\[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
Test:
NMSE example 3.10
Bits:
128 bits
Bits error versus x
Time: 9.3 s
Input Error: 60.9
Output Error: 0.0
Log: ⚲
Profile: 🕒
\(\frac{1}{\frac{\log_* (1 + x)}{\log_* (1 + \left(-x\right))}}\)
  1. Started with
    \[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
    60.9
  2. Applied simplify to get
    \[\color{red}{\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}} \leadsto \color{blue}{\frac{\log \left(1 - x\right)}{\log_* (1 + x)}}\]
    60.0
  3. Using strategy rm
    60.0
  4. Applied sub-neg to get
    \[\frac{\log \color{red}{\left(1 - x\right)}}{\log_* (1 + x)} \leadsto \frac{\log \color{blue}{\left(1 + \left(-x\right)\right)}}{\log_* (1 + x)}\]
    60.0
  5. Applied log1p-def to get
    \[\frac{\color{red}{\log \left(1 + \left(-x\right)\right)}}{\log_* (1 + x)} \leadsto \frac{\color{blue}{\log_* (1 + \left(-x\right))}}{\log_* (1 + x)}\]
    0.0
  6. Using strategy rm
    0.0
  7. Applied clear-num to get
    \[\color{red}{\frac{\log_* (1 + \left(-x\right))}{\log_* (1 + x)}} \leadsto \color{blue}{\frac{1}{\frac{\log_* (1 + x)}{\log_* (1 + \left(-x\right))}}}\]
    0.0

Original test:


(lambda ((x default))
  #:name "NMSE example 3.10"
  (/ (log (- 1 x)) (log (+ 1 x)))
  #:target
  (- (+ (+ (+ 1 x) (/ (sqr x) 2)) (* 5/12 (pow x 3)))))