; LLVM IR from Dutta-SD/Numerical_Methods :: Calculus (Euler_Runge_Kutta)

; Unoptimized IR (clang -disable-llvm-passes):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

@.str.2 = external hidden unnamed_addr constant [62 x i8], align 1
@.str.3 = external hidden unnamed_addr constant [17 x i8], align 1

; Function Attrs: nounwind uwtable
declare dso_local double @f(double noundef, double noundef) #0

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #1

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.start.p0(i64 immarg, ptr nocapture) #2

declare i32 @printf(ptr noundef, ...) #3

; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
declare void @llvm.lifetime.end.p0(i64 immarg, ptr nocapture) #2

; Function Attrs: nounwind uwtable
define dso_local void @Modified_Euler(double noundef %0, double noundef %1, double noundef %2) #0 {
  %4 = alloca double, align 8
  %5 = alloca double, align 8
  %6 = alloca double, align 8
  %7 = alloca double, align 8
  %8 = alloca double, align 8
  %9 = alloca double, align 8
  store double %0, ptr %4, align 8, !tbaa !5
  store double %1, ptr %5, align 8, !tbaa !5
  store double %2, ptr %6, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %7) #4
  %10 = load double, ptr %5, align 8, !tbaa !5
  %11 = load double, ptr %6, align 8, !tbaa !5
  %12 = load double, ptr %4, align 8, !tbaa !5
  %13 = load double, ptr %5, align 8, !tbaa !5
  %14 = call double @f(double noundef %12, double noundef %13)
  %15 = call double @llvm.fmuladd.f64(double %11, double %14, double %10)
  store double %15, ptr %7, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %8) #4
  %16 = load double, ptr %4, align 8, !tbaa !5
  %17 = load double, ptr %6, align 8, !tbaa !5
  %18 = fadd double %16, %17
  store double %18, ptr %8, align 8, !tbaa !5
  call void @llvm.lifetime.start.p0(i64 8, ptr %9) #4
  store double 0.000000e+00, ptr %9, align 8, !tbaa !5
  %19 = call i32 (ptr, ...) @printf(ptr noundef @.str.2)
  br label %20

20:                                               ; preds = %26, %3
  %21 = load double, ptr %9, align 8, !tbaa !5
  %22 = load double, ptr %7, align 8, !tbaa !5
  %23 = fsub double %21, %22
  %24 = call double @llvm.fabs.f64(double %23)
  %25 = fcmp ogt double %24, 1.000000e-08
  br i1 %25, label %26, label %40

26:                                               ; preds = %20
  %27 = load double, ptr %7, align 8, !tbaa !5
  store double %27, ptr %9, align 8, !tbaa !5
  %28 = load double, ptr %5, align 8, !tbaa !5
  %29 = load double, ptr %4, align 8, !tbaa !5
  %30 = load double, ptr %5, align 8, !tbaa !5
  %31 = call double @f(double noundef %29, double noundef %30)
  %32 = load double, ptr %8, align 8, !tbaa !5
  %33 = load double, ptr %7, align 8, !tbaa !5
  %34 = call double @f(double noundef %32, double noundef %33)
  %35 = fadd double %31, %34
  %36 = load double, ptr %6, align 8, !tbaa !5
  %37 = fmul double %35, %36
  %38 = fdiv double %37, 2.000000e+00
  %39 = fadd double %28, %38
  store double %39, ptr %7, align 8, !tbaa !5
  br label %20, !llvm.loop !9

40:                                               ; preds = %20
  %41 = load double, ptr %8, align 8, !tbaa !5
  %42 = load double, ptr %7, align 8, !tbaa !5
  %43 = call i32 (ptr, ...) @printf(ptr noundef @.str.3, double noundef %41, double noundef %42)
  call void @llvm.lifetime.end.p0(i64 8, ptr %9) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %8) #4
  call void @llvm.lifetime.end.p0(i64 8, ptr %7) #4
  ret void
}

; Function Attrs: nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fabs.f64(double) #1

attributes #0 = { nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #1 = { nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #2 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
attributes #3 = { "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #4 = { nounwind }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = !{!6, !6, i64 0}
!6 = !{!"double", !7, i64 0}
!7 = !{!"omnipotent char", !8, i64 0}
!8 = !{!"Simple C/C++ TBAA"}
!9 = distinct !{!9, !10}
!10 = !{!"llvm.loop.mustprogress"}


; Optimized IR (opt -passes='default<O3>'):
target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
target triple = "x86_64-unknown-linux-gnu"

@.str.2 = external hidden unnamed_addr constant [62 x i8], align 1
@.str.3 = external hidden unnamed_addr constant [17 x i8], align 1

; Function Attrs: nounwind uwtable
declare dso_local double @f(double noundef, double noundef) local_unnamed_addr #0

; Function Attrs: mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fmuladd.f64(double, double, double) #1

; Function Attrs: nofree nounwind
declare noundef i32 @printf(ptr nocapture noundef readonly, ...) local_unnamed_addr #2

; Function Attrs: nounwind uwtable
define dso_local void @Modified_Euler(double noundef %0, double noundef %1, double noundef %2) local_unnamed_addr #0 {
  %4 = tail call double @f(double noundef %0, double noundef %1)
  %5 = tail call double @llvm.fmuladd.f64(double %2, double %4, double %1)
  %6 = fadd double %0, %2
  %7 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.2)
  %8 = fsub double 0.000000e+00, %5
  %9 = tail call double @llvm.fabs.f64(double %8)
  %10 = fcmp ogt double %9, 1.000000e-08
  br i1 %10, label %.lr.ph, label %._crit_edge

.lr.ph:                                           ; preds = %3, %.lr.ph
  %.01718 = phi double [ %16, %.lr.ph ], [ %5, %3 ]
  %11 = tail call double @f(double noundef %0, double noundef %1)
  %12 = tail call double @f(double noundef %6, double noundef %.01718)
  %13 = fadd double %11, %12
  %14 = fmul double %13, %2
  %15 = fmul double %14, 5.000000e-01
  %16 = fadd double %15, %1
  %17 = fsub double %.01718, %16
  %18 = tail call double @llvm.fabs.f64(double %17)
  %19 = fcmp ogt double %18, 1.000000e-08
  br i1 %19, label %.lr.ph, label %._crit_edge, !llvm.loop !5

._crit_edge:                                      ; preds = %.lr.ph, %3
  %.017.lcssa = phi double [ %5, %3 ], [ %16, %.lr.ph ]
  %20 = tail call i32 (ptr, ...) @printf(ptr noundef nonnull dereferenceable(1) @.str.3, double noundef %6, double noundef %.017.lcssa)
  ret void
}

; Function Attrs: mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none)
declare double @llvm.fabs.f64(double) #1

attributes #0 = { nounwind uwtable "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
attributes #1 = { mustprogress nocallback nofree nosync nounwind speculatable willreturn memory(none) }
attributes #2 = { nofree nounwind "no-trapping-math"="true" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }

!llvm.module.flags = !{!0, !1, !2, !3}
!llvm.ident = !{!4}

!0 = !{i32 1, !"wchar_size", i32 4}
!1 = !{i32 8, !"PIC Level", i32 2}
!2 = !{i32 7, !"PIE Level", i32 2}
!3 = !{i32 7, !"uwtable", i32 2}
!4 = !{!"clang version 19.1.0 (git@github.com:llvm/llvm-project.git a4bf6cd7cfb1a1421ba92bca9d017b49936c55e4)"}
!5 = distinct !{!5, !6}
!6 = !{!"llvm.loop.mustprogress"}


; Effective O3 passes: GVNPass,GlobalOptPass,InferFunctionAttrsPass,InstCombinePass,InstSimplifyPass,JumpThreadingPass,LCSSAPass,LoopRotatePass,LoopSimplifyPass,LoopUnrollPass,ReassociatePass,SROAPass,SimplifyCFGPass,TailCallElimPass