# Inverse fma
**URL:** https://discourse.julialang.org/t/inverse-fma/11812
**Category:** General Usage
**Tags:** question
**Created:** [June 20, 2018, 9:10am UTC](https://discourse.julialang.org/t/inverse-fma/11812 "2018-06-20T09:10:20Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [June 20, 2018, 9:10am UTC](https://discourse.julialang.org/t/inverse-fma/11812/1 "2018-06-20T09:10:20Z")
Is there an inverse of `fma`, in the sense of
```julia
y = fma(x, A, B)
x2 = ???(y, A, B) # this is what I am looking for
x ≈ x2 # "reasonably" close
```
I found that sometimes either `(y - B)/A` or `fma(y, inv(A), -B/A)` is more accurate, but it really depends on the magnitude of `B` vs `A`.
---
### Author:  [@Per](https://discourse.julialang.org/u/Per)
#### Post date: [June 20, 2018, 9:57am UTC](https://discourse.julialang.org/t/inverse-fma/11812/2 "2018-06-20T09:57:32Z")
You should not define “accuracy” based on the difference between `x` and `x2`. If `x*A` is smaller than `B`, then there will be many values of `x` that map to the same `y` and your inverse function cannot possibly know which one is your original `x`. Better to compare `fma(x, A, B)` to `fma(x2, A, B)`.
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### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [June 20, 2018, 10:53am UTC](https://discourse.julialang.org/t/inverse-fma/11812/3 "2018-06-20T10:53:56Z")
Good point, but I would still like a `(y - B)/A` that is as accurate as it can be, given `B` and `A` and recognizing that it can’t be a bijection.
Of course I can always go to `BigFloat` and back, but that is rather slow.
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### Author:  [@Per](https://discourse.julialang.org/u/Per)
#### Post date: [June 20, 2018, 11:20am UTC](https://discourse.julialang.org/t/inverse-fma/11812/4 "2018-06-20T11:20:47Z")
```julia
function invfma(y, A, B)
x2 = (y-B)/A
y2 = fma(x2, A, B)
x2 + (y-y2)/A
end
```
---
### Author:  [@jw3126](https://discourse.julialang.org/u/jw3126)
#### Post date: [June 20, 2018, 11:25am UTC](https://discourse.julialang.org/t/inverse-fma/11812/5 "2018-06-20T11:25:18Z")
Another alternative to `BigFloat` is `Base.TwicePrecision`.