Average Error: 30.9 → 0.6
Time: 8.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) sin(x))));
}

↓
double code(double x) {
	double VAR;
	if ((x <= -0.024164467200655196)) {
		VAR = ((double) (((double) (((double) log(((double) sqrt(((double) exp(((double) (((double) pow(1.0, 3.0)) - ((double) pow(((double) cos(x)), 3.0)))))))))) + ((double) log(((double) sqrt(((double) exp(((double) (((double) pow(1.0, 3.0)) - ((double) pow(((double) cos(x)), 3.0)))))))))))) / ((double) (((double) (((double) (1.0 * 1.0)) + ((double) (((double) cos(x)) * ((double) (1.0 + ((double) cos(x)))))))) * ((double) sin(x))))));
	} else {
		double VAR_1;
		if ((x <= 0.01952280889875721)) {
			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) (((double) log(((double) exp(((double) (((double) pow(1.0, 3.0)) - ((double) pow(((double) cos(x)), 3.0)))))))) / ((double) (((double) sin(x)) * ((double) (((double) (1.0 * 1.0)) + ((double) (((double) cos(x)) * ((double) (((double) (((double) (1.0 * 1.0)) - ((double) pow(((double) cos(x)), 2.0)))) / ((double) (1.0 - ((double) cos(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
Original30.9
Target0.0
Herbie0.6
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  x  < -0.024164467200655196
    1. Initial program 0.9
      \[\]
    2. Using strategy rm
    3. Applied flip3--1.0
      \[\leadsto \]
    4. Applied associate-/l/1.0
      \[\leadsto \]
    5. Simplified1.0
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-log-exp1.1
      \[\leadsto \]
    8. Applied add-log-exp1.1
      \[\leadsto \]
    9. Applied diff-log1.2
      \[\leadsto \]
    10. Simplified1.1
      \[\leadsto \]
    11. Using strategy rm
    12. Applied add-sqr-sqrt1.3
      \[\leadsto \]
    13. Applied log-prod1.3
      \[\leadsto \]
    if -0.024164467200655196 <  x  < 0.01952280889875721
    1. Initial program 59.9
      \[\]
    2. Taylor expanded around 0 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if 0.01952280889875721 <  x 
    1. Initial program 0.9
      \[\]
    2. Using strategy rm
    3. Applied flip3--1.0
      \[\leadsto \]
    4. Applied associate-/l/1.0
      \[\leadsto \]
    5. Simplified1.0
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-log-exp1.1
      \[\leadsto \]
    8. Applied add-log-exp1.1
      \[\leadsto \]
    9. Applied diff-log1.1
      \[\leadsto \]
    10. Simplified1.0
      \[\leadsto \]
    11. Using strategy rm
    12. Applied flip-+1.1
      \[\leadsto \]
    13. Simplified1.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "tanhf (example 3.4)"
  :precision binary64
  :herbie-expected 2

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

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