Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r114946 = 1.0;
        double r114947 = x;
        double r114948 = r114947 - r114946;
        double r114949 = r114946 / r114948;
        double r114950 = r114947 + r114946;
        double r114951 = r114947 / r114950;
        double r114952 = r114949 + r114951;
        return r114952;
}
↓
double f(double x) {
        double r114953 = 1.0;
        double r114954 = x;
        double r114955 = r114954 - r114953;
        double r114956 = r114953 / r114955;
        double r114957 = r114954 + r114953;
        double r114958 = r114954 / r114957;
        double r114959 = 3.0;
        double r114960 = pow(r114958, r114959);
        double r114961 = cbrt(r114960);
        double r114962 = r114956 + r114961;
        return r114962;
}

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-cube20.9

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

  4. Applied add-cbrt-cube21.5

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

  5. Applied cbrt-undiv21.5

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))