A minimalist calculator for fermi estimation

This project is a minimalist, stack-based 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
=> 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:

$ fermi
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.

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:
         Clear stack:                      clear | c | .
         Print this help message:          help  | h
         Print debug info:                 debug | d
         Exit:                             exit  | e
         Comment:                          # this is a comment
  Examples:
    + 2
    / 2.5
    * 1 10 (interpreted as lognormal)
    + 1 10
    * beta 1 10
    1 10 (multiplication taken as default operation)
      =: x
    .
    1 100
    + x
    # this is a comment
    * 1 12 # this is an operation followed by a comment
    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
• Because the model reads from standard input, you can pipe a model to it. For instance, try cat more/piano-tuners.f | fermi

Different levels of complexity

The top level f.go file (400 lines) has a bunch of complexity: variables, parenthesis, samples, beta distributions. 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

To (possibly) do:

• Document parenthesis syntax
• 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