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 r29131 = x;
        double r29132 = 1.0;
        double r29133 = r29131 + r29132;
        double r29134 = r29132 - r29131;
        double r29135 = r29133 / r29134;
        return r29135;
}
↓
double f(double x) {
        double r29136 = x;
        double r29137 = 1.0;
        double r29138 = r29136 + r29137;
        double r29139 = r29137 - r29136;
        double r29140 = r29138 / r29139;
        double r29141 = 3.0;
        double r29142 = pow(r29140, r29141);
        double r29143 = pow(r29142, r29141);
        double r29144 = cbrt(r29143);
        double r29145 = cbrt(r29144);
        return r29145;
}

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