if eps < -1.2532876517739886e-27 or 339.99651990139387 < eps

1. Started with
   \[\cos \left(x + \varepsilon\right) - \cos x\]
   30.7
2. Using strategy rm
   30.7
3. Applied cos-sum to get
   \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
   2.5

if -1.2532876517739886e-27 < eps < 3.119849469787152e-113

1. Started with
   \[\cos \left(x + \varepsilon\right) - \cos x\]
   41.8
2. Applied taylor to get
   \[\cos \left(x + \varepsilon\right) - \cos x \leadsto \frac{1}{6} \cdot \left(\varepsilon \cdot {x}^{3}\right) - \left(\frac{1}{2} \cdot {\varepsilon}^2 + \varepsilon \cdot x\right)\]
   7.9
3. Taylor expanded around 0 to get
   \[\color{red}{\frac{1}{6} \cdot \left(\varepsilon \cdot {x}^{3}\right) - \left(\frac{1}{2} \cdot {\varepsilon}^2 + \varepsilon \cdot x\right)} \leadsto \color{blue}{\frac{1}{6} \cdot \left(\varepsilon \cdot {x}^{3}\right) - \left(\frac{1}{2} \cdot {\varepsilon}^2 + \varepsilon \cdot x\right)}\]
   7.9
4. Applied simplify to get
   \[\color{red}{\frac{1}{6} \cdot \left(\varepsilon \cdot {x}^{3}\right) - \left(\frac{1}{2} \cdot {\varepsilon}^2 + \varepsilon \cdot x\right)} \leadsto \color{blue}{\left(\varepsilon \cdot \frac{1}{6}\right) \cdot {x}^3 - \varepsilon \cdot \left(\varepsilon \cdot \frac{1}{2} + x\right)}\]
   7.9

if 3.119849469787152e-113 < eps < 339.99651990139387

1. Started with
   \[\cos \left(x + \varepsilon\right) - \cos x\]
   60.1
2. Using strategy rm
   60.1
3. Applied cos-sum to get
   \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
   58.3
4. Using strategy rm
   58.3
5. Applied add-cbrt-cube to get
   \[\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \color{red}{\sin \varepsilon}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \sin x \cdot \color{blue}{\sqrt[3]{{\left(\sin \varepsilon\right)}^3}}\right) - \cos x\]
   58.3
6. Applied add-cbrt-cube to get
   \[\left(\cos x \cdot \cos \varepsilon - \color{red}{\sin x} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{\sqrt[3]{{\left(\sin x\right)}^3}} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3}\right) - \cos x\]
   58.3
7. Applied cbrt-unprod to get
   \[\left(\cos x \cdot \cos \varepsilon - \color{red}{\sqrt[3]{{\left(\sin x\right)}^3} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3}}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{\sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}}\right) - \cos x\]
   58.3
8. Applied taylor to get
   \[\left(\cos x \cdot \cos \varepsilon - \sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}\right) - \cos x \leadsto -\left(\frac{1}{2} \cdot {\varepsilon}^2 + \sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}\right)\]
   4.8
9. Taylor expanded around 0 to get
   \[\color{red}{-\left(\frac{1}{2} \cdot {\varepsilon}^2 + \sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}\right)} \leadsto \color{blue}{-\left(\frac{1}{2} \cdot {\varepsilon}^2 + \sqrt[3]{{\left(\sin x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}\right)}\]
   4.8