Average Error: 15.2 → 14.7
Time: 3.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (1.0 - ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (1.0 / ((double) hypot(1.0, x))))))))))));
}

↓
double code(double x) {
	return ((double) (((double) (1.0 * ((double) (((double) (1.0 - 0.5)) - ((double) log(((double) exp(((double) (0.5 / ((double) hypot(1.0, x)))))))))))) / ((double) (1.0 + ((double) sqrt(((double) (1.0 * ((double) (0.5 + ((double) (0.5 / ((double) hypot(1.0, x))))))))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 15.2
    \[\]
  2. Using strategy rm
  3. Applied flip--15.2
    \[\leadsto \]
  4. Simplified14.7
    \[\leadsto \]
  5. Simplified14.7
    \[\leadsto \]
  6. Using strategy rm
  7. Applied add-log-exp14.7
    \[\leadsto \]
  8. Final simplification14.7
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))