Average Error: 15.4 → 0.0
Time: 1.6s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (x / ((double) (((double) (x * x)) + 1.0))));
}

↓
double code(double x) {
	double VAR;
	if (((x <= -4.34418770362715e+45) || !(x <= 412.3562449850672))) {
		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
Original15.4
Target0.1
Herbie0.0
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x  < -4.3441877036271499e45 or 412.35624498506718 <  x 
    1. Initial program 33.1
      \[\]
    2. Taylor expanded around inf 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if -4.3441877036271499e45 <  x  < 412.35624498506718
    1. Initial program 0.0
      \[\]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x)
  :name "x / (x^2 + 1)"
  :precision binary64

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

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