\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 9.3 s
Input Error: 22.2
Output Error: 3.1
Log:
Profile: 🕒
\(\begin{cases} 100 \cdot \frac{(e^{(e^{\log_* (1 + \log_* (1 + \frac{i}{n}))} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}} & \text{when } i \le 539244.06f0 \\ 0 & \text{otherwise} \end{cases}\)

    if i < 539244.06f0

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      23.0
    2. Using strategy rm
      23.0
    3. Applied add-exp-log to get
      \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
      23.0
    4. Applied pow-exp to get
      \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
      23.0
    5. Applied expm1-def to get
      \[100 \cdot \frac{\color{red}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{(e^{\log \left(1 + \frac{i}{n}\right) \cdot n} - 1)^*}}{\frac{i}{n}}\]
      19.3
    6. Using strategy rm
      19.3
    7. Applied expm1-log1p-u to get
      \[100 \cdot \frac{(e^{\color{red}{\log \left(1 + \frac{i}{n}\right)} \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{\color{blue}{(e^{\log_* (1 + \log \left(1 + \frac{i}{n}\right))} - 1)^*} \cdot n} - 1)^*}{\frac{i}{n}}\]
      19.3
    8. Applied simplify to get
      \[100 \cdot \frac{(e^{(e^{\color{red}{\log_* (1 + \log \left(1 + \frac{i}{n}\right))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}} \leadsto 100 \cdot \frac{(e^{(e^{\color{blue}{\log_* (1 + \log_* (1 + \frac{i}{n}))}} - 1)^* \cdot n} - 1)^*}{\frac{i}{n}}\]
      4.1

    if 539244.06f0 < i

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      20.0
    2. Applied taylor to get
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot 0\]
      0
    3. Taylor expanded around 0 to get
      \[100 \cdot \color{red}{0} \leadsto 100 \cdot \color{blue}{0}\]
      0
    4. Applied simplify to get
      \[\color{red}{100 \cdot 0} \leadsto \color{blue}{0}\]
      0

  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))))