Average Error: 16.7 → 6.2
Time: 3.4s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double alpha, double beta) {
	return ((double) (((double) (((double) (((double) (beta - alpha)) / ((double) (((double) (alpha + beta)) + 2.0)))) + 1.0)) / 2.0));
}

↓
double code(double alpha, double beta) {
	double VAR;
	if ((alpha <= 6.5531379149477994e+19)) {
		VAR = ((double) (((double) (((double) (1.0 / ((double) (((double) (alpha + ((double) (beta + 2.0)))) / beta)))) - ((double) (((double) (alpha * ((double) (1.0 / ((double) (alpha + ((double) (beta + 2.0)))))))) - 1.0)))) / 2.0));
	} else {
		VAR = ((double) (((double) (((double) (((double) (((double) cbrt(beta)) * ((double) (((double) cbrt(beta)) / ((double) (((double) cbrt(((double) (alpha + ((double) (beta + 2.0)))))) * ((double) cbrt(((double) (alpha + ((double) (beta + 2.0)))))))))))) / ((double) (((double) cbrt(((double) (alpha + ((double) (beta + 2.0)))))) / ((double) cbrt(beta)))))) - ((double) (((double) (((double) (((double) (4.0 / alpha)) - 2.0)) / alpha)) - ((double) (8.0 / ((double) pow(alpha, 3.0)))))))) / 2.0));
	}
	return VAR;
}

Error
Bits error versus alpha
Bits error versus beta
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  alpha  < 65531379149477994500
    1. Initial program 0.6
      \[\]
    2. Using strategy rm
    3. Applied div-sub0.6
      \[\leadsto \]
    4. Applied associate-+l-0.6
      \[\leadsto \]
    5. Simplified0.6
      \[\leadsto \]
    6. Using strategy rm
    7. Applied clear-num0.6
      \[\leadsto \]
    8. Simplified0.6
      \[\leadsto \]
    9. Using strategy rm
    10. Applied div-inv0.6
      \[\leadsto \]
    11. Simplified0.6
      \[\leadsto \]
    if 65531379149477994500 <  alpha 
    1. Initial program 50.3
      \[\]
    2. Using strategy rm
    3. Applied div-sub50.3
      \[\leadsto \]
    4. Applied associate-+l-48.7
      \[\leadsto \]
    5. Simplified48.7
      \[\leadsto \]
    6. Using strategy rm
    7. Applied clear-num48.7
      \[\leadsto \]
    8. Simplified48.7
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cube-cbrt48.8
      \[\leadsto \]
    11. Applied add-cube-cbrt48.7
      \[\leadsto \]
    12. Applied times-frac48.7
      \[\leadsto \]
    13. Applied associate-/r*48.7
      \[\leadsto \]
    14. Simplified48.7
      \[\leadsto \]
    15. Taylor expanded around inf 18.0
      \[\leadsto \]
    16. Simplified18.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification6.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0))