Average Error: 30.3 → 0.8
Time: 8.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) sin(x))));
}

↓
double code(double x) {
	double VAR;
	if ((((double) (((double) (1.0 - ((double) cos(x)))) / ((double) sin(x)))) <= -0.002267160644340566)) {
		VAR = ((double) (((double) sqrt(((double) (1.0 - ((double) cos(x)))))) / ((double) (((double) sin(x)) / ((double) sqrt(((double) (1.0 - ((double) cos(x))))))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (1.0 - ((double) cos(x)))) / ((double) sin(x)))) <= 0.0)) {
			VAR_1 = ((double) (((double) (0.041666666666666664 * ((double) pow(x, 3.0)))) + ((double) (((double) (0.004166666666666667 * ((double) pow(x, 5.0)))) + ((double) (x * 0.5))))));
		} else {
			VAR_1 = ((double) log(((double) exp(((double) (((double) (((double) (((double) (1.0 * 1.0)) - ((double) (((double) cos(x)) * ((double) cos(x)))))) / ((double) (1.0 + ((double) cos(x)))))) / ((double) sin(x))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original30.3
Target0.0
Herbie0.8
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  (/ (- 1.0 (cos x)) (sin x))  < -0.002267160644340566
    1. Initial program 0.9
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.1
      \[\leadsto \]
    4. Applied associate-/l*1.1
      \[\leadsto \]
    if -0.002267160644340566 <  (/ (- 1.0 (cos x)) (sin x))  < 0.0
    1. Initial program 60.3
      \[\]
    2. Taylor expanded around 0 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if 0.0 <  (/ (- 1.0 (cos x)) (sin x)) 
    1. Initial program 1.5
      \[\]
    2. Using strategy rm
    3. Applied add-log-exp1.6
      \[\leadsto \]
    4. Using strategy rm
    5. Applied flip--2.0
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :precision binary64
  :herbie-expected 2

  :herbie-target
  (tan (/ x 2.0))

  (/ (- 1.0 (cos x)) (sin x)))