A minimalist calculator 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.

Motivation

Sometimes, Squiggle, simple squiggle or 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

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

$ fermi -n 1000000
$ fermi -n 1_000_000

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
• Because the model reads from standard input, you can pipe a model to it. For instance, try cat more/piano-tuners.f | fermi
• You can also save a session to a logfile with tee. Try 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:

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

To (possibly) do:

• Figure out how to make models executable, by adding a #!/bin/bash-style command at the top?
• 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