Lua translation!

Haskell translation

Scala translation

C# Translation (straightforward 1-1 to my earlier c++ translation).

C translation

Python translation

Python translation, please review.

JS tests. In the fixed tests, this block:

  describe("large terms",()=>{
    it("exp",()=>{
      assert.approximately( take(51)(exp())[50], 1/30414093201713378043612608166064768844377641568960512000000000000, 1e-72 );
    });
    it("sin",()=>{
      assert.approximately( take(52)(exp())[51], 1/1551118753287382280224243016469303211063259720016986112000000000000, 1e-74 );
    });
    it("cos",()=>{
      assert.approximately( take(53)(exp())[52], 1/80658175170943878571660636856403766975289505440883277824000000000000, 1e-75 );
   ` });

should be replaced by:

  describe("large terms",()=>{
    it("exp",()=>{
      assert.approximately( take(51)(exp())[50], 1/30414093201713378043612608166064768844377641568960512000000000000, 1e-72 );
    });
    it("sin",()=>{
      assert.approximately( take(52)(sin())[51], -1/1551118753287382280224243016469303211063259720016986112000000000000, 1e-74 );
    });
    it("cos",()=>{
      assert.approximately( take(53)(cos())[52], 1/80658175170943878571660636856403766975289505440883277824000000000000, 1e-75 );
   ` });

(Testing sin and cos, and changing the value for sin.)

My implementation returns the 1.000.000th element of the sequence in about 400ms. Why do the tests time out?

Sorry, I beat you to it. (Duplicate)

Very nice one!
It seems that the value of n can be easily cranked up to 5 * 10^6...

module name is mispelt, everywhere.