formation of numbers - The 10,958 Problem

Here is the task:

Write down 10958 using all 1-9 digits in ascending order and only one time.

You are allowed to:
1) group digits into numbers
2) use 5 basic operations: + - * / ^ ("^" means power)
3) set order of operations with brackets ()

For example, 10957 = (1+2)^(3+4)*5-67+89

Sounds simple, right? If you are interested, there is a video on this topic, which says it is known that you can write this way all numbers from 1 to 11111... all, but 10958, for which they don't know the solution at the moment.

And there is cheaty solution by that guy:

10958 = 1 * 2||3 + ((4*5*6)||7+8)*9,
where "||" states for a twisted rule #1: concatenation operation.

I believe in SE, there should be a guy who will find the true solution! Or, even if not true, may be some other a bit cheaty, but close to the solution. Try it out.

Answer

I wrote a program to solve all possible conditions including everything. The code is running for some days now and I have found lots of close results. According to the benchmark, it will take a couple of days to go and as a result I would have checked every single possibility and share the result with you guys.

For $1,2,3,4,5,6,7,8,9$, I am going to update close ones to the below:

1

$(1+234)*5/6*7*8-9=10957.67 \simeq 10958$

2

$(12*3*4/5*6*7+8)*9=10958.4\simeq 10958$

3

$-1+(234-5/6)*(7*8-9)=10957.83\simeq 10958$

4

$1+((((2+34)/(5))^6)*(7/89))=10958.28\simeq 10958$

5.

$(((1+(2+3)^{4})*56)-7)^{8/9}=10957.50\simeq 10958$

6.

$1+(2+3^{4/5+6+(7+8)/9})=10958.36\simeq 10958$

7.

$(1+((2-3/(4*56))^7))*89=10957.61\simeq 10958$

8.

$-1+(2+((3/4)^{5-6*7*8/9}))=10957.85\simeq 10958$

9

$1+(2*3)^{4-1/8*(5/6)^7}*9=10958.25\simeq 10958$

10

$((1+(2/3+4))^5*6-7)^{8/9}=10958.12\simeq 10958$

11

$-1+2-3+4^{5-(6-7)/8}*9=10957.73\simeq 10958$

12

$(((1+2/3)/4)^5)^{6 + 7/8 - 9}=10958.33\simeq 10958$

13

$((1+(2^{3^{(4/(5 + 6)} + 7)-8})^9=10957.63 \simeq 10958$

14

$(-1/(2 + 3) + 4^{5 - (6 - 7)/8}*9=10957.93\simeq 10958$

15

$-1-2/3-4^{5-(6-7)/8}*9=10958.06 \simeq 10958$

16 Closest One

$-(1 - 2^{3^4/5}/(6 + 7/8) - 9)=10957.98 \simeq 10958$

I believe this is close enough to be accepted as an answer!

Moreover, I have found exact solution without using number $6$ as below:

$1-2+3*457*8-9=10958$