Average Error: 24.1 → 12.1
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 <= 9.293412699166225e+39)) {
		VAR = ((double) (((double) (((double) (((double) (((double) cbrt(beta)) * ((double) cbrt(beta)))) / ((double) (((double) (((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))) / ((double) (((double) (((double) cbrt(((double) cbrt(beta)))) * ((double) cbrt(((double) cbrt(beta)))))) * ((double) cbrt(((double) (((double) cbrt(((double) cbrt(beta)))) * ((double) cbrt(((double) (((double) cbrt(beta)) * ((double) cbrt(beta)))))))))))))) * ((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)))))) - ((double) (((double) (alpha / ((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))))))) - 1.0)))) / 2.0));
	} else {
		double VAR_1;
		if (((alpha <= 2.6496394980429403e+123) || !(alpha <= 5.599357149971467e+201))) {
			VAR_1 = ((double) (((double) (((double) (beta / ((double) (((double) (alpha + ((double) (beta + ((double) (2.0 * i)))))) * ((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)))))) - ((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) (1.0 + ((double) (((double) (beta - alpha)) / ((double) (((double) cbrt(((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))))))) * ((double) (((double) cbrt(((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))))))) * ((double) cbrt(((double) (((double) (((double) (((double) (2.0 + ((double) (2.0 * i)))) / ((double) (alpha + beta)))) + 1.0)) * ((double) (beta + ((double) (alpha + ((double) (2.0 * i)))))))))))))))))) / 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  < 9.2934126991662246e39
    1. Initial program 11.5
      \[\]
    2. Simplified1.1
      \[\leadsto \]
    3. Using strategy rm
    4. Applied div-sub1.1
      \[\leadsto \]
    5. Applied associate-+l-1.0
      \[\leadsto \]
    6. Simplified1.0
      \[\leadsto \]
    7. Using strategy rm
    8. Applied add-cube-cbrt1.2
      \[\leadsto \]
    9. Applied associate-/l*1.2
      \[\leadsto \]
    10. Simplified1.2
      \[\leadsto \]
    11. Using strategy rm
    12. Applied add-cube-cbrt1.3
      \[\leadsto \]
    13. Using strategy rm
    14. Applied add-cube-cbrt1.3
      \[\leadsto \]
    15. Applied cbrt-prod1.3
      \[\leadsto \]
    if 9.2934126991662246e39 <  alpha  < 2.6496394980429403e123 or 5.59935714997146709e201 <  alpha 
    1. Initial program 53.6
      \[\]
    2. Simplified41.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied div-sub41.5
      \[\leadsto \]
    5. Applied associate-+l-40.2
      \[\leadsto \]
    6. Simplified40.2
      \[\leadsto \]
    7. Taylor expanded around inf 37.6
      \[\leadsto \]
    8. Simplified37.6
      \[\leadsto \]
    if 2.6496394980429403e123 <  alpha  < 5.59935714997146709e201
    1. Initial program 56.3
      \[\]
    2. Simplified39.6
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt39.7
      \[\leadsto \]
    5. Simplified39.7
      \[\leadsto \]
    6. Simplified39.7
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification12.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(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))