# The built-in complex division is unreasonably slow
**URL:** https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026
**Category:** Performance
**Created:** [November 30, 2022, 3:14am UTC](https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026 "2022-11-30T03:14:27Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@photor](https://discourse.julialang.org/u/photor)
#### Post date: [November 30, 2022, 3:14am UTC](https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026/1 "2022-11-30T03:14:27Z")
```julia
@btime x/y setup=(x=rand(ComplexF64);y=rand(ComplexF64));
```
gives
```julia
9.853 ns (0 allocations: 0 bytes)
```
while
```julia
function frac(x::ComplexF64, y::ComplexF64)
y2=y.re^2+y.im^2
return Complex((x.re*y.re+x.im*y.im)/y2, (x.im*y.re-x.re*y.im)/y2)
end
@btime frac(x,y) setup=(x=rand(ComplexF64);y=rand(ComplexF64));
```
gives only
```julia
3.694 ns (0 allocations: 0 bytes)
```
Why?
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [November 30, 2022, 3:19am UTC](https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026/2 "2022-11-30T03:19:25Z")
the short answer is getting good accuracy for these is hard. If you look at `@btime @fastmath x/y` you’ll see faster results results.
---
### Author:  [@mikmoore](https://discourse.julialang.org/u/mikmoore)
#### Post date: [November 30, 2022, 5:10pm UTC](https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026/3 "2022-11-30T17:10:15Z")
To elaborate just a little: the extra runtime is spent ensuring proper behavior for `Inf` and for cases where intermediate quantities (such as your `y2=y.re^2+y.im^2`) would over/underflow. You can take a look at the current implementation in [the source code](https://github.com/JuliaLang/julia/blob/master/base/complex.jl#L391).
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [November 30, 2022, 5:13pm UTC](https://discourse.julialang.org/t/the-built-in-complex-division-is-unreasonably-slow/91026/4 "2022-11-30T17:13:29Z")
It might be possible to add a better fast path (similar to [faster `inv` for normal sized `ComplexF64` by oscardssmith · Pull Request #47255 · JuliaLang/julia · GitHub](https://github.com/JuliaLang/julia/pull/47255)).