Average Error: 14.9 → 0.0
Time: 1.5s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (x / ((double) (((double) (x * x)) + 1.0))));
}

↓
double code(double x) {
	double VAR;
	if (((x <= -6.253179014396205e+22) || !(x <= 3182659.7275122805))) {
		VAR = ((double) (((double) (1.0 / ((double) pow(x, 5.0)))) + ((double) (((double) (1.0 / x)) - ((double) (1.0 / ((double) pow(x, 3.0))))))));
	} else {
		VAR = ((double) (x / ((double) (1.0 + ((double) (x * x))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original14.9
Target0.1
Herbie0.0
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x  < -6.25317901439620486e22 or 3182659.7275122805 <  x 
    1. Initial program 31.5
      \[\]
    2. Taylor expanded around inf 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if -6.25317901439620486e22 <  x  < 3182659.7275122805
    1. Initial program 0.0
      \[\]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "x / (x^2 + 1)"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ x (/ 1.0 x)))

  (/ x (+ (* x x) 1.0)))