Average Error: 3.5 → 2.2
Time: 8.5s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double alpha, double beta) {
	return (((((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);
}

↓
double code(double alpha, double beta) {
	double tmp;
	if (alpha <= 1.423893672330808e+162) {
		tmp = (((((alpha + beta) + (alpha * beta)) + 1.0) / ((alpha + beta) + (1.0 * 2.0))) / ((alpha + beta) + (1.0 * 2.0))) / (alpha + (beta + 3.0));
	} else {
		tmp = 0.0;
	}
	return tmp;
}

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  < 1.4238936723308079e162
    1. Initial program 1.1
      \[\]
    2. Taylor expanded around 0 1.1
      \[\leadsto \]
    3. Simplified1.1
      \[\leadsto \]
    if 1.4238936723308079e162 <  alpha 
    1. Initial program 16.1
      \[\]
    2. Taylor expanded around inf 7.9
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification2.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020338 
(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)))