Average Error: 0.0 → 0.0
Time: 2.8m
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{x}{1 + x} + \log \left(e^{\sqrt[3]{\frac{1}{\left(-1 + x\right) \cdot \left(\left(-1 + x\right) \cdot \left(-1 + x\right)\right)}}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{x}{1 + x} + \log \left(e^{\sqrt[3]{\frac{1}{\left(-1 + x\right) \cdot \left(\left(-1 + x\right) \cdot \left(-1 + x\right)\right)}}}\right)
double f(double x) {
        double r26849273 = 1.0;
        double r26849274 = x;
        double r26849275 = r26849274 - r26849273;
        double r26849276 = r26849273 / r26849275;
        double r26849277 = r26849274 + r26849273;
        double r26849278 = r26849274 / r26849277;
        double r26849279 = r26849276 + r26849278;
        return r26849279;
}
↓
double f(double x) {
        double r26849280 = x;
        double r26849281 = 1.0;
        double r26849282 = r26849281 + r26849280;
        double r26849283 = r26849280 / r26849282;
        double r26849284 = -1.0;
        double r26849285 = r26849284 + r26849280;
        double r26849286 = r26849285 * r26849285;
        double r26849287 = r26849285 * r26849286;
        double r26849288 = r26849281 / r26849287;
        double r26849289 = cbrt(r26849288);
        double r26849290 = exp(r26849289);
        double r26849291 = log(r26849290);
        double r26849292 = r26849283 + r26849291;
        return r26849292;
}

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

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

  8. Applied add-log-exp0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))