Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\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)}
double f(double x) {
        double r1833235 = 1.0;
        double r1833236 = x;
        double r1833237 = r1833236 - r1833235;
        double r1833238 = r1833235 / r1833237;
        double r1833239 = r1833236 + r1833235;
        double r1833240 = r1833236 / r1833239;
        double r1833241 = r1833238 + r1833240;
        return r1833241;
}
↓
double f(double x) {
        double r1833242 = 1.0;
        double r1833243 = x;
        double r1833244 = r1833243 - r1833242;
        double r1833245 = r1833242 / r1833244;
        double r1833246 = r1833243 + r1833242;
        double r1833247 = r1833243 / r1833246;
        double r1833248 = r1833245 + r1833247;
        double r1833249 = r1833248 * r1833248;
        double r1833250 = r1833249 * r1833248;
        double r1833251 = cbrt(r1833250);
        return r1833251;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))