Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\]
\frac{x + 1}{1 - x}
↓
\sqrt[3]{{\left(\frac{x + 1}{1 - x}\right)}^{3}}
double f(double x) {
        double r41621 = x;
        double r41622 = 1.0;
        double r41623 = r41621 + r41622;
        double r41624 = r41622 - r41621;
        double r41625 = r41623 / r41624;
        return r41625;
}
↓
double f(double x) {
        double r41626 = x;
        double r41627 = 1.0;
        double r41628 = r41626 + r41627;
        double r41629 = r41627 - r41626;
        double r41630 = r41628 / r41629;
        double r41631 = 3.0;
        double r41632 = pow(r41630, r41631);
        double r41633 = cbrt(r41632);
        return r41633;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))