Average Error: 36.9 → 15.4
Time: 16.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double eps) {
	return ((double) (((double) tan(((double) (x + eps)))) - ((double) tan(x))));
}

↓
double code(double x, double eps) {
	double VAR;
	if ((eps <= -6.583395804010651e-55)) {
		VAR = ((double) (((double) (((double) (((double) tan(x)) + ((double) tan(eps)))) / ((double) (1.0 - ((double) (((double) (((double) tan(x)) * ((double) sin(eps)))) / ((double) cos(eps)))))))) - ((double) tan(x))));
	} else {
		double VAR_1;
		if ((eps <= 2.6174394417726606e-73)) {
			VAR_1 = ((double) (eps + ((double) (x * ((double) (eps * ((double) (eps + x))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (((double) (((double) (((double) cos(eps)) * ((double) sin(x)))) + ((double) (((double) sin(eps)) * ((double) cos(x)))))) / ((double) (((double) cos(eps)) * ((double) cos(x)))))) / ((double) (1.0 - ((double) (((double) tan(x)) * ((double) tan(eps)))))))) - ((double) tan(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
Target
Original36.9
Target15.1
Herbie15.4
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  eps  < -6.5833958040106514e-55
    1. Initial program 30.1
      \[\]
    2. Using strategy rm
    3. Applied tan-sum4.1
      \[\leadsto \]
    4. Using strategy rm
    5. Applied tan-quot4.2
      \[\leadsto \]
    6. Applied associate-*r/4.2
      \[\leadsto \]
    if -6.5833958040106514e-55 <  eps  < 2.61743944177266056e-73
    1. Initial program 47.8
      \[\]
    2. Taylor expanded around 0 31.6
      \[\leadsto \]
    3. Simplified31.3
      \[\leadsto \]
    if 2.61743944177266056e-73 <  eps 
    1. Initial program 29.7
      \[\]
    2. Using strategy rm
    3. Applied tan-sum5.9
      \[\leadsto \]
    4. Using strategy rm
    5. Applied tan-quot6.1
      \[\leadsto \]
    6. Applied tan-quot6.1
      \[\leadsto \]
    7. Applied frac-add6.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification15.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x eps)
  :name "2tan (problem 3.3.2)"
  :precision binary64

  :herbie-target
  (/ (sin eps) (* (cos x) (cos (+ x eps))))

  (- (tan (+ x eps)) (tan x)))