Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)\right)}^{3}}
double f(double x) {
        double r108193 = 1.0;
        double r108194 = x;
        double r108195 = r108194 - r108193;
        double r108196 = r108193 / r108195;
        double r108197 = r108194 + r108193;
        double r108198 = r108194 / r108197;
        double r108199 = r108196 + r108198;
        return r108199;
}
↓
double f(double x) {
        double r108200 = 1.0;
        double r108201 = x;
        double r108202 = r108201 - r108200;
        double r108203 = r108200 / r108202;
        double r108204 = r108201 + r108200;
        double r108205 = r108201 / r108204;
        double r108206 = exp(r108205);
        double r108207 = log(r108206);
        double r108208 = r108203 + r108207;
        double r108209 = 3.0;
        double r108210 = pow(r108208, r108209);
        double r108211 = cbrt(r108210);
        return r108211;
}

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-log-exp0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))