Here is approximating Fibonacci with polynomials. Evidently I wrote this in June, 2014:

  #include <math.h>
  #include <stdio.h>

  int fib(int n)
  {
    double out = 0.002579370;
    out *= n; out -= 0.065277776;
    out *= n; out += 0.659722220;
    out *= n; out -= 3.381944442;
    out *= n; out += 9.230555548;
    out *= n; out -= 12.552777774;
    out *= n; out += 7.107142857;
    out *= n;
    return floor(out + 0.5);
  }

  int main(void)
  {
    int i;
    for (i = 0; i < 9; i++) {
      printf("fib(%d) = %d\n", i, fib(i));
      switch (i) {
      case 7:
        puts("^ So, is this calculation fib or not?");
        break;
      case 8:
        puts("^ Answer to life, universe & everything responds negatively!");
      }
    }
    return 0;
  }

Run:

  $ ./fib2
  fib(0) = 0
  fib(1) = 1
  fib(2) = 1
  fib(3) = 2
  fib(4) = 3
  fib(5) = 5
  fib(6) = 8
  fib(7) = 13
  ^ So, is this calculation fib or not?
  fib(8) = 42
  ^ Answer to life, universe & everything responds negatively