Average Error: 0.0 → 0.0
Time: 10.8s
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 r104224 = 1.0;
        double r104225 = x;
        double r104226 = r104225 - r104224;
        double r104227 = r104224 / r104226;
        double r104228 = r104225 + r104224;
        double r104229 = r104225 / r104228;
        double r104230 = r104227 + r104229;
        return r104230;
}
↓
double f(double x) {
        double r104231 = 1.0;
        double r104232 = x;
        double r104233 = r104232 - r104231;
        double r104234 = r104231 / r104233;
        double r104235 = r104232 + r104231;
        double r104236 = r104232 / r104235;
        double r104237 = r104234 + r104236;
        double r104238 = 3.0;
        double r104239 = pow(r104237, r104238);
        double r104240 = cbrt(r104239);
        return r104240;
}

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 2019351 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))