if b < 7.845028771220709e+223

1. Started with
   \[\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}\]
   25.4
2. Using strategy rm
   25.4
3. Applied associate-/r* to get
   \[\sqrt{\color{red}{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}} \leadsto \sqrt{\color{blue}{\frac{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}}{\left|a\right|}}}\]
   23.9
4. Using strategy rm
   23.9
5. Applied sqrt-div to get
   \[\color{red}{\sqrt{\frac{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}}{\left|a\right|}}} \leadsto \color{blue}{\frac{\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}}}{\sqrt{\left|a\right|}}}\]
   8.9
6. Using strategy rm
   8.9
7. Applied expm1-log1p-u to get
   \[\frac{\color{red}{\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}}}}{\sqrt{\left|a\right|}} \leadsto \frac{\color{blue}{(e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}})} - 1)^*}}{\sqrt{\left|a\right|}}\]
   10.3
8. Applied taylor to get
   \[\frac{(e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{a \cdot b}})} - 1)^*}{\sqrt{\left|a\right|}} \leadsto \sqrt{\frac{1}{\left|a\right|}} \cdot (e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot a}})} - 1)^*\]
   10.3
9. Taylor expanded around 0 to get
   \[\color{red}{\sqrt{\frac{1}{\left|a\right|}} \cdot (e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot a}})} - 1)^*} \leadsto \color{blue}{\sqrt{\frac{1}{\left|a\right|}} \cdot (e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot a}})} - 1)^*}\]
   10.3
10. Applied simplify to get
    \[\sqrt{\frac{1}{\left|a\right|}} \cdot (e^{\log_* (1 + \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot a}})} - 1)^* \leadsto \sqrt{\frac{\frac{-2.839573235346269 \cdot 10^{-37}}{b}}{a}} \cdot \sqrt{\frac{1}{\left|a\right|}}\]
    8.3

---

11. Applied final simplification

if 7.845028771220709e+223 < b

1. Started with
   \[\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}\]
   14.7
2. Using strategy rm
   14.7
3. Applied clear-num to get
   \[\sqrt{\color{red}{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}} \leadsto \sqrt{\color{blue}{\frac{1}{\frac{\left(a \cdot b\right) \cdot \left|a\right|}{-2.839573235346269 \cdot 10^{-37}}}}}\]
   15.2