Average Error: 3.8 → 2.5
Time: 7.9s
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 ((beta <= 1.2687380306321451e+191)) {
		VAR = ((double) (((double) (((double) (((double) sqrt(((double) (((double) (((double) (beta + alpha)) + ((double) (beta * alpha)))) + 1.0)))) / ((double) sqrt(((double) (((double) (beta + alpha)) + ((double) (1.0 * 2.0)))))))) / ((double) sqrt(((double) (((double) (beta + alpha)) + ((double) (1.0 * 2.0)))))))) / ((double) (((double) (((double) (alpha + ((double) (beta + ((double) (1.0 + ((double) (1.0 * 2.0)))))))) / ((double) sqrt(((double) (alpha + ((double) (beta + ((double) (((double) (beta * alpha)) + 1.0)))))))))) * ((double) (alpha + ((double) (beta + ((double) (1.0 * 2.0))))))))));
	} else {
		VAR = ((double) (((double) (((double) cbrt(((double) (((double) (alpha * 0.1875)) + ((double) (0.125 + ((double) (beta * 0.1875)))))))) / ((double) (((double) (beta + alpha)) + ((double) (1.0 * 2.0)))))) / ((double) (1.0 + ((double) (((double) (beta + alpha)) + ((double) (1.0 * 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  beta  < 1.26873803063214509e191
    1. Initial program 1.8
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt2.3
      \[\leadsto \]
    4. Applied add-sqr-sqrt2.7
      \[\leadsto \]
    5. Applied add-sqr-sqrt2.6
      \[\leadsto \]
    6. Applied times-frac2.6
      \[\leadsto \]
    7. Applied times-frac2.4
      \[\leadsto \]
    8. Applied associate-/l*2.4
      \[\leadsto \]
    9. Simplified1.8
      \[\leadsto \]
    if 1.26873803063214509e191 <  beta 
    1. Initial program 17.7
      \[\]
    2. Using strategy rm
    3. Applied add-cbrt-cube18.0
      \[\leadsto \]
    4. Applied add-cbrt-cube64.0
      \[\leadsto \]
    5. Applied cbrt-undiv64.0
      \[\leadsto \]
    6. Simplified17.8
      \[\leadsto \]
    7. Taylor expanded around 0 6.7
      \[\leadsto \]
    8. Simplified6.7
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification2.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(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)))