# A calculator for distributions, for Fermi estimation

This project is a minimalist, calculator-style DSL for fermi estimation. It can multiply, divide, add and substract scalars, lognormals and beta distributions, and supports variables.

## Motivation

Sometimes, [Squiggle](https://github.com/quantified-uncertainty/squiggle), [simple squiggle](https://git.nunosempere.com/quantified.uncertainty/simple-squiggle) or [squiggle.c](https://git.nunosempere.com/personal/squiggle.c) are still too complicated and un-unix-like.

## Installation

```
make build
sudo make install
fermi 
```

## Usage

```
$ fermi
5000000 12000000
=> 5.0M 12.0M
* beta 1 200
=> 1.9K 123.1K
* 30 180
=> 122.9K 11.7M
/ 48 52
=> 2.5K 234.6K
/ 5 6
=> 448.8 43.0K
/ 6 8
=> 64.5 6.2K
/ 60
=> 1.1 103.7
```

Perhaps this example is more understandable with comments and better units:

```
$ fermi
5M 12M           # number of people living in Chicago
beta 1 200       # fraction of people that have a piano
30 180           # minutes it takes to tune a piano, including travel time
/ 48 52          # weeks a year that piano tuners work for
/ 5 6            # days a week in which piano tuners work
/ 6 8            # hours a day in which piano tuners work
/ 60             # minutes to an hour
=: piano_tuners
```

If you type "help", you can see a small grammar:

```
$ fermi
help
  Operation | Variable assignment | Special
    Operation:                             operator operand
          operator:                        (empty) | * | / | + | -
          operand:                         scalar | lognormal | beta | variable
            lognormal:                     low high
            beta:                          beta alpha beta
    Variable assignment:                   =: variable_name
    Variable assignment and clear stack:   =. variable_name
    Special:
         Comment:                          # this is a comment
         Clear stack:                      clear | c | .
         Print debug info:                 debug | d
         Print help message:               help  | h
         Start additional stack:           operator (
         Return from additional stack      )
         Exit:                             exit  | e
  Examples:
    + 2
                    # this is a comment
    / 2.5           # this is an operation followed by a comment
    * 1 10          # "low high" is interpreted as lognormal
    + 1 10
    * beta 1 10
    1 10            # multiplication taken as default operation)
    =: x
    .               # return the stack to 1.
    1 100
    + x
    * 1 12 
    * (
    1 10
    + beta 1 100
    )
    =. y            # save to variable and clear stack
    exit
```

## Tips & tricks

- It's conceptually clearer to have all the multiplications first and then all the divisions
- For things between 0 and 1, consider using a beta distribution

### Command line options

You can specify the number of samples to draw when algebraic manipulations are not sufficient: 

```
$ fermi -n 1000000
$ fermi -n 1_000_000
```

You also run a file with the -f option

```
$ fermi -f more/piano-tuners.fermi 
```

### Integrations with linux utilities

Because the model reads from standard input, you can a model to it:

```
$ cat more/piano-tuners.fermi | fermi
```

You can make a model an executable file by running `$ chmod -x model.fermi` and then adding the following at the top!

```
#!/bin/usr/fermi -f
```

You can save a session to a logfile with tee:

```
fermi | tee -a fermi.log
```

## Different levels of complexity

The top level f.go file (420 lines) has a bunch of complexity: variables, parenthesis, samples, beta distributions, number of samples, etc. In the simple/ folder:

- f_simple.go (370 lines) strips variables and parenthesis, but keeps beta distributions, samples, and addition and substraction
- f_minimal.go (140 lines) strips everything that isn't lognormal and scalar multiplication and addition, plus a few debug options.

## Roadmap 

Done: 

- [x] Write README
- [x] Add division?
- [x] Read from file?
- [x] Save to file?
- [x] Allow comments?
  - [x] Use a sed filter? 
  - [x] Add proper comment processing
- [x] Add show more info version
- [x] Scalar multiplication and division
- [x] Think how to integrate with squiggle.c to draw samples
  - [x] Copy the time to botec go code
  - [x] Define samplers
  - [x] Call those samplers when operating on distributions that can't be operted on algebraically
- [x] Display output more nicely, with K/M/B/T
- [x] Consider the following: make this into a stack-based DSL, with:
  - [x] Variables that can be saved to and then displayed
  - [x] Other types of distributions, particularly beta distributions? => But then this requires moving to bags of samples. It could still be ~instantaneous though.
  - [x] Added bags of samples to support addition and multiplication of betas and lognormals
- [x] Figure out go syntax for
  - Maps
  - Joint types
  - Enums
- [x] Fix correlation problem, by spinning up a new randomness thing every time some serial computation is done.
- [x] Clean up error code. Right now only needed for division
- [x] Maintain *both* a more complex thing that's more featureful *and* the more simple multiplication of lognormals thing.
- [x] Allow input with K/M/T
- [x] Document parenthesis syntax
- [x] Specify number of samples as a command line option
- [x] Figure out how to make models executable, by adding a #!/bin/bash-style command at the top?

To (possibly) do:

- [ ] Add flag to repeat input lines (useful when reading from files)
- [ ] Make -n flag work
- [ ] Add functions. Now easier to do with an explicit representation of the stakc
- [ ] Think about how to draw a histogram from samples
- [ ] Dump samples to file
- [ ] Represent samples/statistics in some other way
- [ ] Perhaps use qsort rather than full sorting
- [ ] Program into a small device, like a calculator?

Discarded: 

- [ ] ~~Think of some way of calling bc~~