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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1313.139082756415291441953741014003753662:\\ \;\;\;\;\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{7}}\\ \mathbf{elif}\;x \le 33013378.79688735306262969970703125:\\ \;\;\;\;\frac{1 \cdot \left(x \cdot \left(x + 1\right)\right) - \left(x - 1\right) \cdot \left(2 \cdot \left(x + 1\right) - x \cdot 1\right)}{\left(x - 1\right) \cdot \left(x \cdot \left(x + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{{x}^{5}} + \frac{\frac{2}{x \cdot x}}{x}\right) + \frac{2}{{x}^{7}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -1313.139082756415291441953741014003753662:\\
\;\;\;\;\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{7}}\\

\mathbf{elif}\;x \le 33013378.79688735306262969970703125:\\
\;\;\;\;\frac{1 \cdot \left(x \cdot \left(x + 1\right)\right) - \left(x - 1\right) \cdot \left(2 \cdot \left(x + 1\right) - x \cdot 1\right)}{\left(x - 1\right) \cdot \left(x \cdot \left(x + 1\right)\right)}\\

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

\end{array}

double f(double x) {
        double r136790 = 1.0;
        double r136791 = x;
        double r136792 = r136791 + r136790;
        double r136793 = r136790 / r136792;
        double r136794 = 2.0;
        double r136795 = r136794 / r136791;
        double r136796 = r136793 - r136795;
        double r136797 = r136791 - r136790;
        double r136798 = r136790 / r136797;
        double r136799 = r136796 + r136798;
        return r136799;
}

↓

double f(double x) {
        double r136800 = x;
        double r136801 = -1313.1390827564153;
        bool r136802 = r136800 <= r136801;
        double r136803 = 2.0;
        double r136804 = 5.0;
        double r136805 = pow(r136800, r136804);
        double r136806 = r136803 / r136805;
        double r136807 = 3.0;
        double r136808 = pow(r136800, r136807);
        double r136809 = r136803 / r136808;
        double r136810 = r136806 + r136809;
        double r136811 = 7.0;
        double r136812 = pow(r136800, r136811);
        double r136813 = r136803 / r136812;
        double r136814 = r136810 + r136813;
        double r136815 = 33013378.796887353;
        bool r136816 = r136800 <= r136815;
        double r136817 = 1.0;
        double r136818 = r136800 + r136817;
        double r136819 = r136800 * r136818;
        double r136820 = r136817 * r136819;
        double r136821 = r136800 - r136817;
        double r136822 = r136803 * r136818;
        double r136823 = r136800 * r136817;
        double r136824 = r136822 - r136823;
        double r136825 = r136821 * r136824;
        double r136826 = r136820 - r136825;
        double r136827 = r136821 * r136819;
        double r136828 = r136826 / r136827;
        double r136829 = r136800 * r136800;
        double r136830 = r136803 / r136829;
        double r136831 = r136830 / r136800;
        double r136832 = r136806 + r136831;
        double r136833 = r136832 + r136813;
        double r136834 = r136816 ? r136828 : r136833;
        double r136835 = r136802 ? r136814 : r136834;
        return r136835;
}

Original	9.7
Target	0.3
Herbie	0.2

Derivation

Split input into 3 regimes
if x < -1313.1390827564153
1. Initial program 20.1
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Simplified20.1
  \[\leadsto \color{blue}{\frac{1}{x - 1} - \left(\frac{2}{x} - \frac{1}{x + 1}\right)}\]
3. Taylor expanded around inf 0.6
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
4. Simplified0.6
  \[\leadsto \color{blue}{\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{7}}}\]
if -1313.1390827564153 < x < 33013378.796887353
1. Initial program 0.4
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Simplified0.4
  \[\leadsto \color{blue}{\frac{1}{x - 1} - \left(\frac{2}{x} - \frac{1}{x + 1}\right)}\]
3. Using strategy rm
4. Applied frac-sub0.4
  \[\leadsto \frac{1}{x - 1} - \color{blue}{\frac{2 \cdot \left(x + 1\right) - x \cdot 1}{x \cdot \left(x + 1\right)}}\]
5. Applied frac-sub0.0
  \[\leadsto \color{blue}{\frac{1 \cdot \left(x \cdot \left(x + 1\right)\right) - \left(x - 1\right) \cdot \left(2 \cdot \left(x + 1\right) - x \cdot 1\right)}{\left(x - 1\right) \cdot \left(x \cdot \left(x + 1\right)\right)}}\]
if 33013378.796887353 < x
1. Initial program 19.1
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Simplified19.1
  \[\leadsto \color{blue}{\frac{1}{x - 1} - \left(\frac{2}{x} - \frac{1}{x + 1}\right)}\]
3. Taylor expanded around inf 0.5
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
4. Simplified0.5
  \[\leadsto \color{blue}{\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{7}}}\]
5. Using strategy rm
6. Applied unpow30.6
  \[\leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{\color{blue}{\left(x \cdot x\right) \cdot x}}\right) + \frac{2}{{x}^{7}}\]
7. Applied associate-/r*0.1
  \[\leadsto \left(\frac{2}{{x}^{5}} + \color{blue}{\frac{\frac{2}{x \cdot x}}{x}}\right) + \frac{2}{{x}^{7}}\]
Recombined 3 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1313.139082756415291441953741014003753662:\\ \;\;\;\;\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{7}}\\ \mathbf{elif}\;x \le 33013378.79688735306262969970703125:\\ \;\;\;\;\frac{1 \cdot \left(x \cdot \left(x + 1\right)\right) - \left(x - 1\right) \cdot \left(2 \cdot \left(x + 1\right) - x \cdot 1\right)}{\left(x - 1\right) \cdot \left(x \cdot \left(x + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{{x}^{5}} + \frac{\frac{2}{x \cdot x}}{x}\right) + \frac{2}{{x}^{7}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if x < -1313.1390827564153`

`if -1313.1390827564153 < x < 33013378.796887353`

`if 33013378.796887353 < x`

Reproduce

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