Average Error: 53.6 → 15.7
Time: 6.1s
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 <= 2.6665270239172677e+83)) {
		VAR = ((double) (((double) (i * ((double) (i + ((double) (alpha + beta)))))) * ((double) pow(((double) M_E), ((double) (((double) log(((double) (((double) (i * ((double) (i + ((double) (alpha + beta)))))) + ((double) (alpha * beta)))))) - ((double) (((double) log(((double) (((double) (((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))) * ((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))))) - 1.0)))) + ((double) (2.0 * ((double) log(((double) (alpha + ((double) (beta + ((double) (i * 2.0))))))))))))))))));
	} else {
		VAR = 0.0625;
	}
	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  < 2.66652702391726766e83
    1. Initial program 26.3
      \[\]
    2. Simplified22.7
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-exp-log25.1
      \[\leadsto \]
    5. Applied add-exp-log25.3
      \[\leadsto \]
    6. Applied prod-exp25.6
      \[\leadsto \]
    7. Applied add-exp-log25.7
      \[\leadsto \]
    8. Applied prod-exp25.6
      \[\leadsto \]
    9. Applied add-exp-log25.5
      \[\leadsto \]
    10. Applied div-exp19.2
      \[\leadsto \]
    11. Simplified19.2
      \[\leadsto \]
    12. Using strategy rm
    13. Applied *-un-lft-identity19.2
      \[\leadsto \]
    14. Applied exp-prod19.0
      \[\leadsto \]
    15. Simplified19.0
      \[\leadsto \]
    if 2.66652702391726766e83 <  i 
    1. Initial program 64.0
      \[\]
    2. Simplified63.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-exp-log63.5
      \[\leadsto \]
    5. Applied add-exp-log63.5
      \[\leadsto \]
    6. Applied prod-exp63.5
      \[\leadsto \]
    7. Applied add-exp-log63.5
      \[\leadsto \]
    8. Applied prod-exp63.5
      \[\leadsto \]
    9. Applied add-exp-log63.5
      \[\leadsto \]
    10. Applied div-exp52.3
      \[\leadsto \]
    11. Simplified52.3
      \[\leadsto \]
    12. Taylor expanded around inf 52.8
      \[\leadsto \]
    13. Simplified14.5
      \[\leadsto \]
    14. Taylor expanded around 0 14.4
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification15.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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)))