Average Error: 0.0 → 0.0
Time: 14.8s
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 r32245 = x;
        double r32246 = 1.0;
        double r32247 = r32245 + r32246;
        double r32248 = r32246 - r32245;
        double r32249 = r32247 / r32248;
        return r32249;
}
↓
double f(double x) {
        double r32250 = x;
        double r32251 = 1.0;
        double r32252 = r32250 + r32251;
        double r32253 = r32251 - r32250;
        double r32254 = r32252 / r32253;
        double r32255 = 3.0;
        double r32256 = pow(r32254, r32255);
        double r32257 = cbrt(r32256);
        return r32257;
}

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-cube20.9

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

  4. Applied add-cbrt-cube21.6

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

  5. Applied cbrt-undiv21.5

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

  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 2019347 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))