Initial program 37.3
\[\sin \left(x + \varepsilon\right) - \sin x\]
Initial simplification37.3
\[\leadsto \sin \left(\varepsilon + x\right) - \sin x\]
- Using strategy
rm Applied sin-sum22.4
\[\leadsto \color{blue}{\left(\sin \varepsilon \cdot \cos x + \cos \varepsilon \cdot \sin x\right)} - \sin x\]
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 fma-def0.4
\[\leadsto \color{blue}{(\left(\sin \varepsilon\right) \cdot \left(\cos x\right) + \left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right))_*}\]
- Using strategy
rm Applied add-cbrt-cube0.4
\[\leadsto (\left(\sin \varepsilon\right) \cdot \left(\cos x\right) + \color{blue}{\left(\sqrt[3]{\left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right) \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*}\right)})_*\]
Final simplification0.4
\[\leadsto (\left(\sin \varepsilon\right) \cdot \left(\cos x\right) + \left(\sqrt[3]{(\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot \left((\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_* \cdot (\left(\cos \varepsilon\right) \cdot \left(\sin x\right) + \left(-\sin x\right))_*\right)}\right))_*\]
