Average Error: 41.2 → 0.3
Time: 5.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (((double) exp(((double) (2.0 * x)))) - 1.0)) / ((double) (((double) exp(x)) - 1.0))))));
}

↓
double code(double x) {
	double VAR;
	if ((x <= -7.284067260085109e-16)) {
		VAR = ((double) sqrt(((double) (((double) (((double) (((double) pow(((double) exp(x)), 2.0)) - 1.0)) / ((double) (((double) pow(((double) exp(x)), 2.0)) - ((double) (1.0 * 1.0)))))) * ((double) (((double) exp(x)) + 1.0))))));
	} else {
		VAR = ((double) (((double) sqrt(2.0)) + ((double) (((double) (x * ((double) (0.5 / ((double) sqrt(2.0)))))) + ((double) (((double) (((double) cbrt(((double) (x * ((double) (x / ((double) sqrt(2.0)))))))) * ((double) (((double) cbrt(((double) (x * ((double) (x / ((double) sqrt(2.0)))))))) * ((double) cbrt(((double) (x * ((double) (x / ((double) sqrt(2.0)))))))))))) * 0.1875))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  x  < -7.2840672600851088e-16
    1. Initial program 0.9
      \[\]
    2. Simplified0.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied flip--0.0
      \[\leadsto \]
    5. Applied associate-/r/0.0
      \[\leadsto \]
    6. Simplified0.0
      \[\leadsto \]
    if -7.2840672600851088e-16 <  x 
    1. Initial program 62.5
      \[\]
    2. Simplified62.3
      \[\leadsto \]
    3. Taylor expanded around 0 0.5
      \[\leadsto \]
    4. Simplified0.5
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt0.5
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  :precision binary64
  (sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))))