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

↓

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

\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}^{7}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{5}}\\

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

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

\end{array}

double f(double x) {
        double r96059 = 1.0;
        double r96060 = x;
        double r96061 = r96060 + r96059;
        double r96062 = r96059 / r96061;
        double r96063 = 2.0;
        double r96064 = r96063 / r96060;
        double r96065 = r96062 - r96064;
        double r96066 = r96060 - r96059;
        double r96067 = r96059 / r96066;
        double r96068 = r96065 + r96067;
        return r96068;
}

↓

double f(double x) {
        double r96069 = x;
        double r96070 = -1313.1390827564153;
        bool r96071 = r96069 <= r96070;
        double r96072 = 2.0;
        double r96073 = 7.0;
        double r96074 = pow(r96069, r96073);
        double r96075 = r96072 / r96074;
        double r96076 = 3.0;
        double r96077 = pow(r96069, r96076);
        double r96078 = r96072 / r96077;
        double r96079 = r96075 + r96078;
        double r96080 = 5.0;
        double r96081 = pow(r96069, r96080);
        double r96082 = r96072 / r96081;
        double r96083 = r96079 + r96082;
        double r96084 = 33013378.796887353;
        bool r96085 = r96069 <= r96084;
        double r96086 = 1.0;
        double r96087 = r96086 * r96069;
        double r96088 = r96069 + r96086;
        double r96089 = r96088 * r96072;
        double r96090 = r96087 - r96089;
        double r96091 = r96069 - r96086;
        double r96092 = r96090 * r96091;
        double r96093 = r96088 * r96069;
        double r96094 = r96093 * r96086;
        double r96095 = r96092 + r96094;
        double r96096 = r96069 * r96091;
        double r96097 = r96088 * r96096;
        double r96098 = r96095 / r96097;
        double r96099 = r96069 * r96069;
        double r96100 = r96072 / r96099;
        double r96101 = r96100 / r96069;
        double r96102 = r96075 + r96101;
        double r96103 = r96102 + r96082;
        double r96104 = r96085 ? r96098 : r96103;
        double r96105 = r96071 ? r96083 : r96104;
        return r96105;
}

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. Taylor expanded around inf 0.6
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
3. Simplified0.6
  \[\leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{5}}}\]
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. Using strategy rm
3. Applied frac-sub0.4
  \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
4. Applied frac-add0.0
  \[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
5. Using strategy rm
6. Applied associate-*l*0.0
  \[\leadsto \frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\color{blue}{\left(x + 1\right) \cdot \left(x \cdot \left(x - 1\right)\right)}}\]
if 33013378.796887353 < x
1. Initial program 19.1
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Taylor expanded around inf 0.5
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{7}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
3. Simplified0.5
  \[\leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{5}}}\]
4. Using strategy rm
5. Applied unpow30.6
  \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{\color{blue}{\left(x \cdot x\right) \cdot x}}\right) + \frac{2}{{x}^{5}}\]
6. Applied associate-/r*0.1
  \[\leadsto \left(\frac{2}{{x}^{7}} + \color{blue}{\frac{\frac{2}{x \cdot x}}{x}}\right) + \frac{2}{{x}^{5}}\]
Recombined 3 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1313.139082756415291441953741014003753662:\\ \;\;\;\;\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{3}}\right) + \frac{2}{{x}^{5}}\\ \mathbf{elif}\;x \le 33013378.79688735306262969970703125:\\ \;\;\;\;\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(x + 1\right) \cdot \left(x \cdot \left(x - 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{{x}^{7}} + \frac{\frac{2}{x \cdot x}}{x}\right) + \frac{2}{{x}^{5}}\\ \end{array}\]

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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