Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1}\right)}^{3}} + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1}\right)}^{3}} + \frac{x}{x + 1}
double f(double x) {
        double r102945 = 1.0;
        double r102946 = x;
        double r102947 = r102946 - r102945;
        double r102948 = r102945 / r102947;
        double r102949 = r102946 + r102945;
        double r102950 = r102946 / r102949;
        double r102951 = r102948 + r102950;
        return r102951;
}
↓
double f(double x) {
        double r102952 = 1.0;
        double r102953 = x;
        double r102954 = r102953 - r102952;
        double r102955 = r102952 / r102954;
        double r102956 = 3.0;
        double r102957 = pow(r102955, r102956);
        double r102958 = cbrt(r102957);
        double r102959 = r102953 + r102952;
        double r102960 = r102953 / r102959;
        double r102961 = r102958 + r102960;
        return r102961;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))