Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r99190 = 1.0;
        double r99191 = x;
        double r99192 = r99191 - r99190;
        double r99193 = r99190 / r99192;
        double r99194 = r99191 + r99190;
        double r99195 = r99191 / r99194;
        double r99196 = r99193 + r99195;
        return r99196;
}
↓
double f(double x) {
        double r99197 = 1.0;
        double r99198 = x;
        double r99199 = r99198 - r99197;
        double r99200 = r99197 / r99199;
        double r99201 = r99198 + r99197;
        double r99202 = r99198 / r99201;
        double r99203 = r99200 + r99202;
        double r99204 = 3.0;
        double r99205 = pow(r99203, r99204);
        double r99206 = cbrt(r99205);
        return r99206;
}

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

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))