Average Error: 0.0 → 0.0
Time: 2.4s
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 r137114 = 1.0;
        double r137115 = x;
        double r137116 = r137115 - r137114;
        double r137117 = r137114 / r137116;
        double r137118 = r137115 + r137114;
        double r137119 = r137115 / r137118;
        double r137120 = r137117 + r137119;
        return r137120;
}
↓
double f(double x) {
        double r137121 = 1.0;
        double r137122 = x;
        double r137123 = r137122 - r137121;
        double r137124 = r137121 / r137123;
        double r137125 = 3.0;
        double r137126 = pow(r137124, r137125);
        double r137127 = cbrt(r137126);
        double r137128 = r137122 + r137121;
        double r137129 = r137122 / r137128;
        double r137130 = r137127 + r137129;
        return r137130;
}

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 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))