Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\left(\sqrt[3]{\frac{1}{x - 1}} \cdot \sqrt[3]{\frac{1}{x - 1}}\right) \cdot \sqrt[3]{\frac{1}{x - 1}} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r93344 = 1.0;
        double r93345 = x;
        double r93346 = r93345 - r93344;
        double r93347 = r93344 / r93346;
        double r93348 = r93345 + r93344;
        double r93349 = r93345 / r93348;
        double r93350 = r93347 + r93349;
        return r93350;
}
↓
double f(double x) {
        double r93351 = 1.0;
        double r93352 = x;
        double r93353 = r93352 - r93351;
        double r93354 = r93351 / r93353;
        double r93355 = cbrt(r93354);
        double r93356 = r93355 * r93355;
        double r93357 = r93356 * r93355;
        double r93358 = r93352 + r93351;
        double r93359 = r93352 / r93358;
        double r93360 = r93357 + r93359;
        double r93361 = 3.0;
        double r93362 = pow(r93360, r93361);
        double r93363 = cbrt(r93362);
        return r93363;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))