Average Error: 0.0 → 0.0
Time: 5.3s
Precision: 64
\[\frac{x + 1.0}{1.0 - x}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1.0 + x}{1.0 - x}\right)\right)\]
\frac{x + 1.0}{1.0 - x}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1.0 + x}{1.0 - x}\right)\right)
double f(double x) {
        double r1677487 = x;
        double r1677488 = 1.0;
        double r1677489 = r1677487 + r1677488;
        double r1677490 = r1677488 - r1677487;
        double r1677491 = r1677489 / r1677490;
        return r1677491;
}
↓
double f(double x) {
        double r1677492 = 1.0;
        double r1677493 = x;
        double r1677494 = r1677492 + r1677493;
        double r1677495 = r1677492 - r1677493;
        double r1677496 = r1677494 / r1677495;
        double r1677497 = expm1(r1677496);
        double r1677498 = log1p(r1677497);
        return r1677498;
}

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 log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))