Average Error: 58.5 → 0.3
Time: 6.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 / 2.0)) * ((double) log(((double) (((double) (1.0 + x)) / ((double) (1.0 - x))))))));
}

↓
double code(double x) {
	return ((double) (((double) (1.0 / 2.0)) * ((double) (((double) (0.6666666666666666 * ((double) pow(((double) (x / 1.0)), 3.0)))) + ((double) (((double) (2.0 * x)) + ((double) log(((double) pow(((double) exp(0.4)), ((double) (((double) pow(x, 5.0)) / ((double) pow(1.0, 5.0))))))))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 58.5
    \[\]
  2. Using strategy rm
  3. Applied log-div58.5
    \[\leadsto \]
  4. Taylor expanded around 0 0.3
    \[\leadsto \]
  5. Simplified0.3
    \[\leadsto \]
  6. Using strategy rm
  7. Applied add-log-exp0.3
    \[\leadsto \]
  8. Simplified0.3
    \[\leadsto \]
  9. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "Hyperbolic arc-(co)tangent"
  :precision binary64
  (* (/ 1.0 2.0) (log (/ (+ 1.0 x) (- 1.0 x)))))