Average Error: 6.4 → 4.0
Time: 3.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z) {
	return ((double) (((double) (1.0 / x)) / ((double) (y * ((double) (1.0 + ((double) (z * z))))))));
}

↓
double code(double x, double y, double z) {
	double VAR;
	if ((((double) (z * z)) <= 2.1102780698153253e+284)) {
		VAR = ((double) (1.0 / ((double) (x * ((double) (y * ((double) (((double) (z * z)) + 1.0))))))));
	} else {
		VAR = ((double) (((double) (1.0 / ((double) (y * ((double) (z * ((double) (z * x)))))))) - ((double) (1.0 / ((double) (y * ((double) (x * ((double) pow(z, 4.0))))))))));
	}
	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
Original6.4
Target5.7
Herbie4.0
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (* z z)  < 2.11027806981532533e284
    1. Initial program 2.1
      \[\]
    2. Simplified2.4
      \[\leadsto \]
    if 2.11027806981532533e284 <  (* z z) 
    1. Initial program 17.1
      \[\]
    2. Using strategy rm
    3. Applied *-un-lft-identity17.1
      \[\leadsto \]
    4. Applied *-un-lft-identity17.1
      \[\leadsto \]
    5. Applied times-frac17.1
      \[\leadsto \]
    6. Applied times-frac17.2
      \[\leadsto \]
    7. Simplified17.2
      \[\leadsto \]
    8. Simplified17.3
      \[\leadsto \]
    9. Taylor expanded around inf 17.1
      \[\leadsto \]
    10. Simplified8.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification4.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z)
  :name "Statistics.Distribution.CauchyLorentz:$cdensity from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< (* y (+ 1.0 (* z z))) (- INFINITY)) (/ (/ 1.0 y) (* (+ 1.0 (* z z)) x)) (if (< (* y (+ 1.0 (* z z))) 8.680743250567252e+305) (/ (/ 1.0 x) (* (+ 1.0 (* z z)) y)) (/ (/ 1.0 y) (* (+ 1.0 (* z z)) x))))

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