if eps < -6.169079171368681e-49 or 2.0116360245016707e-26 < eps

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   29.9
2. Using strategy rm
   29.9
3. Applied tan-quot to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
   29.8
4. Applied tan-cotan to get
   \[\color{red}{\tan \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x} \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \frac{\sin x}{\cos x}\]
   29.8
5. Applied frac-sub to get
   \[\color{red}{\frac{1}{\cot \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x}} \leadsto \color{blue}{\frac{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x}}\]
   29.7
6. Applied simplify to get
   \[\frac{\color{red}{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   29.7
7. Using strategy rm
   29.7
8. Applied add-cube-cbrt to get
   \[\frac{\cos x - \color{red}{\cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\cos x - \color{blue}{{\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   29.6
9. Using strategy rm
   29.6
10. Applied flip-- to get
    \[\frac{\color{red}{\cos x - {\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\frac{{\left(\cos x\right)}^2 - {\left({\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3\right)}^2}{\cos x + {\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3}}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
    29.6
11. Applied simplify to get
    \[\frac{\frac{{\left(\cos x\right)}^2 - {\left({\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3\right)}^2}{\color{red}{\cos x + {\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3}}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\frac{{\left(\cos x\right)}^2 - {\left({\left(\sqrt[3]{\cot \left(x + \varepsilon\right) \cdot \sin x}\right)}^3\right)}^2}{\color{blue}{\cot \left(\varepsilon + x\right) \cdot \sin x + \cos x}}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
    29.6

if -6.169079171368681e-49 < eps < 2.0116360245016707e-26

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   45.3
2. Applied taylor to get
   \[\tan \left(x + \varepsilon\right) - \tan x \leadsto {x}^{3} \cdot {\varepsilon}^{4} + \left({x}^2 \cdot {\varepsilon}^{3} + \varepsilon\right)\]
   18.3
3. Taylor expanded around 0 to get
   \[\color{red}{{x}^{3} \cdot {\varepsilon}^{4} + \left({x}^2 \cdot {\varepsilon}^{3} + \varepsilon\right)} \leadsto \color{blue}{{x}^{3} \cdot {\varepsilon}^{4} + \left({x}^2 \cdot {\varepsilon}^{3} + \varepsilon\right)}\]
   18.3
4. Applied simplify to get
   \[\color{red}{{x}^{3} \cdot {\varepsilon}^{4} + \left({x}^2 \cdot {\varepsilon}^{3} + \varepsilon\right)} \leadsto \color{blue}{{\varepsilon}^3 \cdot \left(x \cdot x\right) + \left(\varepsilon + {x}^3 \cdot {\varepsilon}^{4}\right)}\]
   18.3
5. Applied simplify to get
   \[\color{red}{{\varepsilon}^3 \cdot \left(x \cdot x\right)} + \left(\varepsilon + {x}^3 \cdot {\varepsilon}^{4}\right) \leadsto \color{blue}{{x}^2 \cdot {\varepsilon}^3} + \left(\varepsilon + {x}^3 \cdot {\varepsilon}^{4}\right)\]
   18.3