Average Error: 16.3 → 6.0
Time: 5.0s
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 <= 1550527369.5997407)) {
		VAR = ((double) (((double) (((double) (((double) (beta * ((double) (((double) (1.0 * 1.0)) + ((double) (((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))) * ((double) (1.0 + ((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))))))))))) - ((double) (((double) (alpha + ((double) (beta + 2.0)))) * ((double) log(((double) exp(((double) (((double) (((double) pow(((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))), 2.0)) + ((double) (1.0 * ((double) (1.0 + ((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))))))))) * ((double) (((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))) - 1.0)))))))))))) / ((double) (((double) (alpha + ((double) (beta + 2.0)))) * ((double) (((double) (1.0 * 1.0)) + ((double) (((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))) * ((double) (1.0 + ((double) (alpha / ((double) (alpha + ((double) (beta + 2.0)))))))))))))))) / 2.0));
	} else {
		VAR = ((double) (((double) (((double) (beta / ((double) (2.0 + ((double) (alpha + beta)))))) - ((double) (((double) (4.0 / ((double) (alpha * alpha)))) - ((double) (((double) (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  < 1550527369.59974074
    1. Initial program 0.1
      \[\]
    2. Using strategy rm
    3. Applied div-sub0.1
      \[\leadsto \]
    4. Applied associate-+l-0.1
      \[\leadsto \]
    5. Simplified0.1
      \[\leadsto \]
    6. Using strategy rm
    7. Applied flip3--0.1
      \[\leadsto \]
    8. Applied frac-sub0.1
      \[\leadsto \]
    9. Simplified0.1
      \[\leadsto \]
    10. Simplified0.1
      \[\leadsto \]
    11. Using strategy rm
    12. Applied add-log-exp0.1
      \[\leadsto \]
    13. Applied add-log-exp0.1
      \[\leadsto \]
    14. Applied diff-log0.1
      \[\leadsto \]
    15. Simplified0.1
      \[\leadsto \]
    16. Using strategy rm
    17. Applied difference-cubes0.1
      \[\leadsto \]
    18. Simplified0.1
      \[\leadsto \]
    if 1550527369.59974074 <  alpha 
    1. Initial program 49.7
      \[\]
    2. Using strategy rm
    3. Applied div-sub49.7
      \[\leadsto \]
    4. Applied associate-+l-48.2
      \[\leadsto \]
    5. Simplified48.2
      \[\leadsto \]
    6. Taylor expanded around inf 18.0
      \[\leadsto \]
    7. Simplified18.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification6.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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))