Average Error: 30.9 → 0.4
Time: 1.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) sqrt(((double) (2.0 * ((double) (x * x))))));
}

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

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 30.9
    \[\]
  2. Using strategy rm
  3. Applied sqrt-prod31.0
    \[\leadsto \]
  4. Simplified0.4
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.4
    \[\leadsto \]
  7. Applied associate-*l*0.4
    \[\leadsto \]
  8. Simplified0.4
    \[\leadsto \]
  9. Using strategy rm
  10. Applied add-cube-cbrt0.4
    \[\leadsto \]
  11. Applied associate-*r*0.4
    \[\leadsto \]
  12. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "sqrt C"
  :precision binary64
  (sqrt (* 2.0 (* x x))))