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

↓

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

double f(double x) {
        double r12672980 = 1.0;
        double r12672981 = 2.0;
        double r12672982 = r12672980 / r12672981;
        double r12672983 = x;
        double r12672984 = r12672980 + r12672983;
        double r12672985 = r12672980 - r12672983;
        double r12672986 = r12672984 / r12672985;
        double r12672987 = log(r12672986);
        double r12672988 = r12672982 * r12672987;
        return r12672988;
}

↓

double f(double x) {
        double r12672989 = 0.4;
        double r12672990 = x;
        double r12672991 = 5.0;
        double r12672992 = pow(r12672990, r12672991);
        double r12672993 = 2.0;
        double r12672994 = r12672993 * r12672990;
        double r12672995 = 0.6666666666666666;
        double r12672996 = r12672990 * r12672990;
        double r12672997 = r12672995 * r12672996;
        double r12672998 = r12672997 * r12672990;
        double r12672999 = r12672994 + r12672998;
        double r12673000 = fma(r12672989, r12672992, r12672999);
        double r12673001 = 0.5;
        double r12673002 = r12673000 * r12673001;
        return r12673002;
}

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

↓

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

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
\[\leadsto \color{blue}{(\frac{2}{5} \cdot \left({x}^{5}\right) + \left(x \cdot (\frac{2}{3} \cdot \left(x \cdot x\right) + 2)_*\right))_*} \cdot \frac{1}{2}\]
Using strategy rm
Applied fma-udef0.2
\[\leadsto (\frac{2}{5} \cdot \left({x}^{5}\right) + \left(x \cdot \color{blue}{\left(\frac{2}{3} \cdot \left(x \cdot x\right) + 2\right)}\right))_* \cdot \frac{1}{2}\]
Applied distribute-lft-in0.2
\[\leadsto (\frac{2}{5} \cdot \left({x}^{5}\right) + \color{blue}{\left(x \cdot \left(\frac{2}{3} \cdot \left(x \cdot x\right)\right) + x \cdot 2\right)})_* \cdot \frac{1}{2}\]
Final simplification0.2
\[\leadsto (\frac{2}{5} \cdot \left({x}^{5}\right) + \left(2 \cdot x + \left(\frac{2}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right))_* \cdot \frac{1}{2}\]

Error

Derivation

Reproduce