Average Error: 6.7 → 5.8
Time: 3.4s
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 ((y <= -2.4731925580585136e-83)) {
		VAR = ((double) (((double) (1.0 / y)) / ((double) (x * ((double) (1.0 + ((double) (z * z))))))));
	} else {
		double VAR_1;
		if ((y <= 4.9431509416741565e-193)) {
			VAR_1 = ((double) (((double) (1.0 / x)) / ((double) (((double) (y * 1.0)) + ((double) (y * ((double) (z * z))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (1.0 / y)) / x)) * ((double) (1.0 / ((double) (1.0 + ((double) (z * 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
Original6.7
Target6.1
Herbie5.8
\[\]
Derivation
  1. Split input into 3 regimes
  2. if  y  < -2.4731925580585136e-83
    1. Initial program 4.5
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*2.4
      \[\leadsto \]
    4. Simplified2.7
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-/r*2.4
      \[\leadsto \]
    7. Using strategy rm
    8. Applied div-inv2.5
      \[\leadsto \]
    9. Applied associate-/l*2.4
      \[\leadsto \]
    10. Simplified2.4
      \[\leadsto \]
    if -2.4731925580585136e-83 <  y  < 4.9431509416741565e-193
    1. Initial program 12.8
      \[\]
    2. Using strategy rm
    3. Applied distribute-lft-in12.8
      \[\leadsto \]
    if 4.9431509416741565e-193 <  y 
    1. Initial program 4.9
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*4.5
      \[\leadsto \]
    4. Simplified4.7
      \[\leadsto \]
    5. Using strategy rm
    6. Applied associate-/r*4.5
      \[\leadsto \]
    7. Using strategy rm
    8. Applied div-inv4.5
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification5.8
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(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)))))