Average Error: 30.5 → 0.4
Time: 2.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) sqrt(((double) (2.0 * ((double) (x * x))))));
}

↓
double code(double x) {
	return ((double) (((double) sqrt(((double) sqrt(((double) sqrt(2.0)))))) * ((double) (((double) sqrt(((double) sqrt(2.0)))) * ((double) (((double) sqrt(((double) sqrt(((double) sqrt(2.0)))))) * ((double) fabs(x))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 30.5
    \[\]
  2. Using strategy rm
  3. Applied sqrt-prod30.6
    \[\leadsto \]
  4. Simplified0.4
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-sqr-sqrt0.4
    \[\leadsto \]
  7. Applied sqrt-prod0.6
    \[\leadsto \]
  8. Applied associate-*l*0.4
    \[\leadsto \]
  9. Simplified0.4
    \[\leadsto \]
  10. Using strategy rm
  11. Applied add-sqr-sqrt0.4
    \[\leadsto \]
  12. Applied sqrt-prod0.4
    \[\leadsto \]
  13. Applied sqrt-prod0.4
    \[\leadsto \]
  14. Applied associate-*l*0.4
    \[\leadsto \]
  15. Simplified0.4
    \[\leadsto \]
  16. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "sqrt C"
  :precision binary64
  (sqrt (* 2.0 (* x x))))