Average Error: 41.1 → 0.7
Time: 3.4s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) exp(x)) / ((double) (((double) exp(x)) - 1.0))));
}

↓
double code(double x) {
	double VAR;
	if ((((double) exp(x)) <= 0.9896911685182637)) {
		VAR = ((double) (((double) (((double) exp(x)) + 1.0)) * ((double) (((double) (((double) sqrt(((double) exp(x)))) / ((double) (((double) exp(x)) + 1.0)))) * ((double) (((double) sqrt(((double) exp(x)))) / ((double) (((double) exp(x)) - 1.0))))))));
	} else {
		VAR = ((double) (0.5 + ((double) (((double) (x * 0.08333333333333333)) + ((double) (1.0 / x))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original41.1
Target40.6
Herbie0.7
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (exp x)  < 0.98969116851826366
    1. Initial program 0.0
      \[\]
    2. Using strategy rm
    3. Applied flip--0.0
      \[\leadsto \]
    4. Applied associate-/r/0.0
      \[\leadsto \]
    5. Simplified0.0
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-sqr-sqrt0.0
      \[\leadsto \]
    8. Applied unpow-prod-down0.0
      \[\leadsto \]
    9. Applied difference-of-squares0.0
      \[\leadsto \]
    10. Applied add-sqr-sqrt0.0
      \[\leadsto \]
    11. Applied times-frac0.0
      \[\leadsto \]
    12. Simplified0.0
      \[\leadsto \]
    13. Simplified0.0
      \[\leadsto \]
    if 0.98969116851826366 <  (exp x) 
    1. Initial program 61.8
      \[\]
    2. Taylor expanded around 0 1.0
      \[\leadsto \]
    3. Simplified1.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "expq2 (section 3.11)"
  :precision binary64

  :herbie-target
  (/ 1.0 (- 1.0 (exp (neg x))))

  (/ (exp x) (- (exp x) 1.0)))