Average Error: 24.0 → 11.0
Time: 6.4s
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 <= 8.117678325149238e+131)) {
		VAR = ((double) (((double) (((double) (((double) pow(((double) (((double) (beta - alpha)) / ((double) (((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))) * ((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)))))), 3.0)) + ((double) pow(1.0, 3.0)))) / ((double) (((double) (1.0 * 1.0)) - ((double) (((double) (((double) (beta - alpha)) / ((double) (((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))) * ((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)))))) * ((double) (1.0 - ((double) (((double) (beta - alpha)) / ((double) (((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))) * ((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)))))))))))))) / 2.0));
	} else {
		double VAR_1;
		if (((alpha <= 4.0300115290250407e+155) || !(alpha <= 8.880827712970242e+187))) {
			VAR_1 = ((double) (((double) (((double) (beta / ((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))))))) - ((double) (((double) (4.0 / ((double) (alpha * alpha)))) - ((double) (((double) (2.0 / alpha)) + ((double) (8.0 / ((double) pow(alpha, 3.0)))))))))) / 2.0));
		} else {
			VAR_1 = ((double) (((double) (((double) log(((double) exp(((double) (beta / ((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))))))))))) - ((double) cbrt(((double) pow(((double) (((double) (alpha / ((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))))))) - 1.0)), 3.0)))))) / 2.0));
		}
		VAR = VAR_1;
	}
	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 3 regimes
  2. if  alpha  < 8.1176783251492383e131
    1. Initial program 14.8
      \[\]
    2. Simplified4.2
      \[\leadsto \]
    3. Using strategy rm
    4. Applied flip3-+4.2
      \[\leadsto \]
    5. Simplified4.2
      \[\leadsto \]
    6. Simplified4.2
      \[\leadsto \]
    if 8.1176783251492383e131 <  alpha  < 4.03001152902504068e155 or 8.88082771297024187e187 <  alpha 
    1. Initial program 61.2
      \[\]
    2. Simplified48.0
      \[\leadsto \]
    3. Using strategy rm
    4. Applied div-sub48.0
      \[\leadsto \]
    5. Applied associate-+l-46.4
      \[\leadsto \]
    6. Simplified46.4
      \[\leadsto \]
    7. Taylor expanded around inf 38.7
      \[\leadsto \]
    8. Simplified38.7
      \[\leadsto \]
    if 4.03001152902504068e155 <  alpha  < 8.88082771297024187e187
    1. Initial program 64.0
      \[\]
    2. Simplified39.8
      \[\leadsto \]
    3. Using strategy rm
    4. Applied div-sub39.8
      \[\leadsto \]
    5. Applied associate-+l-38.9
      \[\leadsto \]
    6. Simplified38.9
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-log-exp39.8
      \[\leadsto \]
    9. Using strategy rm
    10. Applied add-cbrt-cube39.9
      \[\leadsto \]
    11. Simplified39.9
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification11.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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))