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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -132.1257463208951321576023474335670471191:\\ \;\;\;\;\frac{2}{{x}^{5}} + \left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{7}}\right)\\ \mathbf{elif}\;x \le 111.637593887486829657973430585116147995:\\ \;\;\;\;\left(1 - \frac{1 + x}{\frac{x}{2}}\right) \cdot \frac{1}{1 + x} + \frac{1}{x - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{x}^{5}} + \left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{7}}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -132.1257463208951321576023474335670471191:\\
\;\;\;\;\frac{2}{{x}^{5}} + \left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{7}}\right)\\

\mathbf{elif}\;x \le 111.637593887486829657973430585116147995:\\
\;\;\;\;\left(1 - \frac{1 + x}{\frac{x}{2}}\right) \cdot \frac{1}{1 + x} + \frac{1}{x - 1}\\

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

\end{array}

double f(double x) {
        double r5570030 = 1.0;
        double r5570031 = x;
        double r5570032 = r5570031 + r5570030;
        double r5570033 = r5570030 / r5570032;
        double r5570034 = 2.0;
        double r5570035 = r5570034 / r5570031;
        double r5570036 = r5570033 - r5570035;
        double r5570037 = r5570031 - r5570030;
        double r5570038 = r5570030 / r5570037;
        double r5570039 = r5570036 + r5570038;
        return r5570039;
}

↓

double f(double x) {
        double r5570040 = x;
        double r5570041 = -132.12574632089513;
        bool r5570042 = r5570040 <= r5570041;
        double r5570043 = 2.0;
        double r5570044 = 5.0;
        double r5570045 = pow(r5570040, r5570044);
        double r5570046 = r5570043 / r5570045;
        double r5570047 = r5570043 / r5570040;
        double r5570048 = r5570040 * r5570040;
        double r5570049 = r5570047 / r5570048;
        double r5570050 = 7.0;
        double r5570051 = pow(r5570040, r5570050);
        double r5570052 = r5570043 / r5570051;
        double r5570053 = r5570049 + r5570052;
        double r5570054 = r5570046 + r5570053;
        double r5570055 = 111.63759388748683;
        bool r5570056 = r5570040 <= r5570055;
        double r5570057 = 1.0;
        double r5570058 = r5570057 + r5570040;
        double r5570059 = r5570040 / r5570043;
        double r5570060 = r5570058 / r5570059;
        double r5570061 = r5570057 - r5570060;
        double r5570062 = 1.0;
        double r5570063 = r5570062 / r5570058;
        double r5570064 = r5570061 * r5570063;
        double r5570065 = r5570040 - r5570057;
        double r5570066 = r5570057 / r5570065;
        double r5570067 = r5570064 + r5570066;
        double r5570068 = r5570056 ? r5570067 : r5570054;
        double r5570069 = r5570042 ? r5570054 : r5570068;
        return r5570069;
}

Original	10.1
Target	0.2
Herbie	0.1

Derivation

Split input into 2 regimes
if x < -132.12574632089513 or 111.63759388748683 < x
1. Initial program 20.2
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm
3. Applied frac-sub52.5
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
4. Using strategy rm
5. Applied flip-+52.5
  \[\leadsto \frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x - 1}} \cdot x} + \frac{1}{x - 1}\]
6. Applied associate-*l/59.6
  \[\leadsto \frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\color{blue}{\frac{\left(x \cdot x - 1 \cdot 1\right) \cdot x}{x - 1}}} + \frac{1}{x - 1}\]
7. Applied associate-/r/59.6
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x \cdot x - 1 \cdot 1\right) \cdot x} \cdot \left(x - 1\right)} + \frac{1}{x - 1}\]
8. Applied fma-def59.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x \cdot x - 1 \cdot 1\right) \cdot x}, x - 1, \frac{1}{x - 1}\right)}\]
9. Taylor expanded around inf 0.4
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{3}} + 2 \cdot \frac{1}{{x}^{5}}\right)}\]
10. Simplified0.1
  \[\leadsto \color{blue}{\frac{2}{{x}^{5}} + \left(\frac{2}{{x}^{7}} + \frac{\frac{2}{x}}{x \cdot x}\right)}\]
if -132.12574632089513 < x < 111.63759388748683
1. Initial program 0.1
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm
3. Applied frac-sub0.1
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
4. Using strategy rm
5. Applied *-un-lft-identity0.1
  \[\leadsto \frac{\color{blue}{1 \cdot \left(1 \cdot x - \left(x + 1\right) \cdot 2\right)}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\]
6. Applied times-frac0.1
  \[\leadsto \color{blue}{\frac{1}{x + 1} \cdot \frac{1 \cdot x - \left(x + 1\right) \cdot 2}{x}} + \frac{1}{x - 1}\]
7. Simplified0.1
  \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\left(1 - \frac{x + 1}{\frac{x}{2}}\right)} + \frac{1}{x - 1}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -132.1257463208951321576023474335670471191:\\ \;\;\;\;\frac{2}{{x}^{5}} + \left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{7}}\right)\\ \mathbf{elif}\;x \le 111.637593887486829657973430585116147995:\\ \;\;\;\;\left(1 - \frac{1 + x}{\frac{x}{2}}\right) \cdot \frac{1}{1 + x} + \frac{1}{x - 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{{x}^{5}} + \left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{7}}\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if x < -132.12574632089513 or 111.63759388748683 < x`

`if -132.12574632089513 < x < 111.63759388748683`

Reproduce

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