\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
Test:
Compound Interest
Bits:
128 bits
Bits error versus i
Bits error versus n
Time: 25.9 s
Input Error: 52.8
Output Error: 4.6
Log:
Profile: 🕒
\(\begin{cases} 100 \cdot \frac{e^{\log_* (1 + \frac{i}{n}) \cdot n} - 1}{\frac{i}{n}} & \text{when } i \le -5.345773354661283 \cdot 10^{-20} \\ \left(100 \cdot \frac{(i * \left(\frac{1}{2} \cdot i\right) + i)_*}{i}\right) \cdot n & \text{when } i \le 2.8990758295946513 \cdot 10^{-08} \\ \frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}} & \text{when } i \le 7.9197159869026 \cdot 10^{+209} \\ \frac{(e^{\frac{\log n - \log i}{n}} - 1)^*}{\frac{\frac{i}{100}}{n}} & \text{otherwise} \end{cases}\)

    if i < -5.345773354661283e-20

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      30.4
    2. Using strategy rm
      30.4
    3. Applied add-exp-log to get
      \[100 \cdot \frac{{\color{red}{\left(1 + \frac{i}{n}\right)}}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{{\color{blue}{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}}^{n} - 1}{\frac{i}{n}}\]
      30.4
    4. Applied pow-exp to get
      \[100 \cdot \frac{\color{red}{{\left(e^{\log \left(1 + \frac{i}{n}\right)}\right)}^{n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}}\]
      30.4
    5. Applied simplify to get
      \[100 \cdot \frac{e^{\color{red}{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\color{blue}{\log_* (1 + \frac{i}{n}) \cdot n}} - 1}{\frac{i}{n}}\]
      7.5

    if -5.345773354661283e-20 < i < 2.8990758295946513e-08

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      61.7
    2. Applied taylor to get
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
      61.0
    3. Taylor expanded around 0 to get
      \[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
      61.0
    4. Applied simplify to get
      \[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{\frac{i}{n}}}\]
      15.7
    5. Using strategy rm
      15.7
    6. Applied associate-/r/ to get
      \[(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{red}{\frac{100}{\frac{i}{n}}} \leadsto (i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \color{blue}{\left(\frac{100}{i} \cdot n\right)}\]
      15.9
    7. Applied associate-*r* to get
      \[\color{red}{(i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \left(\frac{100}{i} \cdot n\right)} \leadsto \color{blue}{\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{i}\right) \cdot n}\]
      0.5
    8. Applied taylor to get
      \[\left((i * \left(\frac{1}{2} \cdot i\right) + i)_* \cdot \frac{100}{i}\right) \cdot n \leadsto \left(100 \cdot \frac{(i * \left(\frac{1}{2} \cdot i\right) + i)_*}{i}\right) \cdot n\]
      0.0
    9. Taylor expanded around 0 to get
      \[\color{red}{\left(100 \cdot \frac{(i * \left(\frac{1}{2} \cdot i\right) + i)_*}{i}\right)} \cdot n \leadsto \color{blue}{\left(100 \cdot \frac{(i * \left(\frac{1}{2} \cdot i\right) + i)_*}{i}\right)} \cdot n\]
      0.0

    if 2.8990758295946513e-08 < i < 7.9197159869026e+209

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      36.0
    2. Using strategy rm
      36.0
    3. Applied associate-*r/ to get
      \[\color{red}{100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}} \leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}}\]
      36.0

    if 7.9197159869026e+209 < i

    1. Started with
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
      62.6
    2. Applied taylor to get
      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}\]
      29.9
    3. Taylor expanded around inf to get
      \[100 \cdot \frac{\color{red}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{e^{\frac{\log n - \log i}{n}} - 1}}{\frac{i}{n}}\]
      29.9
    4. Applied simplify to get
      \[\color{red}{100 \cdot \frac{e^{\frac{\log n - \log i}{n}} - 1}{\frac{i}{n}}} \leadsto \color{blue}{\frac{(e^{\frac{\log n - \log i}{n}} - 1)^*}{\frac{\frac{i}{100}}{n}}}\]
      1.7

  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))))