Average Error: 30.4 → 0.5
Time: 2.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) (2.0 * x)) * x))));
}

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

Error
Bits error versus x
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Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 30.4
    \[\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt30.7
    \[\leadsto \]
  4. Simplified30.7
    \[\leadsto \]
  5. Simplified30.7
    \[\leadsto \]
  6. Using strategy rm
  7. Applied sqrt-prod30.7
    \[\leadsto \]
  8. Applied sqrt-prod30.6
    \[\leadsto \]
  9. Applied associate-*l*30.6
    \[\leadsto \]
  10. Simplified0.4
    \[\leadsto \]
  11. Using strategy rm
  12. Applied associate-*r*0.5
    \[\leadsto \]
  13. Final simplification0.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "sqrt B"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))