Average Error: 0.0 → 0.0
Time: 8.0s
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 r92254 = 1.0;
        double r92255 = x;
        double r92256 = r92255 - r92254;
        double r92257 = r92254 / r92256;
        double r92258 = r92255 + r92254;
        double r92259 = r92255 / r92258;
        double r92260 = r92257 + r92259;
        return r92260;
}
↓
double f(double x) {
        double r92261 = 1.0;
        double r92262 = x;
        double r92263 = r92262 - r92261;
        double r92264 = r92261 / r92263;
        double r92265 = r92262 + r92261;
        double r92266 = r92262 / r92265;
        double r92267 = r92264 + r92266;
        double r92268 = 3.0;
        double r92269 = pow(r92267, r92268);
        double r92270 = cbrt(r92269);
        return r92270;
}

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