Initial program 37.5
\[\sin \left(x + \varepsilon\right) - \sin x\]
Initial simplification37.5
\[\leadsto \sin \left(\varepsilon + x\right) - \sin x\]
- Using strategy
rm Applied sin-sum22.3
\[\leadsto \color{blue}{\left(\sin \varepsilon \cdot \cos x + \cos \varepsilon \cdot \sin x\right)} - \sin x\]
Applied associate--l+0.4
\[\leadsto \color{blue}{\sin \varepsilon \cdot \cos x + \left(\cos \varepsilon \cdot \sin x - \sin x\right)}\]
Taylor expanded around inf 22.3
\[\leadsto \color{blue}{\left(\cos x \cdot \sin \varepsilon + \sin x \cdot \cos \varepsilon\right) - \sin x}\]
Simplified0.4
\[\leadsto \color{blue}{(\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\sin x \cdot \cos \varepsilon - \sin x\right))_*}\]
- Using strategy
rm Applied add-log-exp15.0
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\sin x \cdot \cos \varepsilon - \color{blue}{\log \left(e^{\sin x}\right)}\right))_*\]
Applied add-log-exp0.5
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\color{blue}{\log \left(e^{\sin x \cdot \cos \varepsilon}\right)} - \log \left(e^{\sin x}\right)\right))_*\]
Applied diff-log0.5
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \color{blue}{\left(\log \left(\frac{e^{\sin x \cdot \cos \varepsilon}}{e^{\sin x}}\right)\right)})_*\]
Simplified0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\log \color{blue}{\left(e^{\cos \varepsilon \cdot \sin x - \sin x}\right)}\right))_*\]
Final simplification0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\log \left(e^{\cos \varepsilon \cdot \sin x - \sin x}\right)\right))_*\]
