\[\frac{1}{x - 1} + \frac{x}{x + 1}\]

↓

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

double f(double x) {
        double r24332701 = 1.0;
        double r24332702 = x;
        double r24332703 = r24332702 - r24332701;
        double r24332704 = r24332701 / r24332703;
        double r24332705 = r24332702 + r24332701;
        double r24332706 = r24332702 / r24332705;
        double r24332707 = r24332704 + r24332706;
        return r24332707;
}

↓

double f(double x) {
        double r24332708 = 1.0;
        double r24332709 = x;
        double r24332710 = r24332709 - r24332708;
        double r24332711 = r24332708 / r24332710;
        double r24332712 = r24332709 + r24332708;
        double r24332713 = r24332709 / r24332712;
        double r24332714 = r24332711 + r24332713;
        double r24332715 = r24332714 * r24332714;
        double r24332716 = r24332709 * r24332709;
        double r24332717 = r24332716 - r24332708;
        double r24332718 = r24332708 / r24332717;
        double r24332719 = r24332718 * r24332712;
        double r24332720 = r24332713 + r24332719;
        double r24332721 = r24332715 * r24332720;
        double r24332722 = cbrt(r24332721);
        return r24332722;
}

\frac{1}{x - 1} + \frac{x}{x + 1}

↓

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

Derivation

Initial program 0.0
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
Using strategy rm
Applied add-cbrt-cube0.0
\[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}}\]
Using strategy rm
Applied flip--0.0
\[\leadsto \sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x + 1}}} + \frac{x}{x + 1}\right)}\]
Applied associate-/r/0.0
\[\leadsto \sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\color{blue}{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right)} + \frac{x}{x + 1}\right)}\]
Final simplification0.0
\[\leadsto \sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{x}{x + 1} + \frac{1}{x \cdot x - 1} \cdot \left(x + 1\right)\right)}\]

Error

Derivation

Reproduce