Average Error: 39.3 → 0.7
Time: 6.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) cos(((double) (x + eps)))) - ((double) cos(x))));
}

↓
double code(double x, double eps) {
	double VAR;
	if ((eps <= -0.0026009505018971444)) {
		VAR = ((double) (((double) (((double) cos(x)) * ((double) cos(eps)))) - ((double) (((double) cos(x)) + ((double) (((double) sin(x)) * ((double) sin(eps))))))));
	} else {
		double VAR_1;
		if ((eps <= 0.029940739140316575)) {
			VAR_1 = ((double) (-2.0 * ((double) (((double) sin(((double) (eps / 2.0)))) * ((double) sin(((double) (((double) (x + ((double) (eps + x)))) / 2.0))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (((double) cos(x)) * ((double) cos(eps)))) - ((double) (((double) sin(x)) * ((double) sin(eps)))))) - ((double) cos(x))));
		}
		VAR = VAR_1;
	}
	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 3 regimes
  2. if  eps  < -0.00260095050189714438
    1. Initial program 29.4
      \[\]
    2. Using strategy rm
    3. Applied cos-sum0.8
      \[\leadsto \]
    4. Applied associate--l-0.8
      \[\leadsto \]
    5. Simplified0.8
      \[\leadsto \]
    if -0.00260095050189714438 <  eps  < 0.0299407391403165753
    1. Initial program 49.0
      \[\]
    2. Using strategy rm
    3. Applied diff-cos37.2
      \[\leadsto \]
    4. Simplified0.6
      \[\leadsto \]
    if 0.0299407391403165753 <  eps 
    1. Initial program 29.7
      \[\]
    2. Using strategy rm
    3. Applied cos-sum0.8
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (x eps)
  :name "2cos (problem 3.3.5)"
  :precision binary64
  (- (cos (+ x eps)) (cos x)))