if eps < -3.484092632009674e-67

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   31.1
2. Using strategy rm
   31.1
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   5.3
4. Using strategy rm
   5.3
5. Applied add-cbrt-cube to get
   \[\left(\sin x \cdot \color{red}{\cos \varepsilon} + \cos x \cdot \sin \varepsilon\right) - \sin x \leadsto \left(\sin x \cdot \color{blue}{\sqrt[3]{{\left(\cos \varepsilon\right)}^3}} + \cos x \cdot \sin \varepsilon\right) - \sin x\]
   5.4
6. Applied add-cbrt-cube to get
   \[\left(\color{red}{\sin x} \cdot \sqrt[3]{{\left(\cos \varepsilon\right)}^3} + \cos x \cdot \sin \varepsilon\right) - \sin x \leadsto \left(\color{blue}{\sqrt[3]{{\left(\sin x\right)}^3}} \cdot \sqrt[3]{{\left(\cos \varepsilon\right)}^3} + \cos x \cdot \sin \varepsilon\right) - \sin x\]
   5.4
7. Applied cbrt-unprod to get
   \[\left(\color{red}{\sqrt[3]{{\left(\sin x\right)}^3} \cdot \sqrt[3]{{\left(\cos \varepsilon\right)}^3}} + \cos x \cdot \sin \varepsilon\right) - \sin x \leadsto \left(\color{blue}{\sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\cos \varepsilon\right)}^3}} + \cos x \cdot \sin \varepsilon\right) - \sin x\]
   5.3

if -3.484092632009674e-67 < eps < 2.1094196219887136e-42

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   45.8
2. Applied taylor to get
   \[\sin \left(x + \varepsilon\right) - \sin x \leadsto \varepsilon - \left(\frac{1}{2} \cdot \left(\varepsilon \cdot {x}^2\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot x\right)\right)\]
   10.1
3. Taylor expanded around 0 to get
   \[\color{red}{\varepsilon - \left(\frac{1}{2} \cdot \left(\varepsilon \cdot {x}^2\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot x\right)\right)} \leadsto \color{blue}{\varepsilon - \left(\frac{1}{2} \cdot \left(\varepsilon \cdot {x}^2\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot x\right)\right)}\]
   10.1
4. Applied simplify to get
   \[\color{red}{\varepsilon - \left(\frac{1}{2} \cdot \left(\varepsilon \cdot {x}^2\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot x\right)\right)} \leadsto \color{blue}{\varepsilon - \frac{1}{2} \cdot \left(\left(\varepsilon + x\right) \cdot \left(x \cdot \varepsilon\right)\right)}\]
   0.1

if 2.1094196219887136e-42 < eps

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   29.0
2. Using strategy rm
   29.0
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   3.2
4. Using strategy rm
   3.2
5. Applied add-log-exp to get
   \[\left(\color{red}{\sin x \cdot \cos \varepsilon} + \cos x \cdot \sin \varepsilon\right) - \sin x \leadsto \left(\color{blue}{\log \left(e^{\sin x \cdot \cos \varepsilon}\right)} + \cos x \cdot \sin \varepsilon\right) - \sin x\]
   3.4