\[-\log \left(\frac{1}{x} - 1\right)\]
Test:
neg log
Bits:
128 bits
Bits error versus x
Time: 7.7 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(-\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\)
  1. Started with
    \[-\log \left(\frac{1}{x} - 1\right)\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied add-sqr-sqrt to get
    \[-\log \color{red}{\left(\frac{1}{x} - 1\right)} \leadsto -\log \color{blue}{\left({\left(\sqrt{\frac{1}{x} - 1}\right)}^2\right)}\]
    0.1
  4. Using strategy rm
    0.1
  5. Applied square-mult to get
    \[-\log \color{red}{\left({\left(\sqrt{\frac{1}{x} - 1}\right)}^2\right)} \leadsto -\log \color{blue}{\left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)}\]
    0.1
  6. Applied log-prod to get
    \[-\color{red}{\log \left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)} \leadsto -\color{blue}{\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)}\]
    0.1

Original test:


(lambda ((x default))
  #:name "neg log"
  (- (log (- (/ 1 x) 1))))