Average Error: 9.5 → 0.3
Time: 3.4s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (((double) (1.0 / ((double) (x + 1.0)))) - ((double) (2.0 / x)))) + ((double) (1.0 / ((double) (x - 1.0))))));
}

↓
double code(double x) {
	double VAR;
	if (((x <= -838439.3309523697) || !(x <= 511.7848760495989))) {
		VAR = ((double) (((double) (2.0 / ((double) pow(x, 7.0)))) + ((double) (((double) (2.0 / ((double) pow(x, 5.0)))) + ((double) (2.0 / ((double) pow(x, 3.0))))))));
	} else {
		VAR = ((double) (((double) (((double) (((double) (x - 1.0)) * ((double) (((double) (x * 1.0)) - ((double) (2.0 * ((double) (x + 1.0)))))))) + ((double) (1.0 * ((double) (x * ((double) (x + 1.0)))))))) / ((double) (x * ((double) (((double) (x * x)) - ((double) (1.0 * 1.0))))))));
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original9.5
Target0.3
Herbie0.3
\[\]
Derivation
  1. Split input into 2 regimes
  2. if  x  < -838439.330952369724 or 511.78487604959889 <  x 
    1. Initial program 18.8
      \[\]
    2. Taylor expanded around inf 0.5
      \[\leadsto \]
    3. Simplified0.5
      \[\leadsto \]
    if -838439.330952369724 <  x  < 511.78487604959889
    1. Initial program 0.2
      \[\]
    2. Using strategy rm
    3. Applied frac-sub0.2
      \[\leadsto \]
    4. Applied frac-add0.0
      \[\leadsto \]
    5. Simplified0.0
      \[\leadsto \]
    6. Simplified0.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  :precision binary64

  :herbie-target
  (/ 2.0 (* x (- (* x x) 1.0)))

  (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))