Average Error: 0.0 → 0.1
Time: 11.5s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]
\frac{x + 1}{1 - x}
↓
\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}
double f(double x) {
        double r58486 = x;
        double r58487 = 1.0;
        double r58488 = r58486 + r58487;
        double r58489 = r58487 - r58486;
        double r58490 = r58488 / r58489;
        return r58490;
}
↓
double f(double x) {
        double r58491 = x;
        double r58492 = 1.0;
        double r58493 = r58491 + r58492;
        double r58494 = r58492 - r58491;
        double r58495 = r58493 / r58494;
        double r58496 = cbrt(r58495);
        double r58497 = exp(r58496);
        double r58498 = log(r58497);
        double r58499 = r58496 * r58498;
        double r58500 = r58499 * r58496;
        return r58500;
}

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-cube-cbrt0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.1

    \[\leadsto \left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \color{blue}{\log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]

  6. Final simplification0.1

    \[\leadsto \left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))