\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 11.6 s
Input Error: 23.1
Output Error: 0.6
Log:
Profile: 🕒
\(\begin{cases} \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{\frac{i}{n}}{100}} & \text{when } i \le -1.8225532f-14 \\ (100 * \left((\left(i \cdot i\right) * \left(n \cdot \frac{1}{6}\right) + n)_*\right) + \left(\left(100 \cdot i\right) \cdot \left(n \cdot \frac{1}{2}\right)\right))_* & \text{when } i \le 6.803177f-14 \\ \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{\frac{i}{n}}{100}} & \text{when } i \le 1.466941f+16 \\ 0 & \text{otherwise} \end{cases}\)

    if i < -1.8225532f-14 or 6.803177f-14 < i < 1.466941f+16

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      17.4
    2. Using strategy rm
      17.4
    3. Applied add-exp-log to get
      \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
      17.4
    4. Applied pow-exp to get
      \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
      17.4
    5. Applied simplify to get
      \[100 \cdot \frac{e^{\color{red}{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1}{\frac{i}{n}}\]
      10.5
    6. Applied taylor to get
      \[100 \cdot \frac{e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}}\]
      10.5
    7. Taylor expanded around 0 to get
      \[100 \cdot \frac{e^{\color{red}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{n \cdot \log_* (1 + \frac{i}{n})}} - 1}{\frac{i}{n}}\]
      10.5
    8. Applied simplify to get
      \[100 \cdot \frac{e^{n \cdot \log_* (1 + \frac{i}{n})} - 1}{\frac{i}{n}} \leadsto \frac{(e^{n \cdot \log_* (1 + \frac{i}{n})} - 1)^*}{\frac{\frac{i}{n}}{100}}\]
      1.5

    9. Applied final simplification

    if -1.8225532f-14 < i < 6.803177f-14

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      29.7
    2. Using strategy rm
      29.7
    3. Applied div-sub to get
      \[100 \cdot \color{red}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \frac{1}{\frac{i}{n}}\right)}\]
      30.0
    4. Applied simplify to get
      \[100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \color{red}{\frac{1}{\frac{i}{n}}}\right) \leadsto 100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \color{blue}{\frac{n}{i}}\right)\]
      30.0
    5. Applied taylor to get
      \[100 \cdot \left(\frac{{\left(1 + \frac{i}{n}\right)}^{n}}{\frac{i}{n}} - \frac{n}{i}\right) \leadsto 100 \cdot \left(n + \left(\frac{1}{6} \cdot \left(n \cdot {i}^2\right) + \frac{1}{2} \cdot \left(n \cdot i\right)\right)\right)\]
      0.0
    6. Taylor expanded around 0 to get
      \[100 \cdot \color{red}{\left(n + \left(\frac{1}{6} \cdot \left(n \cdot {i}^2\right) + \frac{1}{2} \cdot \left(n \cdot i\right)\right)\right)} \leadsto 100 \cdot \color{blue}{\left(n + \left(\frac{1}{6} \cdot \left(n \cdot {i}^2\right) + \frac{1}{2} \cdot \left(n \cdot i\right)\right)\right)}\]
      0.0
    7. Applied simplify to get
      \[100 \cdot \left(n + \left(\frac{1}{6} \cdot \left(n \cdot {i}^2\right) + \frac{1}{2} \cdot \left(n \cdot i\right)\right)\right) \leadsto (100 * \left((\left(i \cdot i\right) * \left(n \cdot \frac{1}{6}\right) + n)_*\right) + \left(\left(100 \cdot i\right) \cdot \left(n \cdot \frac{1}{2}\right)\right))_*\]
      0.0

    8. Applied final simplification

    if 1.466941f+16 < i

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      21.9
    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))))