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Rationalise recurring binary

Given a potentially recurring binary string, output the number it represents, as a fraction in lowest terms.

The notation used in this challenge for recurring digits is non-standard. An `r` is used to indicate that the remaining digits recur. For example, `0.000r10` means the last 2 digits recur, like this: `0.000101010...`. This is the binary representation of $\frac{1}{12}$, which cannot be expressed in binary without recurring digits.

## Input
- A binary string made up of
  - Zero or more of `0`
  - Zero or more of `1`
  - Zero or one of `.`
  - Zero or one of `r`
- If `r` is present then there will always be a `.` somewhere to the left of the `r`
- There may be zero or more leading zeroes
- There may be zero or more trailing zeroes (in both recurring and non-recurring inputs)
- The last character will never be an `r`
- There will always be at least 1 character (the string will not be empty)
- The maximum length of input required to be handled is 15 characters

## Interpretation
- All digits to the right of an `r` are recurring (repeating forever)
- Anything to the left of a `.` represents the integer part of the number (in binary)
- Anything to the right of a `.` represents the fractional part of the number (in binary)
- If the first character is a `.` then the integer part is zero
- If the last character is a `.` then the fractional part is zero
- If there is no `.` then the fractional part is zero

## Output
- A numerator and denominator, in that order, or a rational type if your language supports one
- These can be in a multi-value data type such as a list/array/vector, or as a single string containing a non-numeric separating character (such as a space or a `/`)
- The numerator and denominator must be in lowest terms (that is, their greatest common factor is 1)
- An integer output N is represented as the fraction N/1, a numerator of N and a denominator of 1
- Zero is represented as the fraction 0/1, a numerator of zero and a denominator of 1
- The numerator and denominator are output as base 10 (decimal) - only the input is in binary

## Examples
Throughout these examples binary strings are represented as `fixed width` and all other numbers are base 10 (decimal).

### Non-recurring examples
- `10.00` is the integer 2, represented as 2/1
- `01.00` is the integer 1, represented as 1/1
- `00.10` is the fraction 1/2
- `00.01` is the fraction 1/4

### Recurring examples
- `10.r0` is the same as `10.000...`, the same as `10`, the integer 2, represented as 2/1
- `0.r1` is the same as `0.111...`, the same as `1`, the integer 1, represented as 1/1
- `0.r01` is the same as `0.010101...`, the fraction 1/3
- `0.r10` is the same as `0.101010...`, the fraction 2/3
- `1.r01` is the same as `1.010101...`, the fraction 4/3
- `0.r001` is the same as `0.001001001...`, the fraction 1/7
- `0.r010` is the same as `0.010010010...`, the fraction 2/7
- `0.r100` is the same as `0.100100100...`, the fraction 4/7
- `1.r001` is the same as `1.001001001...`, the fraction 8/7

## Test cases
Test cases are in the format `input : output`

Outputs are in the format `numerator/denominator`

```text
. : 0/1
.0 : 0/1
0. : 0/1
.1 : 1/2
1. : 1/1
0.0 : 0/1
00.00 : 0/1
.r0 : 0/1
.r1 : 1/1
00.r00 : 0/1
11.r11 : 4/1
00.0r0 : 0/1
11.1r1 : 4/1
.0101r01 : 1/3
.1010r10 : 2/3
.r01 : 1/3
.r0101 : 1/3
.r010101 : 1/3
.r0101010 : 42/127
.r0011 : 1/5
.r0110 : 2/5
.r1001 : 3/5
.r1100 : 4/5
.0r01 : 1/6
.00r10 : 1/6
.1r10 : 5/6
.r001 : 1/7
.r010 : 2/7
.r011 : 3/7
.r100 : 4/7
.r101 : 5/7
.r110 : 6/7
.r111 : 1/1
0001000.r01001 : 257/31
.r000111 : 1/9
.0r001110 : 1/9
.00r011100 : 1/9
.000r111000 : 1/9
.0001r110001 : 1/9
.00011r100011 : 1/9
.000111r000111 : 1/9
.r001110 : 2/9
.r011100 : 4/9
.r100011 : 5/9
.r110001 : 7/9
.r111000 : 8/9
1 : 1/1
10 : 2/1
11 : 3/1
100 : 4/1
101 : 5/1
110 : 6/1
111 : 7/1
111. : 7/1
111.0 : 7/1
111.r0 : 7/1
111.0r0 : 7/1
.00000000000r01 : 1/6144
.00000000000r10 : 1/3072
.01010101010r10 : 1/3
.10101010101r01 : 2/3
.01010101010r01 : 2047/6144
.10101010101r10 : 4097/6144
111111111111111 : 32767
111111111111.r1 : 4096
111111111111.r0 : 4095
.00000000000001 : 1/16384
1111111.1111111 : 16383/128
```

> Explanations in answers are optional, but I'm more likely to upvote answers that have one.