Average Error: 14.6 → 0.0
Time: 2.3s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double a, double b) {
	return ((double) sqrt(((double) fabs(((double) (((double) (((double) (a * a)) - ((double) (b * b)))) / ((double) (a * a))))))));
}

↓
double code(double a, double b) {
	return ((double) sqrt(((double) fabs(((double) (1.0 - ((double) (((double) (((double) sqrt(b)) * ((double) fabs(((double) (((double) sqrt(b)) / a)))))) * ((double) (((double) sqrt(b)) * ((double) fabs(((double) (((double) sqrt(b)) / a))))))))))))));
}

Error
Bits error versus a
Bits error versus b
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 14.6
    \[\]
  2. Simplified14.6
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-sqr-sqrt14.6
    \[\leadsto \]
  5. Applied add-sqr-sqrt14.6
    \[\leadsto \]
  6. Applied unswap-sqr14.6
    \[\leadsto \]
  7. Simplified14.6
    \[\leadsto \]
  8. Simplified0.0
    \[\leadsto \]
  9. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (a b)
  :name "Eccentricity of an ellipse"
  :precision binary64
  :pre (<= 0.0 b a 1.0)
  (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))))