Average Error: 6.7 → 3.1
Time: 4.0s
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) (y * ((double) (1.0 + ((double) (z * z)))))) <= -inf.0) || !(((double) (y * ((double) (1.0 + ((double) (z * z)))))) <= 1.096333845866515e+304))) {
		VAR = ((double) (((double) (1.0 / ((double) (z * ((double) (z * ((double) (y * x)))))))) - ((double) (1.0 / ((double) (((double) (y * x)) * ((double) pow(z, 4.0))))))));
	} else {
		VAR = ((double) (((double) (1.0 / ((double) (y * ((double) sqrt(((double) (1.0 + ((double) (z * z)))))))))) / ((double) (x * ((double) sqrt(((double) (1.0 + ((double) (z * 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
Original6.7
Target5.9
Herbie3.1
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  (* y (+ 1.0 (* z z)))  < -inf.0 or 1.09633384586651499e304 <  (* y (+ 1.0 (* z z))) 
    1. Initial program 18.9
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*14.5
      \[\leadsto \]
    4. Simplified14.5
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-sqr-sqrt14.5
      \[\leadsto \]
    7. Applied add-cube-cbrt14.5
      \[\leadsto \]
    8. Applied times-frac14.5
      \[\leadsto \]
    9. Applied times-frac15.9
      \[\leadsto \]
    10. Simplified15.9
      \[\leadsto \]
    11. Simplified16.1
      \[\leadsto \]
    12. Using strategy rm
    13. Applied frac-times16.1
      \[\leadsto \]
    14. Applied associate-*l/16.1
      \[\leadsto \]
    15. Simplified16.1
      \[\leadsto \]
    16. Taylor expanded around inf 19.1
      \[\leadsto \]
    17. Simplified7.0
      \[\leadsto \]
    if -inf.0 <  (* y (+ 1.0 (* z z)))  < 1.09633384586651499e304
    1. Initial program 0.3
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*2.7
      \[\leadsto \]
    4. Simplified2.8
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-sqr-sqrt2.8
      \[\leadsto \]
    7. Applied add-cube-cbrt2.8
      \[\leadsto \]
    8. Applied times-frac2.8
      \[\leadsto \]
    9. Applied times-frac1.0
      \[\leadsto \]
    10. Simplified1.0
      \[\leadsto \]
    11. Simplified1.0
      \[\leadsto \]
    12. Using strategy rm
    13. Applied frac-times1.1
      \[\leadsto \]
    14. Applied associate-*l/1.0
      \[\leadsto \]
    15. Simplified1.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification3.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(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)))))