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 r160 = x;
        double r161 = 1.0;
        double r162 = r160 + r161;
        double r163 = r161 - r160;
        double r164 = r162 / r163;
        return r164;
}
↓
double f(double x) {
        double r165 = x;
        double r166 = 1.0;
        double r167 = r165 + r166;
        double r168 = r166 - r165;
        double r169 = r167 / r168;
        double r170 = 3.0;
        double r171 = pow(r169, r170);
        double r172 = cbrt(r171);
        return r172;
}

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-cube21.3

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

  4. Applied add-cbrt-cube21.9

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

  5. Applied cbrt-undiv21.9

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

  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 2020025 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))