Average Error: 58.5 → 58.5
Time: 2.7s
Precision: binary64
Cost: 7104
\[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]
↓
\[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]
\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)
↓
\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)
(FPCore (x) :precision binary64 (* (/ 1.0 2.0) (log (/ (+ 1.0 x) (- 1.0 x)))))
↓
(FPCore (x) :precision binary64 (* (/ 1.0 2.0) (log (/ (+ 1.0 x) (- 1.0 x)))))
double code(double x) {
	return (1.0 / 2.0) * log((1.0 + x) / (1.0 - x));
}
↓
double code(double x) {
	return (1.0 / 2.0) * log((1.0 + x) / (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 58.5

    \[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "Hyperbolic arc-(co)tangent"
  :precision binary64
  (* (/ 1.0 2.0) (log (/ (+ 1.0 x) (- 1.0 x)))))