\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 13.5 s
Input Error: 22.9
Output Error: 5.4
Log: ⚲
Profile: 🕒
\(100 \cdot \frac{\frac{(e^{\left(n + n\right) \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{e^{\log_* (1 + \frac{i}{n}) \cdot n} + 1}}{\frac{i}{n}}\)
  1. Started with
    \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    22.9
  2. Using strategy rm
    22.9
  3. Applied add-exp-log to get
    \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
    22.9
  4. Applied pow-exp to get
    \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
    22.9
  5. Applied simplify to get
    \[100 \cdot \frac{e^{\color{red}{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1}{\frac{i}{n}}\]
    19.5
  6. Using strategy rm
    19.5
  7. Applied flip-- to get
    \[100 \cdot \frac{\color{red}{e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\frac{{\left(e^{\log_* (1 + \frac{i}{n}) \cdot n}\right)}^2 - {1}^2}{e^{\log_* (1 + \frac{i}{n}) \cdot n} + 1}}}{\frac{i}{n}}\]
    19.5
  8. Applied simplify to get
    \[100 \cdot \frac{\frac{\color{red}{{\left(e^{\log_* (1 + \frac{i}{n}) \cdot n}\right)}^2 - {1}^2}}{e^{\log_* (1 + \frac{i}{n}) \cdot n} + 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\frac{\color{blue}{(e^{\left(n + n\right) \cdot \log_* (1 + \frac{i}{n})} - 1)^*}}{e^{\log_* (1 + \frac{i}{n}) \cdot n} + 1}}{\frac{i}{n}}\]
    5.4
  9. Removed slow pow expressions

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))))