Average Error: 0.0 → 0.0
Time: 27.8s
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 r3776195 = 1.0;
        double r3776196 = x;
        double r3776197 = r3776196 - r3776195;
        double r3776198 = r3776195 / r3776197;
        double r3776199 = r3776196 + r3776195;
        double r3776200 = r3776196 / r3776199;
        double r3776201 = r3776198 + r3776200;
        return r3776201;
}
↓
double f(double x) {
        double r3776202 = 1.0;
        double r3776203 = x;
        double r3776204 = r3776203 - r3776202;
        double r3776205 = r3776202 / r3776204;
        double r3776206 = r3776203 + r3776202;
        double r3776207 = r3776203 / r3776206;
        double r3776208 = r3776205 + r3776207;
        double r3776209 = r3776208 * r3776208;
        double r3776210 = r3776209 * r3776208;
        double r3776211 = cbrt(r3776210);
        return r3776211;
}

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 2019142 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))