\[\sqrt{\left(\sqrt{\tan^{-1} a}\right)^2 + b^2}^* - c \cdot a\]
Test:
(- (hypot (sqrt (atan a)) b) (* c a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 6.6 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\sqrt{\left({\left(\sqrt{\sqrt{\tan^{-1} a}}\right)}^2\right)^2 + b^2}^* - c \cdot a\)
  1. Started with
    \[\sqrt{\left(\sqrt{\tan^{-1} a}\right)^2 + b^2}^* - c \cdot a\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied add-sqr-sqrt to get
    \[\sqrt{\color{red}{\left(\sqrt{\tan^{-1} a}\right)}^2 + b^2}^* - c \cdot a \leadsto \sqrt{\color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1} a}}\right)}^2\right)}^2 + b^2}^* - c \cdot a\]
    0.1

Original test:


(lambda ((a default) (b default) (c default) (d default))
  #:name "(- (hypot (sqrt (atan a)) b) (* c a))"
  (- (hypot (sqrt (atan a)) b) (* c a)))