if eps < -3.452204119992624e-20 or 10651329494355302.0 < eps

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   29.7
2. Using strategy rm
   29.7
3. Applied tan-quot to get
   \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{\frac{\sin \left(x + \varepsilon\right)}{\cos \left(x + \varepsilon\right)}} - \tan x\]
   29.7
4. Using strategy rm
   29.7
5. Applied sin-sum to get
   \[\frac{\color{red}{\sin \left(x + \varepsilon\right)}}{\cos \left(x + \varepsilon\right)} - \tan x \leadsto \frac{\color{blue}{\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon}}{\cos \left(x + \varepsilon\right)} - \tan x\]
   27.8

if -3.452204119992624e-20 < eps < 10651329494355302.0

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   45.2
2. Applied taylor to get
   \[\tan \left(x + \varepsilon\right) - \tan x \leadsto \varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)\]
   22.2
3. Taylor expanded around 0 to get
   \[\color{red}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)} \leadsto \color{blue}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)}\]
   22.2
4. Applied taylor to get
   \[\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right) \leadsto \varepsilon\]
   0
5. Taylor expanded around 0 to get
   \[\color{red}{\varepsilon} \leadsto \color{blue}{\varepsilon}\]
   0
6. Applied simplify to get
   \[\varepsilon \leadsto \varepsilon\]
   0

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7. Applied final simplification