Average Error: 40.0 → 0.7
Time: 8.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return cos(x + eps) - cos(x);
}

↓
double code(double x, double eps) {
	double tmp;
	if (eps <= -1.3830861607967381e-05) {
		tmp = (cos(x) * cos(eps)) - (cos(x) + (sin(x) * sin(eps)));
	} else if (eps <= 2.3419086364105904e-05) {
		tmp = -2.0 * (sin(eps / 2.0) * sin((x + (eps + x)) / 2.0));
	} else {
		tmp = ((cos(x) * cos(eps)) - (sin(x) * sin(eps))) - cos(x);
	}
	return tmp;
}

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  < -1.3830861607967381e-5
    1. Initial program 31.1
      \[\]
    2. Using strategy rm
    3. Applied cos-sum0.9
      \[\leadsto \]
    4. Applied associate--l-0.9
      \[\leadsto \]
    5. Simplified0.9
      \[\leadsto \]
    if -1.3830861607967381e-5 <  eps  < 2.3419086364105904e-5
    1. Initial program 49.6
      \[\]
    2. Using strategy rm
    3. Applied diff-cos37.8
      \[\leadsto \]
    4. Simplified0.4
      \[\leadsto \]
    if 2.3419086364105904e-5 <  eps 
    1. Initial program 29.8
      \[\]
    2. Using strategy rm
    3. Applied cos-sum1.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(FPCore (x eps)
  :name "2cos (problem 3.3.5)"
  :precision binary64
  (- (cos (+ x eps)) (cos x)))