Average Error: 15.0 → 1.8
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)) <= 6.0408872496917e-312) || !(((double) (x * y)) <= 1.6736867795136718e+224))) {
		VAR = ((double) (((double) (((double) cbrt(y)) * ((double) (((double) (((double) cbrt(y)) / z)) * ((double) (x * ((double) (((double) cbrt(((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) / z)))))))) * ((double) (((double) cbrt(((double) cbrt(y)))) / ((double) (z + 1.0))))));
	} else {
		VAR = ((double) (((double) (((double) (x * y)) / ((double) (z * ((double) (z + 1.0)))))) / z));
	}
	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
Original15.0
Target4.2
Herbie1.8
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (* x y)  < 6.04088724969169e-312 or 1.67368677951367175e224 <  (* x y) 
    1. Initial program 18.9
      \[\]
    2. Simplified14.9
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt15.2
      \[\leadsto \]
    5. Applied times-frac9.6
      \[\leadsto \]
    6. Applied associate-*r*4.5
      \[\leadsto \]
    7. Simplified4.5
      \[\leadsto \]
    8. Using strategy rm
    9. Applied add-cube-cbrt4.5
      \[\leadsto \]
    10. Applied cbrt-prod4.6
      \[\leadsto \]
    11. Applied times-frac3.0
      \[\leadsto \]
    12. Applied associate-*r*1.9
      \[\leadsto \]
    13. Simplified2.5
      \[\leadsto \]
    if 6.04088724969169e-312 <  (* x y)  < 1.67368677951367175e224
    1. Initial program 7.7
      \[\]
    2. Simplified11.5
      \[\leadsto \]
    3. Using strategy rm
    4. Applied add-cube-cbrt11.9
      \[\leadsto \]
    5. Applied times-frac8.2
      \[\leadsto \]
    6. Applied associate-*r*1.0
      \[\leadsto \]
    7. Simplified1.0
      \[\leadsto \]
    8. Using strategy rm
    9. Applied associate-*r/1.0
      \[\leadsto \]
    10. Applied associate-*l/0.9
      \[\leadsto \]
    11. Applied associate-*l/0.9
      \[\leadsto \]
    12. Simplified0.3
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification1.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(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))))