Average Error: 0.0 → 0.0
Time: 10.8s
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 f(double x) {
        double r38260 = x;
        double r38261 = 1.0;
        double r38262 = r38260 + r38261;
        double r38263 = r38261 - r38260;
        double r38264 = r38262 / r38263;
        return r38264;
}
↓
double f(double x) {
        double r38265 = x;
        double r38266 = 1.0;
        double r38267 = r38265 + r38266;
        double r38268 = r38266 - r38265;
        double r38269 = r38267 / r38268;
        double r38270 = exp(r38269);
        double r38271 = log(r38270);
        return r38271;
}

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 2020043 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))