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

↓

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

double f(double x) {
        double r13566077 = 1.0;
        double r13566078 = 2.0;
        double r13566079 = r13566077 / r13566078;
        double r13566080 = x;
        double r13566081 = r13566077 + r13566080;
        double r13566082 = r13566077 - r13566080;
        double r13566083 = r13566081 / r13566082;
        double r13566084 = log(r13566083);
        double r13566085 = r13566079 * r13566084;
        return r13566085;
}

↓

double f(double x) {
        double r13566086 = 0.4;
        double r13566087 = x;
        double r13566088 = 5.0;
        double r13566089 = pow(r13566087, r13566088);
        double r13566090 = 2.0;
        double r13566091 = r13566090 * r13566087;
        double r13566092 = 0.6666666666666666;
        double r13566093 = r13566087 * r13566087;
        double r13566094 = r13566092 * r13566093;
        double r13566095 = r13566094 * r13566087;
        double r13566096 = r13566091 + r13566095;
        double r13566097 = fma(r13566086, r13566089, r13566096);
        double r13566098 = 0.5;
        double r13566099 = r13566097 * r13566098;
        return r13566099;
}

\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