Average Error: 15.2 → 3.0
Time: 4.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) / ((double) (((double) (z * z)) * ((double) (z + 1.0))))));
}

↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (x * y)) <= -3.311109352139864e+18)) {
		VAR = ((double) (((double) (((double) (x / z)) * ((double) (((double) cbrt(1.0)) / ((double) (z / ((double) cbrt(1.0)))))))) * ((double) (y * ((double) (((double) cbrt(1.0)) / ((double) (z + 1.0))))))));
	} else {
		double VAR_1;
		if ((((double) (x * y)) <= 3.016946665275098e+105)) {
			VAR_1 = ((double) (1.0 / ((double) (((double) (z * ((double) (z + 1.0)))) / ((double) (y * ((double) (x / z))))))));
		} else {
			VAR_1 = ((double) (((double) (x / z)) * ((double) (((double) (y / ((double) (z + 1.0)))) / z))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original15.2
Target4.0
Herbie3.0
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  (* x y)  < -3311109352139864100
    1. Initial program 19.1
      \[\]
    2. Using strategy rm
    3. Applied clear-num19.2
      \[\leadsto \]
    4. Simplified5.0
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt5.0
      \[\leadsto \]
    7. Applied times-frac5.0
      \[\leadsto \]
    8. Simplified4.9
      \[\leadsto \]
    9. Simplified4.9
      \[\leadsto \]
    if -3311109352139864100 <  (* x y)  < 3.0169466652750978e105
    1. Initial program 12.1
      \[\]
    2. Using strategy rm
    3. Applied clear-num12.2
      \[\leadsto \]
    4. Simplified6.5
      \[\leadsto \]
    5. Using strategy rm
    6. Applied frac-times2.5
      \[\leadsto \]
    if 3.0169466652750978e105 <  (* x y) 
    1. Initial program 26.4
      \[\]
    2. Using strategy rm
    3. Applied clear-num26.5
      \[\leadsto \]
    4. Simplified3.6
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-*l/2.7
      \[\leadsto \]
    7. Applied associate-/r/2.8
      \[\leadsto \]
    8. Simplified2.5
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification3.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))