if x < 5.7961881794813385e-210 or 3.032522519349629e+77 < x < 5.53483801270981e+142

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   34.1
2. Using strategy rm
   34.1
3. Applied add-cbrt-cube to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}}\]
   34.2
4. Using strategy rm
   34.2
5. Applied add-cbrt-cube to get
   \[\sqrt[3]{{\color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}\right)}}^3}\]
   34.2

if 5.7961881794813385e-210 < x < 0.9995081705491148

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   61.3
2. Applied taylor to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - {x}^{\left(\frac{1}{n}\right)}\]
   28.5
3. Taylor expanded around inf to get
   \[\color{red}{\left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \color{blue}{\left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   28.5
4. Applied taylor to get
   \[\left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - {x}^{\left(\frac{1}{n}\right)} \leadsto \left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - e^{\frac{\log x}{n}}\]
   28.5
5. Taylor expanded around 0 to get
   \[\left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - \color{red}{e^{\frac{\log x}{n}}} \leadsto \left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - \color{blue}{e^{\frac{\log x}{n}}}\]
   28.5
6. Applied simplify to get
   \[\left(\left(1 + \frac{1}{n \cdot x}\right) - \frac{\log x}{n}\right) - e^{\frac{\log x}{n}} \leadsto \left(\left(\frac{1}{n \cdot x} + 1\right) - e^{\frac{\log x}{n}}\right) - \frac{\log x}{n}\]
   27.8

---

7. Applied final simplification

if 0.9995081705491148 < x < 3.032522519349629e+77

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   56.4
2. Using strategy rm
   56.4
3. Applied add-cbrt-cube to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}}\]
   56.4
4. Applied taylor to get
   \[\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3} \leadsto \sqrt[3]{{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}^3}\]
   39.1
5. Taylor expanded around inf to get
   \[\sqrt[3]{{\color{red}{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}}^3}\]
   39.1
6. Applied simplify to get
   \[\color{red}{\sqrt[3]{{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}^3}} \leadsto \color{blue}{\left(\frac{1}{n \cdot x} - \frac{\frac{\log x}{n \cdot x}}{n}\right) - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}}\]
   1.0

if 5.53483801270981e+142 < x < 1.7041594190127375e+179

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   43.9
2. Using strategy rm
   43.9
3. Applied add-cbrt-cube to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}}\]
   43.9
4. Applied taylor to get
   \[\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3} \leadsto \sqrt[3]{{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}^3}\]
   44.6
5. Taylor expanded around inf to get
   \[\sqrt[3]{{\color{red}{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}}^3}\]
   44.6
6. Applied simplify to get
   \[\color{red}{\sqrt[3]{{\left(\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\right)}^3}} \leadsto \color{blue}{\left(\frac{1}{n \cdot x} - \frac{\frac{\log x}{n \cdot x}}{n}\right) - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x}}\]
   30.1
7. Applied taylor to get
   \[\left(\frac{1}{n \cdot x} - \frac{\frac{\log x}{n \cdot x}}{n}\right) - \frac{\frac{\frac{1}{2}}{x}}{n \cdot x} \leadsto \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\]
   9.2
8. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}} \leadsto \color{blue}{\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}}\]
   9.2
9. Applied simplify to get
   \[\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2} \leadsto \left(\frac{\frac{1}{n}}{x} - \frac{\frac{1}{2}}{{x}^2 \cdot n}\right) + \frac{\log x}{x \cdot \left(n \cdot n\right)}\]
   8.5

---

10. Applied final simplification

if 1.7041594190127375e+179 < x

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   8.8
2. Using strategy rm
   8.8
3. Applied add-cbrt-cube to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}}\]
   8.8
4. Using strategy rm
   8.8
5. Applied add-cbrt-cube to get
   \[\sqrt[3]{{\color{red}{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\sqrt[3]{{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right)}^3}\right)}}^3}\]
   8.8