Average Error: 0.0 → 0.1
Time: 1.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) log(((double) (((double) (1.0 / x)) + ((double) (((double) sqrt(((double) (1.0 - ((double) (x * x)))))) / x))))));
}

↓
double code(double x) {
	return ((double) (((double) (2.0 * ((double) log(((double) cbrt(((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (x * x)))))))))))))) + ((double) log(((double) (((double) cbrt(((double) (1.0 + ((double) sqrt(((double) (1.0 - ((double) (x * x)))))))))) / x))))));
}

Error
Bits error versus x
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 *-un-lft-identity0.0
    \[\leadsto \]
  5. Applied add-cube-cbrt0.1
    \[\leadsto \]
  6. Applied times-frac0.1
    \[\leadsto \]
  7. Applied log-prod0.1
    \[\leadsto \]
  8. Simplified0.1
    \[\leadsto \]
  9. Final simplification0.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  :precision binary64
  (log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))