\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -117.2709864418915515216212952509522438049:\\ \;\;\;\;\frac{\frac{\frac{2}{x}}{x}}{x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\ \mathbf{elif}\;x \le 115.5593852642430903188142110593616962433:\\ \;\;\;\;\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{x}}{x \cdot x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\ \end{array}\]

\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}

↓

\begin{array}{l}
\mathbf{if}\;x \le -117.2709864418915515216212952509522438049:\\
\;\;\;\;\frac{\frac{\frac{2}{x}}{x}}{x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\

\mathbf{elif}\;x \le 115.5593852642430903188142110593616962433:\\
\;\;\;\;\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{2}{x}}{x \cdot x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\

\end{array}

double f(double x) {
        double r101263 = 1.0;
        double r101264 = x;
        double r101265 = r101264 + r101263;
        double r101266 = r101263 / r101265;
        double r101267 = 2.0;
        double r101268 = r101267 / r101264;
        double r101269 = r101266 - r101268;
        double r101270 = r101264 - r101263;
        double r101271 = r101263 / r101270;
        double r101272 = r101269 + r101271;
        return r101272;
}

↓

double f(double x) {
        double r101273 = x;
        double r101274 = -117.27098644189155;
        bool r101275 = r101273 <= r101274;
        double r101276 = 2.0;
        double r101277 = r101276 / r101273;
        double r101278 = r101277 / r101273;
        double r101279 = r101278 / r101273;
        double r101280 = 7.0;
        double r101281 = pow(r101273, r101280);
        double r101282 = r101276 / r101281;
        double r101283 = 5.0;
        double r101284 = pow(r101273, r101283);
        double r101285 = r101276 / r101284;
        double r101286 = r101282 + r101285;
        double r101287 = r101279 + r101286;
        double r101288 = 115.55938526424309;
        bool r101289 = r101273 <= r101288;
        double r101290 = 1.0;
        double r101291 = r101290 * r101273;
        double r101292 = r101273 + r101290;
        double r101293 = r101292 * r101276;
        double r101294 = r101291 - r101293;
        double r101295 = r101292 * r101273;
        double r101296 = r101294 / r101295;
        double r101297 = r101273 - r101290;
        double r101298 = r101290 / r101297;
        double r101299 = r101296 + r101298;
        double r101300 = r101273 * r101273;
        double r101301 = r101277 / r101300;
        double r101302 = r101301 + r101286;
        double r101303 = r101289 ? r101299 : r101302;
        double r101304 = r101275 ? r101287 : r101303;
        return r101304;
}

Original	9.8
Target	0.2
Herbie	0.1

Derivation

Split input into 3 regimes
if x < -117.27098644189155
1. Initial program 20.5
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm
3. Applied frac-sub52.6
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
4. Taylor expanded around inf 0.3
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
5. Simplified0.3
  \[\leadsto \color{blue}{\frac{2}{{x}^{3}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)}\]
6. Using strategy rm
7. Applied cube-mult0.4
  \[\leadsto \frac{2}{\color{blue}{x \cdot \left(x \cdot x\right)}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
8. Applied associate-/r*0.1
  \[\leadsto \color{blue}{\frac{\frac{2}{x}}{x \cdot x}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
9. Using strategy rm
10. Applied associate-/r*0.1
  \[\leadsto \color{blue}{\frac{\frac{\frac{2}{x}}{x}}{x}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
if -117.27098644189155 < x < 115.55938526424309
1. Initial program 0.0
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm
3. Applied frac-sub0.0
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
if 115.55938526424309 < x
1. Initial program 18.8
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm
3. Applied frac-sub51.6
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
4. Taylor expanded around inf 0.6
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
5. Simplified0.6
  \[\leadsto \color{blue}{\frac{2}{{x}^{3}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)}\]
6. Using strategy rm
7. Applied cube-mult0.6
  \[\leadsto \frac{2}{\color{blue}{x \cdot \left(x \cdot x\right)}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
8. Applied associate-/r*0.1
  \[\leadsto \color{blue}{\frac{\frac{2}{x}}{x \cdot x}} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
Recombined 3 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -117.2709864418915515216212952509522438049:\\ \;\;\;\;\frac{\frac{\frac{2}{x}}{x}}{x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\ \mathbf{elif}\;x \le 115.5593852642430903188142110593616962433:\\ \;\;\;\;\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{x}}{x \cdot x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if x < -117.27098644189155`

`if -117.27098644189155 < x < 115.55938526424309`

`if 115.55938526424309 < x`

Reproduce

In
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