Initial program 36.8
\[\sin \left(x + \varepsilon\right) - \sin x\]
Initial simplification36.8
\[\leadsto \sin \left(\varepsilon + x\right) - \sin x\]
- Using strategy
rm Applied sin-sum22.1
\[\leadsto \color{blue}{\left(\sin \varepsilon \cdot \cos x + \cos \varepsilon \cdot \sin x\right)} - \sin x\]
Applied associate--l+0.4
\[\leadsto \color{blue}{\sin \varepsilon \cdot \cos x + \left(\cos \varepsilon \cdot \sin x - \sin x\right)}\]
- Using strategy
rm Applied fma-neg0.4
\[\leadsto \sin \varepsilon \cdot \cos x + \color{blue}{(\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*}\]
- Using strategy
rm Applied add-cbrt-cube0.4
\[\leadsto \sin \varepsilon \cdot \cos x + \color{blue}{\sqrt[3]{\left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right) \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*}}\]
- Using strategy
rm Applied add-log-exp0.5
\[\leadsto \sin \varepsilon \cdot \cos x + \sqrt[3]{\left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right) \cdot \color{blue}{\log \left(e^{(\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*}\right)}}\]
Final simplification0.5
\[\leadsto \cos x \cdot \sin \varepsilon + \sqrt[3]{\log \left(e^{(\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*}\right) \cdot \left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right)}\]
