if eps < -0.7220817f0 or 0.00019073929f0 < eps

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   14.2
2. Using strategy rm
   14.2
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   0.4
4. Applied associate--l+ to get
   \[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
   0.4
5. Using strategy rm
   0.4
6. Applied add-cbrt-cube to get
   \[\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \color{red}{\sin \varepsilon} - \sin x\right) \leadsto \sin x \cdot \cos \varepsilon + \left(\cos x \cdot \color{blue}{\sqrt[3]{{\left(\sin \varepsilon\right)}^3}} - \sin x\right)\]
   0.4
7. Applied add-cbrt-cube to get
   \[\sin x \cdot \cos \varepsilon + \left(\color{red}{\cos x} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3} - \sin x\right) \leadsto \sin x \cdot \cos \varepsilon + \left(\color{blue}{\sqrt[3]{{\left(\cos x\right)}^3}} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3} - \sin x\right)\]
   0.4
8. Applied cbrt-unprod to get
   \[\sin x \cdot \cos \varepsilon + \left(\color{red}{\sqrt[3]{{\left(\cos x\right)}^3} \cdot \sqrt[3]{{\left(\sin \varepsilon\right)}^3}} - \sin x\right) \leadsto \sin x \cdot \cos \varepsilon + \left(\color{blue}{\sqrt[3]{{\left(\cos x\right)}^3 \cdot {\left(\sin \varepsilon\right)}^3}} - \sin x\right)\]
   0.5

if -0.7220817f0 < eps < 0.00019073929f0

1. Started with
   \[\sin \left(x + \varepsilon\right) - \sin x\]
   19.9
2. Using strategy rm
   19.9
3. Applied sin-sum to get
   \[\color{red}{\sin \left(x + \varepsilon\right)} - \sin x \leadsto \color{blue}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right)} - \sin x\]
   13.0
4. Applied associate--l+ to get
   \[\color{red}{\left(\sin x \cdot \cos \varepsilon + \cos x \cdot \sin \varepsilon\right) - \sin x} \leadsto \color{blue}{\sin x \cdot \cos \varepsilon + \left(\cos x \cdot \sin \varepsilon - \sin x\right)}\]
   13.0
5. Using strategy rm
   13.0
6. Applied add-cube-cbrt to get
   \[\color{red}{\sin x \cdot \cos \varepsilon} + \left(\cos x \cdot \sin \varepsilon - \sin x\right) \leadsto \color{blue}{{\left(\sqrt[3]{\sin x \cdot \cos \varepsilon}\right)}^3} + \left(\cos x \cdot \sin \varepsilon - \sin x\right)\]
   19.5
7. Applied taylor to get
   \[{\left(\sqrt[3]{\sin x \cdot \cos \varepsilon}\right)}^3 + \left(\cos x \cdot \sin \varepsilon - \sin x\right) \leadsto \left(\sin x - \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right) + \left(\cos x \cdot \sin \varepsilon - \sin x\right)\]
   12.6
8. Taylor expanded around 0 to get
   \[\color{red}{\left(\sin x - \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right)} + \left(\cos x \cdot \sin \varepsilon - \sin x\right) \leadsto \color{blue}{\left(\sin x - \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right)} + \left(\cos x \cdot \sin \varepsilon - \sin x\right)\]
   12.6
9. Applied simplify to get
   \[\left(\sin x - \frac{1}{2} \cdot \left({\varepsilon}^2 \cdot \sin x\right)\right) + \left(\cos x \cdot \sin \varepsilon - \sin x\right) \leadsto \left(\cos x \cdot \sin \varepsilon - \left(\sin x - \sin x\right)\right) - \left(\sin x \cdot \frac{1}{2}\right) \cdot \left(\varepsilon \cdot \varepsilon\right)\]
   0.1

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10. Applied final simplification
11. Applied simplify to get
    \[\color{red}{\left(\cos x \cdot \sin \varepsilon - \left(\sin x - \sin x\right)\right) - \left(\sin x \cdot \frac{1}{2}\right) \cdot \left(\varepsilon \cdot \varepsilon\right)} \leadsto \color{blue}{\sin \varepsilon \cdot \cos x - \varepsilon \cdot \left(\left(\frac{1}{2} \cdot \varepsilon\right) \cdot \sin x\right)}\]
    0.1