This exercise covers built-in JavaScript Math functions.

• Generate a plot of Math.sin over the interval [0,2π].
• Generate a plot of Math.cos over the interval [0,2π].

A common measure of numerical accuracy is the root-mean-square error (RMSE). The basic idea is to determine the average deviation of computed values from a known standard. The lower the RMSE, the more accurate the algorithm; the higher the RMSE, the less accurate the algorithm.

• Write a function to compute the root-mean-square error (RMSE).

• Generate a plot showing the sine computed by Math.sin and the sine computed from Julia (Julia results can be found in the ./fixtures directory). The x values over which to compute the sin are included in the fixtures.
• Generate a plot showing the deviations (in units of epsilon) of Math.sin from Julia (include the RMSE in the plot title).
• As a bonus, repeat the test for different Node versions.

• Extend the previous solutions to test the following Math functions:

  • cos
  • tan
  • sqrt
  • pow
  • exp
  • log

  The output should be a single web page showing the deviations in units of epsilon for all functions.

• As a bonus, repeat the tests for different browsers, such as Firefox and Internet Explorer.

• Extend the previous solution to test custom implementations of the above functions.

  • sin: @stdlib/math/base/special/sin
  • cos: @stdlib/math/base/special/cos
  • tan: @stdlib/math/base/special/tan
  • sqrt: @stdlib/math/base/special/sqrt
  • log: @stdlib/math/base/special/ln
  • exp: @stdlib/math/base/special/exp
  • pow: @stdlib/math/base/special/pow

• When calculating the RMSE, consider using Welford's method for robust computation of the mean.
• When generating plots, be sure to specify plot axis labels and the plot title.
• To test against different Node versions, use nvm.
• Testing different browsers may be rather involved. One possible solution would be to launch a browser, load a test script which runs the computations, and then stream the results back to an analysis server which collects the results and generates a plot.

Assuming that each solution is placed in a separate file,

$ node ./path/to/<solution_1>.js
$ node ./path/to/<solution_2>.js
# ...

When all your solutions succeed, proceed to the next exercise.