Average Error: 10.1 → 0.1
Time: 2.8s
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) {
	return ((double) (((double) (2.0 / x)) / ((double) (((double) (x * x)) - ((double) (1.0 * 1.0))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original10.1
Target0.3
Herbie0.1
\[\]
Derivation
  1. Initial program 10.1
    \[\]
  2. Using strategy rm
  3. Applied frac-sub25.8
    \[\leadsto \]
  4. Applied frac-add25.4
    \[\leadsto \]
  5. Simplified25.4
    \[\leadsto \]
  6. Simplified25.4
    \[\leadsto \]
  7. Taylor expanded around 0 0.3
    \[\leadsto \]
  8. Using strategy rm
  9. Applied associate-/r*0.1
    \[\leadsto \]
  10. Final simplification0.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))))