\[\log \left(1 + x\right)\]
Test:
ln(1 + x)
Bits:
128 bits
Bits error versus x
Time: 3.6 s
Input Error: 59.8
Output Error: 0.1
Log: ⚲
Profile: 🕒
\(\left(\frac{1}{3} \cdot x - \frac{1}{2}\right) \cdot {x}^2 + x\)
  1. Started with
    \[\log \left(1 + x\right)\]
    59.8
  2. Applied taylor to get
    \[\log \left(1 + x\right) \leadsto \left(\frac{1}{3} \cdot {x}^{3} + x\right) - \frac{1}{2} \cdot {x}^2\]
    0.1
  3. Taylor expanded around 0 to get
    \[\color{red}{\left(\frac{1}{3} \cdot {x}^{3} + x\right) - \frac{1}{2} \cdot {x}^2} \leadsto \color{blue}{\left(\frac{1}{3} \cdot {x}^{3} + x\right) - \frac{1}{2} \cdot {x}^2}\]
    0.1
  4. Applied simplify to get
    \[\color{red}{\left(\frac{1}{3} \cdot {x}^{3} + x\right) - \frac{1}{2} \cdot {x}^2} \leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{3} - \frac{1}{2}\right) + x}\]
    0.1
  5. Applied simplify to get
    \[\color{red}{\left(x \cdot x\right) \cdot \left(x \cdot \frac{1}{3} - \frac{1}{2}\right)} + x \leadsto \color{blue}{\left(\frac{1}{3} \cdot x - \frac{1}{2}\right) \cdot {x}^2} + x\]
    0.1

Original test:


(lambda ((x default))
  #:name "ln(1 + x)"
  (log (+ 1 x))
  #:target
  (if (= (+ 1 x) 1) x (/ (* x (log (+ 1 x))) (- (+ 1 x) 1))))