\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 9.5 s
Input Error: 22.6
Output Error: 5.2
Log: ⚲
Profile: 🕒
\(100 \cdot \frac{(e^{(e^{\log_* (1 + \log_* (1 + \frac{i}{n}))} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}}\)
  1. Started with
    \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
    22.6
  2. Using strategy rm
    22.6
  3. Applied add-exp-log to get
    \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
    22.6
  4. Applied pow-exp to get
    \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
    22.6
  5. Applied expm1-def to get
    \[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
    19.0
  6. Using strategy rm
    19.0
  7. Applied expm1-log1p-u to get
    \[100 \cdot \frac{(e^{\color{red}{\log \left(1 + \frac{i}{n}\right)} \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{\color{blue}{(e^{\log_* (1 + \log \left(1 + \frac{i}{n}\right))} - 1)^*} \cdot n} - 1)^*}{\frac{i}{n}}\]
    19.1
  8. Applied simplify to get
    \[100 \cdot \frac{(e^{(e^{\color{red}{\log_* (1 + \log \left(1 + \frac{i}{n}\right))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{(e^{\color{blue}{\log_* (1 + \log_* (1 + \frac{i}{n}))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}}\]
    5.2
  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))))