Average Error: 0.0 → 0.9
Time: 5.7s
Precision: 64
\[\frac{x + 1.0}{1.0 - x}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1.0 + x}{1.0 - x}\right)\right)\]
\frac{x + 1.0}{1.0 - x}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1.0 + x}{1.0 - x}\right)\right)
double f(double x) {
        double r612526 = x;
        double r612527 = 1.0;
        double r612528 = r612526 + r612527;
        double r612529 = r612527 - r612526;
        double r612530 = r612528 / r612529;
        return r612530;
}
↓
double f(double x) {
        double r612531 = 1.0;
        double r612532 = x;
        double r612533 = r612531 + r612532;
        double r612534 = r612531 - r612532;
        double r612535 = r612533 / r612534;
        double r612536 = log1p(r612535);
        double r612537 = expm1(r612536);
        return r612537;
}

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

    \[\frac{x + 1.0}{1.0 - x}\]
  2. Using strategy rm

  3. Applied expm1-log1p-u0.9

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x + 1.0}{1.0 - x}\right)\right)}\]

  4. Final simplification0.9

    \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1.0 + x}{1.0 - x}\right)\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))