Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(x - 1\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 1\right)}} + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\frac{\left(1 \cdot 1\right) \cdot 1}{\left(\left(x - 1\right) \cdot \left(x - 1\right)\right) \cdot \left(x - 1\right)}} + \frac{x}{x + 1}
double f(double x) {
        double r12337236 = 1.0;
        double r12337237 = x;
        double r12337238 = r12337237 - r12337236;
        double r12337239 = r12337236 / r12337238;
        double r12337240 = r12337237 + r12337236;
        double r12337241 = r12337237 / r12337240;
        double r12337242 = r12337239 + r12337241;
        return r12337242;
}
↓
double f(double x) {
        double r12337243 = 1.0;
        double r12337244 = r12337243 * r12337243;
        double r12337245 = r12337244 * r12337243;
        double r12337246 = x;
        double r12337247 = r12337246 - r12337243;
        double r12337248 = r12337247 * r12337247;
        double r12337249 = r12337248 * r12337247;
        double r12337250 = r12337245 / r12337249;
        double r12337251 = cbrt(r12337250);
        double r12337252 = r12337246 + r12337243;
        double r12337253 = r12337246 / r12337252;
        double r12337254 = r12337251 + r12337253;
        return r12337254;
}

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Applied cbrt-undiv0.0

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

  6. Simplified0.0

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

  8. Applied frac-times0.0

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

  9. Applied frac-times0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))