Average Error: 3.8 → 2.5
Time: 7.2s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double alpha, double beta) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (alpha + beta)) + ((double) (beta * alpha)))) + 1.0)) / ((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0)))))) / ((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0)))))) / ((double) (((double) (((double) (alpha + beta)) + ((double) (2.0 * 1.0)))) + 1.0))));
}

↓
double code(double alpha, double beta) {
	double VAR;
	if ((alpha <= 5.016831569341494e+161)) {
		VAR = ((double) (((double) (((double) (((double) (((double) (((double) (alpha + beta)) + ((double) (alpha * beta)))) + 1.0)) / ((double) (((double) (alpha + beta)) + ((double) (1.0 * 2.0)))))) / ((double) (((double) (alpha + beta)) + ((double) (1.0 * 2.0)))))) / ((double) (alpha + ((double) (beta + 3.0))))));
	} else {
		VAR = 0.0;
	}
	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  < 5.016831569341494e161
    1. Initial program 1.4
      \[\]
    2. Taylor expanded around 0 1.4
      \[\leadsto \]
    3. Simplified1.4
      \[\leadsto \]
    if 5.016831569341494e161 <  alpha 
    1. Initial program 16.2
      \[\]
    2. Taylor expanded around inf 8.6
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification2.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))