Average Error: 54.0 → 10.4
Time: 9.4s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double alpha, double beta, double i) {
	return ((double) (((double) (((double) (((double) (i * ((double) (((double) (alpha + beta)) + i)))) * ((double) (((double) (beta * alpha)) + ((double) (i * ((double) (((double) (alpha + beta)) + i)))))))) / ((double) (((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))) * ((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))))))) / ((double) (((double) (((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))) * ((double) (((double) (alpha + beta)) + ((double) (2.0 * i)))))) - 1.0))));
}

↓
double code(double alpha, double beta, double i) {
	double VAR;
	if ((i <= 9.562673361052236e+119)) {
		VAR = ((double) (((double) (((double) (i / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) * ((double) (((double) (i + ((double) (alpha + beta)))) / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))))) * ((double) (((double) (((double) (((double) (i * ((double) (i + ((double) (alpha + beta)))))) + ((double) (alpha * beta)))) / ((double) (alpha + ((double) (beta + ((double) (((double) (i * 2.0)) + ((double) sqrt(1.0)))))))))) / ((double) (((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))) - ((double) sqrt(1.0))))))));
	} else {
		VAR = ((double) (((double) sqrt(((double) (((double) (i / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) * ((double) (((double) (((double) (i + ((double) (alpha + beta)))) / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) * ((double) (((double) (((double) (i * 0.5)) + ((double) (((double) (0.125 * ((double) (1.0 / i)))) - ((double) (((double) sqrt(1.0)) * 0.25)))))) / ((double) (alpha + ((double) (beta + ((double) (((double) (i * 2.0)) - ((double) sqrt(1.0)))))))))))))))) * ((double) sqrt(((double) (((double) (i / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) * ((double) (((double) (((double) (i + ((double) (alpha + beta)))) / ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) * ((double) (((double) (((double) (i * 0.5)) + ((double) (((double) (0.125 * ((double) (1.0 / i)))) - ((double) (((double) sqrt(1.0)) * 0.25)))))) / ((double) (alpha + ((double) (beta + ((double) (((double) (i * 2.0)) - ((double) sqrt(1.0))))))))))))))))));
	}
	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  i  < 9.5626733610522361e119
    1. Initial program 38.6
      \[\]
    2. Simplified25.1
      \[\leadsto \]
    3. Using strategy rm
    4. Applied *-un-lft-identity25.1
      \[\leadsto \]
    5. Applied times-frac14.6
      \[\leadsto \]
    6. Applied associate-*r*14.6
      \[\leadsto \]
    7. Simplified14.5
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-sqr-sqrt14.5
      \[\leadsto \]
    10. Applied difference-of-squares14.5
      \[\leadsto \]
    11. Applied associate-/r*9.5
      \[\leadsto \]
    12. Simplified9.5
      \[\leadsto \]
    if 9.5626733610522361e119 <  i 
    1. Initial program 64.0
      \[\]
    2. Simplified63.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied *-un-lft-identity63.7
      \[\leadsto \]
    5. Applied times-frac55.8
      \[\leadsto \]
    6. Applied associate-*r*55.8
      \[\leadsto \]
    7. Simplified55.8
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-sqr-sqrt55.8
      \[\leadsto \]
    10. Applied difference-of-squares55.8
      \[\leadsto \]
    11. Applied associate-/r*55.4
      \[\leadsto \]
    12. Simplified55.4
      \[\leadsto \]
    13. Taylor expanded around inf 10.9
      \[\leadsto \]
    14. Simplified10.9
      \[\leadsto \]
    15. Using strategy rm
    16. Applied add-sqr-sqrt10.9
      \[\leadsto \]
    17. Simplified10.9
      \[\leadsto \]
    18. Simplified10.9
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification10.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0) (> i 1.0))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)))