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Automatic differential in Ruby
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lib add support for comparison Apr 18, 2019
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Work In Progress

Calculating gradient or differential is a very common task when working in Math heavy field like Machine Learning. But deriving gradient by hand is time-consuming and error-prone.

Automatic Differentiation(AD) can calculate gradient of arbitrary function automatically. AD is efficient(for human) and correct(without human error).


require 'autodiff'
# Calculate differential of a function
# df/dx = 3*(x**2)
Autodiff.gradient(2) { |x| x**3} # 12  

# Calculate gradient of a function
# df/dx = y, df/dy = x
Autodiff.gradient([2,3]) { |x, y| x * y } # [3,2]

# Calculate gradient with triangular function
Autodiff.gradient([2,Math::PI]) { |x, y|x * Math.cos(y) }
# [-1.0, -2.4492935982947064e-16] with floating point error

# Calculate gradient of a function that is not in simple math form
# same as 20x+30y
Autodiff.gradient([1, 1]) {|x,y| 10.times.reduce(0){|acc, n| acc + 2*x + 3*y} } # [20, 30]


current supported operators

  • +, -, *, /
  • sin, cos, tan, log

Goal is to add all Numeric & Math functions


Add this line to your application's Gemfile:

gem 'autodiff'

And then execute:

$ bundle

Or install it yourself as:

$ gem install autodiff


After checking out the repo, run bin/setup to install dependencies. Then, run rake test to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and tags, and push the .gem file to


Bug reports and pull requests are welcome on GitHub at This project is intended to be a safe, welcoming space for collaboration, and contributors are expected to adhere to the Contributor Covenant code of conduct.


The gem is available as open source under the terms of the MIT License.

Code of Conduct

Everyone interacting in the Autodiff project’s codebases, issue trackers, chat rooms and mailing lists is expected to follow the code of conduct.

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