Average Error: 30.3 → 0.2
Time: 3.2s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) sqrt(((double) (x + 1.0)))) - ((double) sqrt(x))));
}

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

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original30.3
Target0.2
Herbie0.2
\[\]
Derivation
  1. Initial program 30.3
    \[\]
  2. Using strategy rm
  3. Applied flip--30.1
    \[\leadsto \]
  4. Simplified0.2
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-sqr-sqrt0.3
    \[\leadsto \]
  7. Simplified0.3
    \[\leadsto \]
  8. Simplified0.3
    \[\leadsto \]
  9. Using strategy rm
  10. Applied sqrt-div0.3
    \[\leadsto \]
  11. Applied associate-*r/0.2
    \[\leadsto \]
  12. Final simplification0.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020179 
(FPCore (x)
  :name "2sqrt (example 3.1)"
  :precision binary64

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

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