if eps < -4.9196116f-11

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   14.6
2. Using strategy rm
   14.6
3. Applied tan-cotan to get
   \[\color{red}{\tan \left(x + \varepsilon\right)} - \tan x \leadsto \color{blue}{\frac{1}{\cot \left(x + \varepsilon\right)}} - \tan x\]
   14.4

if -4.9196116f-11 < eps < 8.455499f-07

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   20.7
2. Applied taylor to get
   \[\tan \left(x + \varepsilon\right) - \tan x \leadsto \varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)\]
   9.6
3. Taylor expanded around 0 to get
   \[\color{red}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)} \leadsto \color{blue}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)}\]
   9.6
4. Applied simplify to get
   \[\color{red}{\varepsilon + \left({\varepsilon}^{3} \cdot {x}^2 + {\varepsilon}^{4} \cdot {x}^{3}\right)} \leadsto \color{blue}{\left(\varepsilon + \left(x \cdot x\right) \cdot {\varepsilon}^3\right) + {\varepsilon}^{4} \cdot {x}^3}\]
   9.6

if 8.455499f-07 < eps

1. Started with
   \[\tan \left(x + \varepsilon\right) - \tan x\]
   14.4
2. Using strategy rm
   14.4
3. Applied tan-quot to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\tan x} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\frac{\sin x}{\cos x}}\]
   14.3
4. Using strategy rm
   14.3
5. Applied div-inv to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\frac{\sin x}{\cos x}} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{\sin x \cdot \frac{1}{\cos x}}\]
   14.3
6. Using strategy rm
   14.3
7. Applied add-cube-cbrt to get
   \[\tan \left(x + \varepsilon\right) - \sin x \cdot \color{red}{\frac{1}{\cos x}} \leadsto \tan \left(x + \varepsilon\right) - \sin x \cdot \color{blue}{{\left(\sqrt[3]{\frac{1}{\cos x}}\right)}^3}\]
   14.3
8. Applied add-cube-cbrt to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{\sin x} \cdot {\left(\sqrt[3]{\frac{1}{\cos x}}\right)}^3 \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{{\left(\sqrt[3]{\sin x}\right)}^3} \cdot {\left(\sqrt[3]{\frac{1}{\cos x}}\right)}^3\]
   14.3
9. Applied cube-unprod to get
   \[\tan \left(x + \varepsilon\right) - \color{red}{{\left(\sqrt[3]{\sin x}\right)}^3 \cdot {\left(\sqrt[3]{\frac{1}{\cos x}}\right)}^3} \leadsto \tan \left(x + \varepsilon\right) - \color{blue}{{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\frac{1}{\cos x}}\right)}^3}\]
   14.3