Average Error: 0.0 → 0.0
Time: 3.1s
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 r35603 = x;
        double r35604 = 1.0;
        double r35605 = r35603 + r35604;
        double r35606 = r35604 - r35603;
        double r35607 = r35605 / r35606;
        return r35607;
}
↓
double f(double x) {
        double r35608 = x;
        double r35609 = 1.0;
        double r35610 = r35608 + r35609;
        double r35611 = r35609 - r35608;
        double r35612 = r35610 / r35611;
        double r35613 = exp(r35612);
        double r35614 = log(r35613);
        return r35614;
}

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 2019346 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))