Average Error: 0.0 → 0.0
Time: 31.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \sqrt[3]{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \sqrt[3]{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}
double f(double x) {
        double r4311347 = 1.0;
        double r4311348 = x;
        double r4311349 = r4311348 - r4311347;
        double r4311350 = r4311347 / r4311349;
        double r4311351 = r4311348 + r4311347;
        double r4311352 = r4311348 / r4311351;
        double r4311353 = r4311350 + r4311352;
        return r4311353;
}
↓
double f(double x) {
        double r4311354 = 1.0;
        double r4311355 = x;
        double r4311356 = r4311355 - r4311354;
        double r4311357 = r4311354 / r4311356;
        double r4311358 = r4311355 + r4311354;
        double r4311359 = r4311355 / r4311358;
        double r4311360 = r4311359 * r4311359;
        double r4311361 = r4311359 * r4311360;
        double r4311362 = cbrt(r4311361);
        double r4311363 = r4311357 + r4311362;
        return r4311363;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))