Average Error: 0.0 → 0.0
Time: 5.5s
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 r46507 = x;
        double r46508 = 1.0;
        double r46509 = r46507 + r46508;
        double r46510 = r46508 - r46507;
        double r46511 = r46509 / r46510;
        return r46511;
}
↓
double f(double x) {
        double r46512 = x;
        double r46513 = 1.0;
        double r46514 = r46512 + r46513;
        double r46515 = r46513 - r46512;
        double r46516 = r46514 / r46515;
        double r46517 = 3.0;
        double r46518 = pow(r46516, r46517);
        double r46519 = cbrt(r46518);
        return r46519;
}

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-cube20.0

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

  4. Applied add-cbrt-cube20.6

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

  5. Applied cbrt-undiv20.6

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

  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 2020045 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))