Average Error: 39.1 → 0.4
Time: 10.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) cos(((double) (x + eps)))) - ((double) cos(x))));
}

↓
double code(double x, double eps) {
	return ((double) (-2.0 * ((double) (((double) (((double) sin(x)) * ((double) (((double) cos(((double) (eps * 0.5)))) * ((double) sin(((double) (eps / 2.0)))))))) + ((double) (((double) cos(x)) * ((double) (((double) sin(((double) (eps / 2.0)))) * ((double) sin(((double) (eps * 0.5))))))))))));
}

Error
Bits error versus x
Bits error versus eps
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 39.1
    \[\]
  2. Using strategy rm
  3. Applied diff-cos33.6
    \[\leadsto \]
  4. Simplified15.0
    \[\leadsto \]
  5. Taylor expanded around inf 14.9
    \[\leadsto \]
  6. Simplified14.9
    \[\leadsto \]
  7. Using strategy rm
  8. Applied sin-sum0.4
    \[\leadsto \]
  9. Applied distribute-lft-in0.4
    \[\leadsto \]
  10. Simplified0.4
    \[\leadsto \]
  11. Simplified0.4
    \[\leadsto \]
  12. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x eps)
  :name "2cos (problem 3.3.5)"
  :precision binary64
  (- (cos (+ x eps)) (cos x)))