Average Error: 0.0 → 0.1
Time: 11.3s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\]
\frac{x + 1}{1 - x}
↓
\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)
double f(double x) {
        double r58472 = x;
        double r58473 = 1.0;
        double r58474 = r58472 + r58473;
        double r58475 = r58473 - r58472;
        double r58476 = r58474 / r58475;
        return r58476;
}
↓
double f(double x) {
        double r58477 = x;
        double r58478 = 1.0;
        double r58479 = r58477 + r58478;
        double r58480 = r58478 - r58477;
        double r58481 = r58479 / r58480;
        double r58482 = cbrt(r58481);
        double r58483 = r58482 * r58482;
        double r58484 = exp(r58482);
        double r58485 = log(r58484);
        double r58486 = r58483 * r58485;
        return r58486;
}

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

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

  6. Final simplification0.1

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

Reproduce

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