\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 5.6 s
Input Error: 30.0
Output Error: 0.5
Log: ⚲
Profile: 🕒
\(\left(i \cdot 50 + 100\right) \cdot n\)
  1. Started with
    \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    30.0
  2. Applied taylor to get
    \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
    21.3
  3. Taylor expanded around 0 to get
    \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
    21.3
  4. Applied simplify to get
    \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
    7.8
  5. Applied taylor to get
    \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}} \leadsto 100 \cdot n + 50 \cdot \left(n \cdot i\right)\]
    0.2
  6. Taylor expanded around 0 to get
    \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{100 \cdot n + 50 \cdot \left(n \cdot i\right)}\]
    0.2
  7. Applied simplify to get
    \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{\left(i \cdot 50 + 100\right) \cdot n}\]
    0.5

Original test:


(lambda ((i default) (n default))
  #:name "Compound Interest"
  (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
  #:target
  (* 100 (/ (- (exp (* n (if (= (+ 1 (/ i n)) 1) (/ i n) (/ (* (/ i n) (log (+ 1 (/ i n)))) (- (+ (/ i n) 1) 1))))) 1) (/ i n))))