Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \sqrt[3]{{\left(\frac{x}{x + 1}\right)}^{3}}\right)}^{3}}
double f(double x) {
        double r139203 = 1.0;
        double r139204 = x;
        double r139205 = r139204 - r139203;
        double r139206 = r139203 / r139205;
        double r139207 = r139204 + r139203;
        double r139208 = r139204 / r139207;
        double r139209 = r139206 + r139208;
        return r139209;
}
↓
double f(double x) {
        double r139210 = 1.0;
        double r139211 = x;
        double r139212 = r139211 - r139210;
        double r139213 = r139210 / r139212;
        double r139214 = r139211 + r139210;
        double r139215 = r139211 / r139214;
        double r139216 = 3.0;
        double r139217 = pow(r139215, r139216);
        double r139218 = cbrt(r139217);
        double r139219 = r139213 + r139218;
        double r139220 = pow(r139219, r139216);
        double r139221 = cbrt(r139220);
        return r139221;
}

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

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

  4. Simplified0.0

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

  6. Applied add-cbrt-cube21.0

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

  7. Applied add-cbrt-cube21.6

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

  8. Applied cbrt-undiv21.6

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))