Average Error: 24.2 → 11.0
Time: 6.5s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double alpha, double beta, double i) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (alpha + beta)) * ((double) (beta - alpha)))) / ((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))))) / ((double) (((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))) + 2.0)))) + 1.0)) / 2.0));
}

↓
double code(double alpha, double beta, double i) {
	double VAR;
	if ((alpha <= 2.632083162561644e+221)) {
		VAR = ((double) (((double) (((double) (((double) (((double) (alpha + beta)) * ((double) (((double) cbrt(((double) (((double) (beta - alpha)) / ((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))))))) * ((double) cbrt(((double) (((double) (beta - alpha)) / ((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))))))))))) * ((double) (((double) cbrt(((double) (((double) (beta - alpha)) / ((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))))))) / ((double) (alpha + ((double) (beta + ((double) (2.0 + ((double) (2.0 * i)))))))))))) + 1.0)) / 2.0));
	} else {
		VAR = ((double) (((double) (((double) (2.0 / alpha)) + ((double) (((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
Bits error versus i
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 2 regimes
  2. if  alpha  < 2.632083162561644e221
    1. Initial program 20.0
      \[\]
    2. Simplified15.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied associate-/r*7.9
      \[\leadsto \]
    5. Simplified7.9
      \[\leadsto \]
    6. Using strategy rm
    7. Applied *-un-lft-identity7.9
      \[\leadsto \]
    8. Applied add-cube-cbrt7.9
      \[\leadsto \]
    9. Applied times-frac7.9
      \[\leadsto \]
    10. Applied associate-*r*7.9
      \[\leadsto \]
    11. Simplified7.9
      \[\leadsto \]
    if 2.632083162561644e221 <  alpha 
    1. Initial program 64.0
      \[\]
    2. Simplified56.4
      \[\leadsto \]
    3. Taylor expanded around inf 41.0
      \[\leadsto \]
    4. Simplified41.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification11.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/2"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0) (> i 0.0))
  (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 2.0))