# Inverse functions using TaylorSeries.jl

**URL:** <https://discourse.julialang.org/t/inverse-functions-using-taylorseries-jl/43382>\
**Category:** Machine Learning\
**Created:** [July 19, 2020, 7:48pm UTC](https://discourse.julialang.org/t/inverse-functions-using-taylorseries-jl/43382 "2020-07-19T19:48:54Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![Marc.Cox](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marc.cox/32/7514_2.png) [@Marc.Cox](https://discourse.julialang.org/u/Marc.Cox)\
**Post date:** [July 20, 2020, 3:29am UTC](https://discourse.julialang.org/t/inverse-functions-using-taylorseries-jl/43382/3 "2020-07-20T03:29:00Z")

</div>

Thank You for your response, it spurred me on and below is my (initial) solution to an issue I was having with _TaylorSeries.jl_ , which leads to another question \>\> And more generally I’m interested in using _TaylorSeries.jl_ as an implementation of high-order automatic differentiation - more completely described here \>\> [Interested in using TaylorSeries.jl as an implementation of high-order automatic differentiation / AD , as presented in the book by W. Tucker](https://discourse.julialang.org/t/interested-in-using-taylorseries-jl-as-an-implementation-of-high-order-automatic-differentiation-ad-as-presented-in-the-book-by-w-tucker/43356)

One partial SOLN : Using _TaylorSeries.jl_ to get the inverse function _exp_ by defining _Taylor1_ function _log_ works now

```julia
julia> tBig = Taylor1(BigFloat, 50) # Independent variable with BigFloats, With order 50 precision 1.0 t + ?(t⁵¹)
julia> p = log(tBig + 1.0)
julia> TaylorSeries.evaluate(inverse(p), TaylorSeries.evaluate(p, 0.9))
8.999082e-01
julia> TaylorSeries.evaluate(inverse(p), 0.9)
1.459603
julia> exp(0.9)
2.45960311115695
julia> TaylorSeries.evaluate(inverse(p), 0.9) + 1.0
2.459603111156949

```

cc @lbenet

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