if eps < -1.5194640071230868e-06 or 131297377731453.28 < eps

1. Started with
   \[\cos \left(x + \varepsilon\right) - \cos x\]
   30.2
2. Using strategy rm
   30.2
3. Applied cos-sum to get
   \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
   0.9
4. Using strategy rm
   0.9
5. Applied sub-neg to get
   \[\color{red}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon + \left(-\sin x \cdot \sin \varepsilon\right)\right)} - \cos x\]
   0.9
6. Applied associate--l+ to get
   \[\color{red}{\left(\cos x \cdot \cos \varepsilon + \left(-\sin x \cdot \sin \varepsilon\right)\right) - \cos x} \leadsto \color{blue}{\cos x \cdot \cos \varepsilon + \left(\left(-\sin x \cdot \sin \varepsilon\right) - \cos x\right)}\]
   0.9

if -1.5194640071230868e-06 < eps < 131297377731453.28

1. Started with
   \[\cos \left(x + \varepsilon\right) - \cos x\]
   49.6
2. Using strategy rm
   49.6
3. Applied cos-sum to get
   \[\color{red}{\cos \left(x + \varepsilon\right)} - \cos x \leadsto \color{blue}{\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \sin \varepsilon\right)} - \cos x\]
   49.0
4. Using strategy rm
   49.0
5. Applied add-cube-cbrt to get
   \[\left(\cos x \cdot \cos \varepsilon - \sin x \cdot \color{red}{\sin \varepsilon}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \sin x \cdot \color{blue}{{\left(\sqrt[3]{\sin \varepsilon}\right)}^3}\right) - \cos x\]
   49.0
6. Applied add-cube-cbrt to get
   \[\left(\cos x \cdot \cos \varepsilon - \color{red}{\sin x} \cdot {\left(\sqrt[3]{\sin \varepsilon}\right)}^3\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{{\left(\sqrt[3]{\sin x}\right)}^3} \cdot {\left(\sqrt[3]{\sin \varepsilon}\right)}^3\right) - \cos x\]
   49.0
7. Applied cube-unprod to get
   \[\left(\cos x \cdot \cos \varepsilon - \color{red}{{\left(\sqrt[3]{\sin x}\right)}^3 \cdot {\left(\sqrt[3]{\sin \varepsilon}\right)}^3}\right) - \cos x \leadsto \left(\cos x \cdot \cos \varepsilon - \color{blue}{{\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin \varepsilon}\right)}^3}\right) - \cos x\]
   49.0
8. Applied taylor to get
   \[\left(\cos x \cdot \cos \varepsilon - {\left(\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin \varepsilon}\right)}^3\right) - \cos x \leadsto -\left(\frac{1}{2} \cdot {\varepsilon}^2 + {\left(\sqrt[3]{\sin \varepsilon} \cdot \sqrt[3]{\sin x}\right)}^3\right)\]
   1.1
9. Taylor expanded around 0 to get
   \[\color{red}{-\left(\frac{1}{2} \cdot {\varepsilon}^2 + {\left(\sqrt[3]{\sin \varepsilon} \cdot \sqrt[3]{\sin x}\right)}^3\right)} \leadsto \color{blue}{-\left(\frac{1}{2} \cdot {\varepsilon}^2 + {\left(\sqrt[3]{\sin \varepsilon} \cdot \sqrt[3]{\sin x}\right)}^3\right)}\]
   1.1
10. Applied simplify to get
    \[-\left(\frac{1}{2} \cdot {\varepsilon}^2 + {\left(\sqrt[3]{\sin \varepsilon} \cdot \sqrt[3]{\sin x}\right)}^3\right) \leadsto -(\left(\sin \varepsilon\right) * \left(\sin x\right) + \left(\left(\varepsilon \cdot \varepsilon\right) \cdot \frac{1}{2}\right))_*\]
    0.1

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11. Applied final simplification