Initial program 37.2
\[\sin \left(x + \varepsilon\right) - \sin x\]
- Using strategy
rm Applied +-commutative37.2
\[\leadsto \sin \color{blue}{\left(\varepsilon + x\right)} - \sin x\]
Applied sin-sum21.3
\[\leadsto \color{blue}{\left(\sin \varepsilon \cdot \cos x + \cos \varepsilon \cdot \sin x\right)} - \sin x\]
Applied associate--l+0.4
\[\leadsto \color{blue}{\sin \varepsilon \cdot \cos x + \left(\cos \varepsilon \cdot \sin x - \sin x\right)}\]
- Using strategy
rm Applied *-commutative0.4
\[\leadsto \color{blue}{\cos x \cdot \sin \varepsilon} + \left(\cos \varepsilon \cdot \sin x - \sin x\right)\]
Applied fma-def0.4
\[\leadsto \color{blue}{(\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\cos \varepsilon \cdot \sin x - \sin x\right))_*}\]
- Using strategy
rm Applied *-un-lft-identity0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\cos \varepsilon \cdot \sin x - \color{blue}{1 \cdot \sin x}\right))_*\]
Applied distribute-rgt-out--0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \color{blue}{\left(\sin x \cdot \left(\cos \varepsilon - 1\right)\right)})_*\]
- Using strategy
rm Applied add-log-exp0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\sin x \cdot \color{blue}{\log \left(e^{\cos \varepsilon - 1}\right)}\right))_*\]
Final simplification0.4
\[\leadsto (\left(\cos x\right) \cdot \left(\sin \varepsilon\right) + \left(\sin x \cdot \log \left(e^{\cos \varepsilon - 1}\right)\right))_*\]
