Average Error: 16.7 → 6.2
Time: 4.7s
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 <= 4.4939821187056533e+24)) {
		VAR = ((double) (((double) log(((double) exp(((double) (1.0 + ((double) (((double) (beta / ((double) (alpha + ((double) (beta + 2.0)))))) - ((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))))))))))) / 2.0));
	} else {
		VAR = ((double) (((double) (((double) (beta / ((double) (2.0 + ((double) (alpha + beta)))))) + ((double) (((double) (((double) (2.0 / alpha)) + ((double) (8.0 / ((double) pow(alpha, 3.0)))))) - ((double) (4.0 / ((double) (alpha * alpha)))))))) / 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  < 4.4939821187056533e24
    1. Initial program 0.9
      \[\]
    2. Using strategy rm
    3. Applied div-sub0.9
      \[\leadsto \]
    4. Applied associate-+l-0.9
      \[\leadsto \]
    5. Simplified0.9
      \[\leadsto \]
    6. Using strategy rm
    7. Applied add-log-exp0.9
      \[\leadsto \]
    8. Applied add-log-exp0.9
      \[\leadsto \]
    9. Applied diff-log1.0
      \[\leadsto \]
    10. Applied add-log-exp1.0
      \[\leadsto \]
    11. Applied diff-log1.0
      \[\leadsto \]
    12. Simplified0.9
      \[\leadsto \]
    if 4.4939821187056533e24 <  alpha 
    1. Initial program 51.5
      \[\]
    2. Using strategy rm
    3. Applied div-sub51.5
      \[\leadsto \]
    4. Applied associate-+l-49.8
      \[\leadsto \]
    5. Simplified49.8
      \[\leadsto \]
    6. Taylor expanded around inf 17.8
      \[\leadsto \]
    7. Simplified17.8
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification6.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))