\[-\log \left(\frac{1}{x} - 1\right)\]
Test:
neg log
Bits:
128 bits
Bits error versus x
Time: 7.8 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(-\log \left((e^{\log_* (1 + \left(\frac{1}{x} - 1\right))} - 1)^*\right)\)
  1. Started with
    \[-\log \left(\frac{1}{x} - 1\right)\]
    0.1
  2. Using strategy rm
    0.1
  3. Applied expm1-log1p-u to get
    \[-\log \color{red}{\left(\frac{1}{x} - 1\right)} \leadsto -\log \color{blue}{\left((e^{\log_* (1 + \left(\frac{1}{x} - 1\right))} - 1)^*\right)}\]
    0.1
  4. Removed slow pow expressions

Original test:


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