Average Error: 19.9 → 0.3
Time: 4.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(x)))) - ((double) (1.0 / ((double) sqrt(((double) (x + 1.0))))))));
}

↓
double code(double x) {
	return ((double) (((double) (1.0 / ((double) sqrt(x)))) * ((double) (1.0 / ((double) (((double) (1.0 + x)) + ((double) (((double) sqrt(x)) * ((double) sqrt(((double) (1.0 + x))))))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original19.9
Target0.6
Herbie0.3
\[\]
Derivation
  1. Initial program 19.9
    \[\]
  2. Using strategy rm
  3. Applied frac-sub19.9
    \[\leadsto \]
  4. Simplified19.9
    \[\leadsto \]
  5. Simplified19.9
    \[\leadsto \]
  6. Using strategy rm
  7. Applied flip--19.7
    \[\leadsto \]
  8. Simplified0.4
    \[\leadsto \]
  9. Using strategy rm
  10. Applied times-frac0.4
    \[\leadsto \]
  11. Simplified0.3
    \[\leadsto \]
  12. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "2isqrt (example 3.6)"
  :precision binary64

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

  (- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))