Initial program 60.1
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
Taylor expanded around 0 53.0
\[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]
- Using strategy
rm Applied add-cube-cbrt53.0
\[\leadsto \color{blue}{\left(\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}} \cdot \sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}\right) \cdot \sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}} - \frac{1}{3} \cdot {x}^{3}\]
Applied fma-neg53.0
\[\leadsto \color{blue}{(\left(\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}} \cdot \sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}\right) \cdot \left(\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}\right) + \left(-\frac{1}{3} \cdot {x}^{3}\right))_*}\]
Simplified53.0
\[\leadsto (\color{blue}{\left(\sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*} \cdot \sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*}\right)} \cdot \left(\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}\right) + \left(-\frac{1}{3} \cdot {x}^{3}\right))_*\]
- Using strategy
rm Applied log1p-expm1-u53.0
\[\leadsto (\left(\sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*} \cdot \sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*}\right) \cdot \color{blue}{\left(\log_* (1 + (e^{\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}} - 1)^*)\right)} + \left(-\frac{1}{3} \cdot {x}^{3}\right))_*\]
- Using strategy
rm Applied log1p-expm1-u53.0
\[\leadsto (\left(\sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*} \cdot \color{blue}{\log_* (1 + (e^{\sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*}} - 1)^*)}\right) \cdot \left(\log_* (1 + (e^{\sqrt[3]{x + \frac{2}{15} \cdot {x}^{5}}} - 1)^*)\right) + \left(-\frac{1}{3} \cdot {x}^{3}\right))_*\]
Final simplification53.0
\[\leadsto (\left(\log_* (1 + (e^{\sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*}} - 1)^*) \cdot \sqrt[3]{(\frac{2}{15} \cdot \left({x}^{5}\right) + x)_*}\right) \cdot \left(\log_* (1 + (e^{\sqrt[3]{{x}^{5} \cdot \frac{2}{15} + x}} - 1)^*)\right) + \left(\frac{-1}{3} \cdot {x}^{3}\right))_*\]
