\[\sqrt{\left(\sqrt{b^2 + a^2}^* \cdot \sin^{-1} \left(\sqrt{\left( 6.625427173769556 \cdot 10^{-183} \right)^2 + b^2}^*\right)\right)^2 + b^2}^*\]
Test:
(hypot (* (hypot b a) (asin (hypot 6.625427173769556e-183 b))) b)
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 5.2 s
Input Error: 0.0
Output Error: 0.0
Log: ⚲
Profile: 🕒
\(\sqrt{\left(\sqrt{b^2 + a^2}^* \cdot \log_* (1 + (e^{\sin^{-1} \left(\sqrt{\left( 6.625427173769556 \cdot 10^{-183} \right)^2 + b^2}^*\right)} - 1)^*)\right)^2 + b^2}^*\)
  1. Started with
    \[\sqrt{\left(\sqrt{b^2 + a^2}^* \cdot \sin^{-1} \left(\sqrt{\left( 6.625427173769556 \cdot 10^{-183} \right)^2 + b^2}^*\right)\right)^2 + b^2}^*\]
    0.0
  2. Using strategy rm
    0.0
  3. Applied log1p-expm1-u to get
    \[\sqrt{\left(\sqrt{b^2 + a^2}^* \cdot \color{red}{\sin^{-1} \left(\sqrt{\left( 6.625427173769556 \cdot 10^{-183} \right)^2 + b^2}^*\right)}\right)^2 + b^2}^* \leadsto \sqrt{\left(\sqrt{b^2 + a^2}^* \cdot \color{blue}{\log_* (1 + (e^{\sin^{-1} \left(\sqrt{\left( 6.625427173769556 \cdot 10^{-183} \right)^2 + b^2}^*\right)} - 1)^*)}\right)^2 + b^2}^*\]
    0.0

Original test:


(lambda ((a default) (b default))
  #:name "(hypot (* (hypot b a) (asin (hypot 6.625427173769556e-183 b))) b)"
  (hypot (* (hypot b a) (asin (hypot 6.625427173769556e-183 b))) b))