToStruct2 (Conj (CFMul (Conj (DiffeRet)), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFMul $x, $x)))))),
                     (InactiveArg) // relerr
                   ],
-                  (ForwardFromSummedReverse),
+                  (ToStruct2 (CFMul (Shadow $x), (CFMul (ConstantCFP<"1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFMul $x, $x))))),
                   [ReadNone, NoUnwind]
                   >;
 
 def : CallPattern<(Op $x, $tbd),
                   ["Faddeeva_erfc"],
                   [
-                    (ToStruct2 (CFMul (DiffeRet), (CFMul (ConstantCFP<"-1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x)))))),
+                    (ToStruct2 (Conj (CFMul (Conj (DiffeRet)), (CFMul (ConstantCFP<"-1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x))))))),
                     (InactiveArg) // relerr
                   ],
-                  (ForwardFromSummedReverse),
+                  (ToStruct2 (CFMul (Shadow $x), (CFMul (ConstantCFP<"-1.1283791670955125738961589031215451716881012586580","0"> $x), (CFExp (CFNeg (CFMul $x, $x)))))),
                   [ReadNone, NoUnwind]
                   >;
 
diff --git a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erf.ll b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erf.ll
index 4722ef548bd8..716cba079e61 100644
--- a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erf.ll
+++ b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erf.ll
@@ -20,6 +20,9 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 
 ; CHECK: define internal { { double, double } } @diffetester({ double, double } %in, { double, double } %differeturn)
 ; CHECK-NEXT: entry:
+; CHECK-NEXT:   %[[a16:.+]] = extractvalue { double, double } %differeturn, 0
+; CHECK-NEXT:   %[[a17:.+]] = extractvalue { double, double } %differeturn, 1
+; CHECK-NEXT:   %[[conj:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[a17]]
 ; CHECK-NEXT:   %[[a0:.+]] = extractvalue { double, double } %in, 0
 ; CHECK-NEXT:   %[[a1:.+]] = extractvalue { double, double } %in, 1
 ; CHECK-DAG:    %[[a2:.+]] = fmul fast double %[[a1]], %[[a1]]
@@ -36,16 +39,15 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 ; CHECK-NEXT:   %[[a13:.+]] = fmul fast double %[[a9]], %[[a12]]
 ; CHECK-NEXT:   %[[a14:.+]] = fmul fast double 0x3FF20DD750429B6D, %[[a11]]
 ; CHECK-NEXT:   %[[a15:.+]] = fmul fast double 0x3FF20DD750429B6D, %[[a13]]
-; CHECK-NEXT:   %[[a16:.+]] = extractvalue { double, double } %differeturn, 0
-; CHECK-NEXT:   %[[a17:.+]] = extractvalue { double, double } %differeturn, 1
 ; CHECK-DAG:    %[[a19:.+]] = fmul fast double %[[a16]], %[[a14]]
-; CHECK-DAG:    %[[a18:.+]] = fmul fast double %[[a17]], %[[a15]]
+; CHECK-DAG:    %[[a18:.+]] = fmul fast double %[[conj]], %[[a15]]
 ; CHECK-NEXT:   %[[a20:.+]] = fsub fast double %[[a19]], %[[a18]]
 ; CHECK-DAG:    %[[a22:.+]] = fmul fast double %[[a16]], %[[a15]]
-; CHECK-DAG:    %[[a21:.+]] = fmul fast double %[[a14]], %[[a17]]
+; CHECK-DAG:    %[[a21:.+]] = fmul fast double %[[a14]], %[[conj]]
 ; CHECK-NEXT:   %[[a23:.+]] = fadd fast double %[[a22]], %[[a21]]
+; CHECK-NEXT:   %[[conj2:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[a23]]
 ; CHECK-NEXT:   %[[insert5:.+]] = insertvalue { double, double } {{(undef|poison)}}, double %[[a20]], 0
-; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[a23]], 1
+; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[conj2]], 1
 ; CHECK-NEXT:   %[[a24:.+]] = insertvalue { { double, double } } undef, { double, double } %[[insert8]], 0
 ; CHECK-NEXT:   ret { { double, double } } %[[a24]]
 ; CHECK-NEXT: }
diff --git a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfc.ll b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfc.ll
index 04c8fee4de92..dabd2674b7ba 100644
--- a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfc.ll
+++ b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfc.ll
@@ -20,6 +20,9 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 
 ; CHECK: define internal { { double, double } } @diffetester({ double, double } %in, { double, double } %differeturn)
 ; CHECK-NEXT: entry:
+; CHECK-NEXT:   %[[a16:.+]] = extractvalue { double, double } %differeturn, 0
+; CHECK-NEXT:   %[[a17:.+]] = extractvalue { double, double } %differeturn, 1
+; CHECK-NEXT:   %[[conj:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[a17]]
 ; CHECK-NEXT:   %[[a0:.+]] = extractvalue { double, double } %in, 0
 ; CHECK-NEXT:   %[[a1:.+]] = extractvalue { double, double } %in, 1
 ; CHECK-DAG:    %[[a2:.+]] = fmul fast double %[[a1]], %[[a1]]
@@ -36,16 +39,15 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 ; CHECK-NEXT:   %[[a13:.+]] = fmul fast double %[[a9]], %[[a12]]
 ; CHECK-NEXT:   %[[a14:.+]] = fmul fast double 0xBFF20DD750429B6D, %[[a11]]
 ; CHECK-NEXT:   %[[a15:.+]] = fmul fast double 0xBFF20DD750429B6D, %[[a13]]
-; CHECK-NEXT:   %[[a16:.+]] = extractvalue { double, double } %differeturn, 0
-; CHECK-NEXT:   %[[a17:.+]] = extractvalue { double, double } %differeturn, 1
 ; CHECK-DAG:    %[[a19:.+]] = fmul fast double %[[a16]], %[[a14]]
-; CHECK-DAG:    %[[a18:.+]] = fmul fast double %[[a17]], %[[a15]]
+; CHECK-DAG:    %[[a18:.+]] = fmul fast double %[[conj]], %[[a15]]
 ; CHECK-NEXT:   %[[a20:.+]] = fsub fast double %[[a19]], %[[a18]]
 ; CHECK-DAG:    %[[a22:.+]] = fmul fast double %[[a16]], %[[a15]]
-; CHECK-DAG:    %[[a21:.+]] = fmul fast double %[[a14]], %[[a17]]
+; CHECK-DAG:    %[[a21:.+]] = fmul fast double %[[a14]], %[[conj]]
 ; CHECK-NEXT:   %[[a23:.+]] = fadd fast double %[[a22]], %[[a21]]
+; CHECK-NEXT:   %[[conj2:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[a23]]
 ; CHECK-NEXT:   %[[insert5:.+]] = insertvalue { double, double } {{(undef|poison)}}, double %[[a20]], 0
-; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[a23]], 1
+; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[conj2]], 1
 ; CHECK-NEXT:   %[[a24:.+]] = insertvalue { { double, double } } undef, { double, double } %[[insert8]], 0
 ; CHECK-NEXT:   ret { { double, double } } %[[a24]]
 ; CHECK-NEXT: }
diff --git a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfi.ll b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfi.ll
index 40932ffb5cf2..c5e5cfba0a90 100644
--- a/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfi.ll
+++ b/enzyme/test/Enzyme/ReverseMode/Faddeeva_erfi.ll
@@ -20,6 +20,9 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 
 ; CHECK: define internal { { double, double } } @diffetester({ double, double } %in, { double, double } %differeturn)
 ; CHECK-NEXT: entry:
+; CHECK-NEXT:   %[[i16:.+]] = extractvalue { double, double } %differeturn, 0
+; CHECK-NEXT:   %[[i17:.+]] = extractvalue { double, double } %differeturn, 1
+; CHECK-NEXT:   %[[conj:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[i17]]
 ; CHECK-NEXT:   %[[a0:.+]] = extractvalue { double, double } %in, 0
 ; CHECK-NEXT:   %[[a1:.+]] = extractvalue { double, double } %in, 1
 ; CHECK-NEXT:   %[[a3:.+]] = fmul fast double %[[a0]], %[[a0]]
@@ -34,16 +37,15 @@ declare { double, double } @__enzyme_autodiff({ double, double } ({ double, doub
 ; CHECK-NEXT:   %[[i13:.+]] = fmul fast double %[[i9]], %[[i12]]
 ; CHECK-NEXT:   %[[i14:.+]] = fmul fast double 0x3FF20DD750429B6D, %[[i11]]
 ; CHECK-NEXT:   %[[i15:.+]] = fmul fast double 0x3FF20DD750429B6D, %[[i13]]
-; CHECK-NEXT:   %[[i16:.+]] = extractvalue { double, double } %differeturn, 0
-; CHECK-NEXT:   %[[i17:.+]] = extractvalue { double, double } %differeturn, 1
 ; CHECK-NEXT:   %[[i19:.+]] = fmul fast double %[[i16]], %[[i14]]
-; CHECK-NEXT:   %[[i18:.+]] = fmul fast double %[[i17]], %[[i15]]
+; CHECK-NEXT:   %[[i18:.+]] = fmul fast double %[[conj]], %[[i15]]
 ; CHECK-NEXT:   %[[i20:.+]] = fsub fast double %[[i19]], %[[i18]]
 ; CHECK-NEXT:   %[[i22:.+]] = fmul fast double %[[i16]], %[[i15]]
-; CHECK-NEXT:   %[[i21:.+]] = fmul fast double %[[i14]], %[[i17]]
+; CHECK-NEXT:   %[[i21:.+]] = fmul fast double %[[i14]], %[[conj]]
 ; CHECK-NEXT:   %[[i23:.+]] = fadd fast double %[[i22]], %[[i21]]
+; CHECK-NEXT:   %[[conj2:.+]] = {{(fsub fast double \-0.000000e\+00,|fneg fast double)}} %[[i23]]
 ; CHECK-NEXT:   %[[insert5:.+]] = insertvalue { double, double } {{(undef|poison)}}, double %[[i20]], 0
-; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[i23]], 1
+; CHECK-NEXT:   %[[insert8:.+]] = insertvalue { double, double } %[[insert5]], double %[[conj2]], 1
 ; CHECK-NEXT:   %[[i24:.+]] = insertvalue { { double, double } } undef, { double, double } %[[insert8]], 0
 ; CHECK-NEXT:   ret { { double, double } } %[[i24]]
 ; CHECK-NEXT: }