Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\log \left(e^{\sqrt[3]{\log \left(e^{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\right)}}\right)\]
\frac{x + 1}{1 - x}
↓
\log \left(e^{\sqrt[3]{\log \left(e^{{\left(\frac{x + 1}{1 - x}\right)}^{3}}\right)}}\right)
double f(double x) {
        double r33385 = x;
        double r33386 = 1.0;
        double r33387 = r33385 + r33386;
        double r33388 = r33386 - r33385;
        double r33389 = r33387 / r33388;
        return r33389;
}
↓
double f(double x) {
        double r33390 = x;
        double r33391 = 1.0;
        double r33392 = r33390 + r33391;
        double r33393 = r33391 - r33390;
        double r33394 = r33392 / r33393;
        double r33395 = 3.0;
        double r33396 = pow(r33394, r33395);
        double r33397 = exp(r33396);
        double r33398 = log(r33397);
        double r33399 = cbrt(r33398);
        double r33400 = exp(r33399);
        double r33401 = log(r33400);
        return r33401;
}

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-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{x + 1}{1 - x}}\right)}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube21.0

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

  6. Applied add-cbrt-cube21.6

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

  7. Applied cbrt-undiv21.6

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

  8. Simplified0.0

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

  10. Applied add-log-exp0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))