Average Error: 41.3 → 0.8
Time: 2.2s
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)) <= 9.853292729842674e-22)) {
		VAR = ((double) (((double) sqrt(((double) exp(x)))) * ((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
Original41.3
Target40.9
Herbie0.8
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (exp x)  < 9.8532927298426739e-22
    1. Initial program 0
      \[\]
    2. Using strategy rm
    3. Applied *-un-lft-identity0
      \[\leadsto \]
    4. Applied add-sqr-sqrt0.0
      \[\leadsto \]
    5. Applied times-frac0.0
      \[\leadsto \]
    6. Simplified0.0
      \[\leadsto \]
    if 9.8532927298426739e-22 <  (exp x) 
    1. Initial program 61.5
      \[\]
    2. Taylor expanded around 0 1.2
      \[\leadsto \]
    3. Simplified1.2
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x)
  :name "expq2 (section 3.11)"
  :precision binary64

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

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