Average Error: 0.0 → 0.0
Time: 2.1s
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 r45909 = x;
        double r45910 = 1.0;
        double r45911 = r45909 + r45910;
        double r45912 = r45910 - r45909;
        double r45913 = r45911 / r45912;
        return r45913;
}
↓
double f(double x) {
        double r45914 = x;
        double r45915 = 1.0;
        double r45916 = r45914 + r45915;
        double r45917 = r45915 - r45914;
        double r45918 = r45916 / r45917;
        double r45919 = exp(r45918);
        double r45920 = log(r45919);
        return r45920;
}

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 2019356 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))