Average Error: 19.8 → 0.4
Time: 3.6s
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) (((double) (1.0 * 1.0)) / ((double) (x + ((double) (((double) (((double) sqrt(x)) * ((double) fabs(((double) cbrt(((double) (1.0 + x)))))))) * ((double) sqrt(((double) cbrt(((double) (1.0 + 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
Original19.8
Target0.7
Herbie0.4
\[\]
Derivation
  1. Initial program 19.8
    \[\]
  2. Using strategy rm
  3. Applied frac-sub19.8
    \[\leadsto \]
  4. Simplified19.8
    \[\leadsto \]
  5. Simplified19.8
    \[\leadsto \]
  6. Using strategy rm
  7. Applied flip--19.6
    \[\leadsto \]
  8. Simplified0.4
    \[\leadsto \]
  9. Using strategy rm
  10. Applied associate-/r*0.4
    \[\leadsto \]
  11. Simplified0.3
    \[\leadsto \]
  12. Using strategy rm
  13. Applied add-cube-cbrt0.4
    \[\leadsto \]
  14. Applied sqrt-prod0.4
    \[\leadsto \]
  15. Applied associate-*r*0.4
    \[\leadsto \]
  16. Simplified0.4
    \[\leadsto \]
  17. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(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)))))