Average Error: 58.6 → 0.3
Time: 4.6s
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) (2.0 * ((double) log(1.0)))) + ((double) (((double) (2.0 * x)) + ((double) (((double) pow(x, 3.0)) * 0.6666666666666665))))))));
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 58.6
    \[\]
  2. Using strategy rm
  3. Applied flip3--58.7
    \[\leadsto \]
  4. Applied associate-/r/58.7
    \[\leadsto \]
  5. Applied log-prod58.7
    \[\leadsto \]
  6. Simplified58.7
    \[\leadsto \]
  7. Taylor expanded around 0 0.3
    \[\leadsto \]
  8. Simplified0.3
    \[\leadsto \]
  9. Taylor expanded around 0 0.3
    \[\leadsto \]
  10. Simplified0.3
    \[\leadsto \]
  11. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (x)
  :name "Hyperbolic arc-(co)tangent"
  :precision binary64
  (* (/ 1.0 2.0) (log (/ (+ 1.0 x) (- 1.0 x)))))