if eps < -1.5175483707585876e-61

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   29.4
2. Using strategy rm
   29.4
3. Applied tan-quot to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
   29.3
4. Applied tan-cotan to get
   \[\color{red}{\tan \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x} \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \frac{\sin x}{\cos x}\]
   29.3
5. Applied frac-sub to get
   \[\color{red}{\frac{1}{\cot \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x}} \leadsto \color{blue}{\frac{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x}}\]
   29.3
6. Applied simplify to get
   \[\frac{\color{red}{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   29.3
7. Using strategy rm
   29.3
8. Applied add-cbrt-cube to get
   \[\frac{\cos x - \color{red}{\cot \left(\varepsilon + x\right)} \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\cos x - \color{blue}{\sqrt[3]{{\left(\cot \left(\varepsilon + x\right)\right)}^3}} \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   29.3

if -1.5175483707585876e-61 < eps < 639.2159073015437

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   45.7
2. Applied taylor to get
   \[\tan \left(x + \varepsilon\right) - \tan x \leadsto \varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)\]
   17.8
3. Taylor expanded around 0 to get
   \[\color{red}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)} \leadsto \color{blue}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)}\]
   17.8

if 639.2159073015437 < eps

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   30.6
2. Using strategy rm
   30.6
3. Applied tan-quot to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
   30.4
4. Applied tan-cotan to get
   \[\color{red}{\tan \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x} \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \frac{\sin x}{\cos x}\]
   30.5
5. Applied frac-sub to get
   \[\color{red}{\frac{1}{\cot \left(x + \varepsilon\right)} - \frac{\sin x}{\cos x}} \leadsto \color{blue}{\frac{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}{\cot \left(x + \varepsilon\right) \cdot \cos x}}\]
   30.5
6. Applied simplify to get
   \[\frac{\color{red}{1 \cdot \cos x - \cot \left(x + \varepsilon\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   30.5
7. Using strategy rm
   30.5
8. Applied log1p-expm1-u to get
   \[\frac{\color{red}{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x}}{\cot \left(x + \varepsilon\right) \cdot \cos x} \leadsto \frac{\color{blue}{\log_* (1 + (e^{\cos x - \cot \left(\varepsilon + x\right) \cdot \sin x} - 1)^*)}}{\cot \left(x + \varepsilon\right) \cdot \cos x}\]
   30.5