Average Error: 0.0 → 0.0
Time: 9.5s
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 r142194 = 1.0;
        double r142195 = x;
        double r142196 = r142195 - r142194;
        double r142197 = r142194 / r142196;
        double r142198 = r142195 + r142194;
        double r142199 = r142195 / r142198;
        double r142200 = r142197 + r142199;
        return r142200;
}
↓
double f(double x) {
        double r142201 = 1.0;
        double r142202 = x;
        double r142203 = r142202 - r142201;
        double r142204 = r142201 / r142203;
        double r142205 = r142202 + r142201;
        double r142206 = r142202 / r142205;
        double r142207 = r142204 + r142206;
        double r142208 = 3.0;
        double r142209 = pow(r142207, r142208);
        double r142210 = cbrt(r142209);
        return r142210;
}

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 2019209 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))