Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\log \left(e^{\frac{x + 1}{1 - x}}\right)\]
\frac{x + 1}{1 - x}
↓
\log \left(e^{\frac{x + 1}{1 - x}}\right)
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-exp0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))