Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\sqrt[3]{{\left(\frac{1}{x - 1}\right)}^{3}}}\right) + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\sqrt[3]{{\left(\frac{1}{x - 1}\right)}^{3}}}\right) + \frac{x}{x + 1}
double f(double x) {
        double r149299 = 1.0;
        double r149300 = x;
        double r149301 = r149300 - r149299;
        double r149302 = r149299 / r149301;
        double r149303 = r149300 + r149299;
        double r149304 = r149300 / r149303;
        double r149305 = r149302 + r149304;
        return r149305;
}
↓
double f(double x) {
        double r149306 = 1.0;
        double r149307 = x;
        double r149308 = r149307 - r149306;
        double r149309 = r149306 / r149308;
        double r149310 = 3.0;
        double r149311 = pow(r149309, r149310);
        double r149312 = cbrt(r149311);
        double r149313 = exp(r149312);
        double r149314 = log(r149313);
        double r149315 = r149307 + r149306;
        double r149316 = r149307 / r149315;
        double r149317 = r149314 + r149316;
        return r149317;
}

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-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{1}{x - 1}}\right)} + \frac{x}{x + 1}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.0

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

  6. Applied add-cbrt-cube0.0

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

  7. Applied cbrt-undiv0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))