Average Error: 37.3 → 37.3
Time: 2.8s
Precision: binary64
\[\cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)\]
↓
\[\cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)\]
\cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)
↓
\cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)
double code(double x) {
	return ((double) (((double) cos(((double) (1.0 / ((double) (x + 1.0)))))) - ((double) cos(((double) (1.0 / x))))));
}
↓
double code(double x) {
	return ((double) (((double) cos(((double) (1.0 / ((double) (x + 1.0)))))) - ((double) cos(((double) (1.0 / x))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 37.3

    \[\cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)\]

  2. Final simplification37.3

    \[\leadsto \cos \left(\frac{1}{x + 1}\right) - \cos \left(\frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(- (cos (/ 1 (+ x 1))) (cos (/ 1 x)))"
  :precision binary64
  (- (cos (/ 1.0 (+ x 1.0))) (cos (/ 1.0 x))))