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

↓

\[\frac{1}{2} \cdot \left({x}^{5} \cdot \frac{2}{5} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{2}{3}\right)\right) \cdot x\right)\right)\]

double f(double x) {
        double r9824649 = 1.0;
        double r9824650 = 2.0;
        double r9824651 = r9824649 / r9824650;
        double r9824652 = x;
        double r9824653 = r9824649 + r9824652;
        double r9824654 = r9824649 - r9824652;
        double r9824655 = r9824653 / r9824654;
        double r9824656 = log(r9824655);
        double r9824657 = r9824651 * r9824656;
        return r9824657;
}

↓

double f(double x) {
        double r9824658 = 0.5;
        double r9824659 = x;
        double r9824660 = 5.0;
        double r9824661 = pow(r9824659, r9824660);
        double r9824662 = 0.4;
        double r9824663 = r9824661 * r9824662;
        double r9824664 = 2.0;
        double r9824665 = r9824664 * r9824659;
        double r9824666 = 0.6666666666666666;
        double r9824667 = r9824659 * r9824666;
        double r9824668 = r9824659 * r9824667;
        double r9824669 = r9824668 * r9824659;
        double r9824670 = r9824665 + r9824669;
        double r9824671 = r9824663 + r9824670;
        double r9824672 = r9824658 * r9824671;
        return r9824672;
}

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

↓

\frac{1}{2} \cdot \left({x}^{5} \cdot \frac{2}{5} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{2}{3}\right)\right) \cdot x\right)\right)

Derivation

Initial program 58.6
\[\frac{1}{2} \cdot \log \left(\frac{1 + x}{1 - x}\right)\]
Simplified58.6
\[\leadsto \color{blue}{\log \left(\frac{x + 1}{1 - x}\right) \cdot \frac{1}{2}}\]
Taylor expanded around 0 0.2
\[\leadsto \color{blue}{\left(2 \cdot x + \left(\frac{2}{3} \cdot {x}^{3} + \frac{2}{5} \cdot {x}^{5}\right)\right)} \cdot \frac{1}{2}\]
Simplified0.2
\[\leadsto \color{blue}{\left(x \cdot \left(x \cdot \left(\frac{2}{3} \cdot x\right) + 2\right) + {x}^{5} \cdot \frac{2}{5}\right)} \cdot \frac{1}{2}\]
Using strategy rm
Applied distribute-lft-in0.2
\[\leadsto \left(\color{blue}{\left(x \cdot \left(x \cdot \left(\frac{2}{3} \cdot x\right)\right) + x \cdot 2\right)} + {x}^{5} \cdot \frac{2}{5}\right) \cdot \frac{1}{2}\]
Final simplification0.2
\[\leadsto \frac{1}{2} \cdot \left({x}^{5} \cdot \frac{2}{5} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{2}{3}\right)\right) \cdot x\right)\right)\]

Error

Derivation

Reproduce