\[\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}\]
Test:
(sqrt (/ -2.839573235346269e-37 (* (* a b) (fabs a))))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 5.5 s
Input Error: 9.6
Output Error: 8.8
Log: ⚲
Profile: 🕒
\(\sqrt{{\left(\sqrt[3]{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}\right)}^3}\)
  1. Started with
    \[\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}}\]
    9.6
  2. Applied taylor to get
    \[\sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{\left(a \cdot b\right) \cdot \left|a\right|}} \leadsto \sqrt{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}\]
    8.7
  3. Taylor expanded around 0 to get
    \[\sqrt{\color{red}{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}} \leadsto \sqrt{\color{blue}{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}}\]
    8.7
  4. Using strategy rm
    8.7
  5. Applied add-cube-cbrt to get
    \[\sqrt{\color{red}{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}} \leadsto \sqrt{\color{blue}{{\left(\sqrt[3]{\frac{-2.839573235346269 \cdot 10^{-37}}{b \cdot \left(\left|a\right| \cdot a\right)}}\right)}^3}}\]
    8.8

Original test:


(lambda ((a default) (b default))
  #:name "(sqrt (/ -2.839573235346269e-37 (* (* a b) (fabs a))))"
  (sqrt (/ -2.839573235346269e-37 (* (* a b) (fabs a)))))