Average Error: 54.0 → 36.4
Time: 6.9s
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 ((beta <= 5.380345921875369e+195)) {
		VAR = ((double) (((double) (i / ((double) (((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))) * ((double) (((double) (alpha + ((double) (beta + ((double) (i * 2.0)))))) / ((double) (i + ((double) (beta + alpha)))))))))) * ((double) (((double) (((double) sqrt(((double) (((double) (i * ((double) (i + ((double) (beta + alpha)))))) + ((double) (beta * alpha)))))) / ((double) (alpha + ((double) (beta + ((double) (((double) (i * 2.0)) + ((double) sqrt(1.0)))))))))) * ((double) (((double) sqrt(((double) (((double) (i * ((double) (i + ((double) (beta + alpha)))))) + ((double) (beta * alpha)))))) / ((double) (alpha + ((double) (beta + ((double) (((double) (i * 2.0)) - ((double) sqrt(1.0))))))))))))));
	} else {
		VAR = 0.0;
	}
	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  beta  < 5.38034592187536923e195
    1. Initial program 52.6
      \[\]
    2. Simplified51.9
      \[\leadsto \]
    3. Using strategy rm
    4. Applied *-un-lft-identity51.9
      \[\leadsto \]
    5. Applied times-frac47.6
      \[\leadsto \]
    6. Applied associate-*r*47.5
      \[\leadsto \]
    7. Simplified47.5
      \[\leadsto \]
    8. Using strategy rm
    9. Applied *-un-lft-identity47.5
      \[\leadsto \]
    10. Applied times-frac37.5
      \[\leadsto \]
    11. Applied associate-*r*37.5
      \[\leadsto \]
    12. Simplified37.5
      \[\leadsto \]
    13. Using strategy rm
    14. Applied add-sqr-sqrt37.5
      \[\leadsto \]
    15. Applied difference-of-squares37.5
      \[\leadsto \]
    16. Applied add-sqr-sqrt37.5
      \[\leadsto \]
    17. Applied times-frac35.2
      \[\leadsto \]
    18. Simplified35.2
      \[\leadsto \]
    19. Simplified35.2
      \[\leadsto \]
    if 5.38034592187536923e195 <  beta 
    1. Initial program 64.0
      \[\]
    2. Simplified56.8
      \[\leadsto \]
    3. Taylor expanded around inf 44.7
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification36.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(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)))