Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double v) {
	return ((double) (((double) (((double) (((double) sqrt(2.0)) / 4.0)) * ((double) sqrt(((double) (1.0 - ((double) (3.0 * ((double) (v * v)))))))))) * ((double) (1.0 - ((double) (v * v))))));
}

↓
double code(double v) {
	return ((double) (((double) sqrt(2.0)) * ((double) exp(((double) log(((double) (((double) sqrt(((double) (1.0 - ((double) (3.0 * ((double) (v * v)))))))) * ((double) (((double) (1.0 - ((double) (v * v)))) / 4.0))))))))));
}

Error
Bits error versus v
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 0.0
    \[\]
  2. Simplified0.0
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-exp-log0.0
    \[\leadsto \]
  5. Applied add-exp-log0.0
    \[\leadsto \]
  6. Applied div-exp0.0
    \[\leadsto \]
  7. Applied add-exp-log0.0
    \[\leadsto \]
  8. Applied prod-exp0.0
    \[\leadsto \]
  9. Simplified0.0
    \[\leadsto \]
  10. Final simplification0.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))