fermi/README.md

# A minimalist calculator for fermi estimation

This project is a minimalist, stack-based DSL for Fermi estimation. It can multiply and divide scalars, lognormals and beta distributions.

## 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.

## Usage

Here is an example

```
$ go run fermi.go
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:

```
$ sed -u "s|#.*||" | sed -u 's|M|000000|g' | go run fermi.go
5M 12M # number of people living in Chicago
=> 5.0M 12.0M
* beta 1 200 # fraction of people that have a piano
1.9K 123.1K
30 180 # minutes it takes to tune a piano, including travel time
122.9K 11.7M
/ 48 52 # weeks a year pianotuners work for
2.5K 234.6K
/ 6 8 # hours a day
353.9 34.1K
/ 60 # minutes to an hour
5.9 568.3
=: piano_tuners_in_Chicago
piano_tuners_in_Chicago => 5.9 568.3
```

Here is instead an example using beta distributions and variables:

```
1 2
=> 1.0 2.0
* 1_000_000_000
=> 1000.0M 2.0B
=: x # assign to variable
x => 1000.0M 2.0B
. # clear the stack, i.e., make it be 1

beta 1 2
=> beta 1.0 2.0
beta 12 300
=> beta 13.0 302.0
=. y # assign to variable and clear the stack (return it to 1)
y => beta 13.0 302.0

x
=> 1000.0M 2.0B
* y
=> samples 31.3M 98.2M
```

The difference between `=: x` and `=. y` is that `=.` clears the stack after the assignment.

## Installation

```
make build
sudo make install
f # rather than the previous go run fermi.go
```

Why use make instead of the built-in go commands? Because the point of make is to be able to share command-line recipes. 

## Usage together with standard Linux utilities

```bash
f
sed -u "s|#.*||" | sed -u 's|M|000000|g' | f

cat more/piano-tuners.f | f
cat more/piano-tuners-commented.f | sed -u "s|#.*||" | sed -u 's|M|000000|g' | f

tee -a input.log | go run fermi.go | tee -a output.log
tee -a io.log | go run fermi.go | tee -a io.log

function f(){
  sed -u "s|#.*||" | 
  sed -u "s|//.*||" | 
  sed -u 's|K|000|g' | 
  sed -u 's|M|000000|g' | 
  sed -u 's|B|000000000|g' | 
  /usr/bin/f
}
```

Note that these sed commands are just hacks, and won't parse e.g., `3.5K` correctly—it will just substitute for 3.5000

## Tips & tricks

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

## Roadmap 

- [x] Write README
- [x] Add division?
- [x] Read from file?
- [x] Save to file?
- [x] Allow comments?
  - [x] Use a sed filter? 
- [x] Add show more info version
- [x] Scalar multiplication and division
- [ ] Program into a small device, like a calculator?
- [-] Think of some way of calling bc
- [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
- [ ] Think about how to draw a histogram from samples
- [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] 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.
- [ ] Dump samples to file
- [ ] Represent samples/statistics in some other way
- [ ] Perhaps use qsort rather than full sorting

Some possible syntax for a more expressive stack-based DSL (now implemented)