Average Error: 15.1 → 0.0
Time: 1.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (x / ((double) (((double) (x * x)) + 1.0))));
}

↓
double code(double x) {
	double VAR;
	if (((x <= -16524538.364294972) || !(x <= 42822.353765390435))) {
		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) (((double) (x / ((double) (((double) pow(x, 4.0)) - ((double) (1.0 * 1.0)))))) * ((double) (((double) (x * x)) - 1.0))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original15.1
Target0.1
Herbie0.0
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x  < -16524538.364294972 or 42822.353765390435 <  x 
    1. Initial program 30.5
      \[\]
    2. Taylor expanded around inf 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if -16524538.364294972 <  x  < 42822.353765390435
    1. Initial program 0.0
      \[\]
    2. Using strategy rm
    3. Applied flip-+0.0
      \[\leadsto \]
    4. Applied associate-/r/0.0
      \[\leadsto \]
    5. Simplified0.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x)
  :name "x / (x^2 + 1)"
  :precision binary64

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

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