Average Error: 0.0 → 0.0
Time: 1.1s
Precision: binary64
\[\frac{x + 1}{1 - x}\]
↓
\[\log \left(e^{\frac{x + 1}{1 - x}}\right)\]
\frac{x + 1}{1 - x}
↓
\log \left(e^{\frac{x + 1}{1 - x}}\right)
(FPCore (x) :precision binary64 (/ (+ x 1.0) (- 1.0 x)))
↓
(FPCore (x) :precision binary64 (log (exp (/ (+ x 1.0) (- 1.0 x)))))
double code(double x) {
	return (x + 1.0) / (1.0 - x);
}
↓
double code(double x) {
	return log(exp((x + 1.0) / (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 0.0

    \[\frac{x + 1}{1 - x}\]
  2. Using strategy rm

  3. Applied add-log-exp_binary640.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x + 1}{1 - x}}\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{x + 1}{1 - x}}\right)\]

Reproduce

herbie shell --seed 2020232 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1.0) (- 1.0 x)))