\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
Test:
arccos
Bits:
128 bits
Bits error versus x
Time: 6.1 s
Input Error: 0.0
Output Error: 0.0
Log: ⚲
Profile: 🕒
\(2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{1 + x} - \frac{x}{1 + x}}\right)\)
  1. Started with
    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
    0.0
  2. Using strategy rm
    0.0
  3. Applied div-sub to get
    \[2 \cdot \tan^{-1} \left(\sqrt{\color{red}{\frac{1 - x}{1 + x}}}\right) \leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\frac{1}{1 + x} - \frac{x}{1 + x}}}\right)\]
    0.0

Original test:


(lambda ((x default))
  #:name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))