\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 20.4 s
Input Error: 51.0
Output Error: 9.4
Log: ⚲
Profile: 🕒
\(\begin{cases} 100 \cdot \frac{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}{\frac{i}{n}} & \text{when } i \le -0.050929361139636635 \\ \left(i \cdot 50 + 100\right) \cdot n & \text{when } i \le 15879525.552212397 \\ \left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot n & \text{otherwise} \end{cases}\)

    if i < -0.050929361139636635

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      28.1
    2. Using strategy rm
      28.1
    3. Applied add-log-exp to get
      \[100 \cdot \frac{\color{red}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\log \left(e^{{\left(1 + \frac{i}{n}\right)}^{n} - 1}\right)}}{\frac{i}{n}}\]
      28.1

    if -0.050929361139636635 < i < 15879525.552212397

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      61.7
    2. Applied taylor to get
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
      58.9
    3. Taylor expanded around 0 to get
      \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
      58.9
    4. Applied simplify to get
      \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
      14.4
    5. Applied taylor to get
      \[\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}} \leadsto 100 \cdot n + 50 \cdot \left(n \cdot i\right)\]
      0.0
    6. Taylor expanded around 0 to get
      \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{100 \cdot n + 50 \cdot \left(n \cdot i\right)}\]
      0.0
    7. Applied simplify to get
      \[\color{red}{100 \cdot n + 50 \cdot \left(n \cdot i\right)} \leadsto \color{blue}{\left(i \cdot 50 + 100\right) \cdot n}\]
      0.0

    if 15879525.552212397 < i

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      29.8
    2. Using strategy rm
      29.8
    3. Applied associate-/r/ to get
      \[100 \cdot \color{red}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)}\]
      29.8
    4. Applied associate-*r* to get
      \[\color{red}{100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \leadsto \color{blue}{\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot n}\]
      29.8
  1. 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))))