Average Error: 15.7 → 15.2
Time: 8.8s
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) (((double) (((double) pow(((double) pow(1.0, 6.0)), 3.0)) - ((double) (((double) pow(((double) pow(((double) (1.0 * ((double) (((double) pow(0.5, 3.0)) + ((double) pow(((double) (0.5 / ((double) hypot(1.0, x)))), 3.0)))))), 3.0)), 3.0)) / ((double) pow(((double) pow(((double) (((double) (0.5 * 0.5)) + ((double) (((double) (0.5 / ((double) hypot(1.0, x)))) * ((double) (((double) (0.5 / ((double) hypot(1.0, x)))) - 0.5)))))), 3.0)), 3.0)))))) / ((double) (((double) (((double) pow(1.0, 12.0)) + ((double) (((double) pow(1.0, 6.0)) * ((double) (((double) pow(((double) (0.5 + ((double) (0.5 / ((double) hypot(1.0, x)))))), 6.0)) + ((double) pow(((double) (1.0 * ((double) (0.5 + ((double) (0.5 / ((double) hypot(1.0, x)))))))), 3.0)))))))) * ((double) (((double) pow(1.0, 4.0)) + ((double) (0.5 * ((double) (1.0 * ((double) (((double) (1.0 + ((double) (0.5 + ((double) (0.5 / ((double) hypot(1.0, x)))))))) * ((double) (1.0 + ((double) (1.0 / ((double) hypot(1.0, x)))))))))))))))))) / ((double) (1.0 + ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (1.0 / ((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 15.7
    \[\]
  2. Using strategy rm
  3. Applied flip--15.7
    \[\leadsto \]
  4. Simplified15.2
    \[\leadsto \]
  5. Using strategy rm
  6. Applied flip3--15.2
    \[\leadsto \]
  7. Simplified15.2
    \[\leadsto \]
  8. Simplified15.2
    \[\leadsto \]
  9. Using strategy rm
  10. Applied flip3--15.2
    \[\leadsto \]
  11. Applied associate-/l/15.2
    \[\leadsto \]
  12. Simplified15.2
    \[\leadsto \]
  13. Using strategy rm
  14. Applied flip3-+15.2
    \[\leadsto \]
  15. Applied associate-*r/15.2
    \[\leadsto \]
  16. Applied cube-div15.2
    \[\leadsto \]
  17. Applied cube-div15.2
    \[\leadsto \]
  18. Simplified15.2
    \[\leadsto \]
  19. Final simplification15.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "Given's Rotation SVD example, simplified"
  :precision binary64
  (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))