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, simple squiggle or 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

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

• Write README
• Add division?
• Read from file?
• Save to file?
• Allow comments?
  • Use a sed filter?
• Add show more info version
• Scalar multiplication and division
• Program into a small device, like a calculator?
• [-] Think of some way of calling bc
• 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
• Think about how to draw a histogram from samples
• 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.
• 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.
• Maintain both a more complex thing that's more featureful and the more simple multiplication of lognormals thing.
• Clean up error code. Right now only needed for division
• 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)