.. _sphx_glr_api_gallery_calculus_dual_numbers:

Dual numbers
------------

Forward-mode automatic differentiation: exact derivatives with no
finite-difference truncation error.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Dual numbers compute a function&#x27;s value and its exact derivative together, with no finite-difference step-size tradeoff between truncation error (large h) and floating-point cancellation (small h).">

.. only:: html

  .. image:: /api/gallery/calculus/dual_numbers/images/thumb/sphx_glr_plot_01_forward_mode_autodiff_thumb.png
    :alt:

  :doc:`/api/gallery/calculus/dual_numbers/plot_01_forward_mode_autodiff`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Forward-mode automatic differentiation via dual numbers</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/calculus/dual_numbers/plot_01_forward_mode_autodiff