Average Error: 39.2 → 1.3
Time: 6.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) cos(((double) (x + eps)))) - ((double) cos(x))));
}

↓
double code(double x, double eps) {
	double VAR;
	if (((eps <= -1.35117877873764e+26) || !(eps <= 2.9676922165611374e-05))) {
		VAR = ((double) (((double) (((double) (((double) cos(x)) * ((double) cos(eps)))) - ((double) (((double) sin(x)) * ((double) sin(eps)))))) - ((double) cos(x))));
	} else {
		VAR = ((double) (((double) (((double) sin(((double) (eps / 2.0)))) * -2.0)) * ((double) sin(((double) (((double) (x + ((double) (eps + x)))) / 2.0))))));
	}
	return VAR;
}

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. Split input into 2 regimes
  2. if  eps  < -1.35117877873763993e26 or 2.9676922165611374e-5 <  eps 
    1. Initial program 29.1
      \[\]
    2. Using strategy rm
    3. Applied cos-sum0.8
      \[\leadsto \]
    if -1.35117877873763993e26 <  eps  < 2.9676922165611374e-5
    1. Initial program 48.9
      \[\]
    2. Using strategy rm
    3. Applied diff-cos38.1
      \[\leadsto \]
    4. Simplified1.7
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-*r*1.7
      \[\leadsto \]
    7. Simplified1.7
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification1.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x eps)
  :name "2cos (problem 3.3.5)"
  :precision binary64
  (- (cos (+ x eps)) (cos x)))