if eps < -1.5194640071230868e-06 or 6.019887702751239e-12 < eps

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   29.6
2. Using strategy rm
   29.6
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   0.7
4. Applied associate--l+ to get
   \[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
   0.7
5. Using strategy rm
   0.7
6. Applied add-log-exp to get
   \[\color{red}{\sin x \cdot \cos \varepsilon} + \left(\cos x \cdot \sin \varepsilon - \sin x\right) \leadsto \color{blue}{\log \left(e^{\sin x \cdot \cos \varepsilon}\right)} + \left(\cos x \cdot \sin \varepsilon - \sin x\right)\]
   0.8

if -1.5194640071230868e-06 < eps < 6.019887702751239e-12

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   44.7
2. Using strategy rm
   44.7
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   44.4
4. Applied associate--l+ to get
   \[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
   44.4
5. Using strategy rm
   44.4
6. Applied add-cube-cbrt to get
   \[\color{red}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\right)}^3}\]
   44.8
7. Applied simplify to get
   \[{\color{red}{\left(\sqrt[3]{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\right)}}^3 \leadsto {\color{blue}{\left(\sqrt[3]{(\left(\sin x\right) * \left(\cos \varepsilon\right) + \left(\sin \varepsilon \cdot \cos x - \sin x\right))_*}\right)}}^3\]
   44.8
8. Using strategy rm
   44.8
9. Applied fma-udef to get
   \[{\left(\sqrt[3]{\color{red}{(\left(\sin x\right) * \left(\cos \varepsilon\right) + \left(\sin \varepsilon \cdot \cos x - \sin x\right))_*}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\sin x \cdot \cos \varepsilon + \left(\sin \varepsilon \cdot \cos x - \sin x\right)}}\right)}^3\]
   44.8
10. Applied taylor to get
    \[{\left(\sqrt[3]{\sin x \cdot \cos \varepsilon + \left(\sin \varepsilon \cdot \cos x - \sin x\right)}\right)}^3 \leadsto \varepsilon \cdot \cos x - \left(\frac{1}{6} \cdot \left({\varepsilon}^{3} \cdot \cos x\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right)\]
    0.1
11. Taylor expanded around 0 to get
    \[\color{red}{\varepsilon \cdot \cos x - \left(\frac{1}{6} \cdot \left({\varepsilon}^{3} \cdot \cos x\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right)} \leadsto \color{blue}{\varepsilon \cdot \cos x - \left(\frac{1}{6} \cdot \left({\varepsilon}^{3} \cdot \cos x\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right)}\]
    0.1
12. Applied simplify to get
    \[\varepsilon \cdot \cos x - \left(\frac{1}{6} \cdot \left({\varepsilon}^{3} \cdot \cos x\right) + \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right) \leadsto \cos x \cdot \left(\varepsilon - \frac{1}{6} \cdot {\varepsilon}^3\right) - \left(\frac{1}{2} \cdot \sin x\right) \cdot {\varepsilon}^2\]
    0.1

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13. Applied final simplification