Average Error: 0.0 → 0.0
Time: 22.1s
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 r15860990 = 1.0;
        double r15860991 = x;
        double r15860992 = r15860991 - r15860990;
        double r15860993 = r15860990 / r15860992;
        double r15860994 = r15860991 + r15860990;
        double r15860995 = r15860991 / r15860994;
        double r15860996 = r15860993 + r15860995;
        return r15860996;
}
↓
double f(double x) {
        double r15860997 = 1.0;
        double r15860998 = x;
        double r15860999 = r15860998 - r15860997;
        double r15861000 = r15860997 / r15860999;
        double r15861001 = r15860998 + r15860997;
        double r15861002 = r15860998 / r15861001;
        double r15861003 = r15861000 + r15861002;
        double r15861004 = r15861003 * r15861003;
        double r15861005 = r15861004 * r15861003;
        double r15861006 = cbrt(r15861005);
        return r15861006;
}

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 2019107 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))