Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\sqrt[3]{\sqrt[3]{{\left({\left(\frac{x + 1}{1 - x}\right)}^{3}\right)}^{3}}}\]
\frac{x + 1}{1 - x}
↓
\sqrt[3]{\sqrt[3]{{\left({\left(\frac{x + 1}{1 - x}\right)}^{3}\right)}^{3}}}
double f(double x) {
        double r41576 = x;
        double r41577 = 1.0;
        double r41578 = r41576 + r41577;
        double r41579 = r41577 - r41576;
        double r41580 = r41578 / r41579;
        return r41580;
}
↓
double f(double x) {
        double r41581 = x;
        double r41582 = 1.0;
        double r41583 = r41581 + r41582;
        double r41584 = r41582 - r41581;
        double r41585 = r41583 / r41584;
        double r41586 = 3.0;
        double r41587 = pow(r41585, r41586);
        double r41588 = pow(r41587, r41586);
        double r41589 = cbrt(r41588);
        double r41590 = cbrt(r41589);
        return r41590;
}

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-cbrt-cube20.6

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

  4. Applied add-cbrt-cube21.2

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

  5. Applied cbrt-undiv21.2

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

  6. Simplified0.0

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

  8. Applied add-cbrt-cube0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))