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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \le -4.943788105127082 \cdot 10^{+295}:\\ \;\;\;\;\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}\\ \mathbf{if}\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \le -3.185864819664644 \cdot 10^{-208}:\\ \;\;\;\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right)\\ \mathbf{if}\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \le 5.601788448279894 \cdot 10^{-249}:\\ \;\;\;\;\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)\\ \mathbf{if}\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \le 1.5893655743611886 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)\\ \end{array}\]

Original	46.8
Target	46.8
Herbie	16.4

Derivation

Split input into 5 regimes
if (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < -4.943788105127082e+295
1. Initial program 15.9
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Using strategy rm
3. Applied associate-*r/15.9
  \[\leadsto \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}}\]
if -4.943788105127082e+295 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < -3.185864819664644e-208
1. Initial program 56.7
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 28.4
  \[\leadsto 100 \cdot \frac{\color{blue}{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}}{\frac{i}{n}}\]
3. Using strategy rm
4. Applied div-inv28.4
  \[\leadsto 100 \cdot \frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{\color{blue}{i \cdot \frac{1}{n}}}\]
5. Applied associate-/r*13.9
  \[\leadsto 100 \cdot \color{blue}{\frac{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}{\frac{1}{n}}}\]
6. Using strategy rm
7. Applied *-un-lft-identity13.9
  \[\leadsto 100 \cdot \frac{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}{\color{blue}{1 \cdot \frac{1}{n}}}\]
8. Applied add-cube-cbrt13.9
  \[\leadsto 100 \cdot \frac{\color{blue}{\left(\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}} \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}\right) \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}}{1 \cdot \frac{1}{n}}\]
9. Applied times-frac13.9
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}} \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{1} \cdot \frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{\frac{1}{n}}\right)}\]
10. Applied simplify13.9
  \[\leadsto 100 \cdot \left(\color{blue}{\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)}\right)} \cdot \frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{\frac{1}{n}}\right)\]
11. Applied simplify13.8
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)}\right) \cdot \color{blue}{\left(n \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(1 + \frac{1}{2} \cdot i\right) + \left(i \cdot i\right) \cdot \frac{1}{6}\right)}\right)}\right)\]
12. Taylor expanded around 0 13.9
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \color{blue}{\left(\frac{1}{6} \cdot i + \left(\frac{1}{36} \cdot {i}^{2} + 1\right)\right)}\right) \cdot \left(n \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(1 + \frac{1}{2} \cdot i\right) + \left(i \cdot i\right) \cdot \frac{1}{6}\right)}\right)\right)\]
13. Applied simplify13.9
  \[\leadsto \color{blue}{\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right)}\]
if -3.185864819664644e-208 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < 5.601788448279894e-249
1. Initial program 20.8
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around inf 48.5
  \[\leadsto 100 \cdot \color{blue}{\frac{\left(e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n} - 1\right) \cdot n}{i}}\]
3. Applied simplify21.4
  \[\leadsto \color{blue}{\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}\]
if 5.601788448279894e-249 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < 1.5893655743611886e+306
1. Initial program 56.7
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around 0 28.3
  \[\leadsto 100 \cdot \frac{\color{blue}{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}}{\frac{i}{n}}\]
3. Using strategy rm
4. Applied div-inv28.4
  \[\leadsto 100 \cdot \frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{\color{blue}{i \cdot \frac{1}{n}}}\]
5. Applied associate-/r*14.1
  \[\leadsto 100 \cdot \color{blue}{\frac{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}{\frac{1}{n}}}\]
6. Using strategy rm
7. Applied *-un-lft-identity14.1
  \[\leadsto 100 \cdot \frac{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}{\color{blue}{1 \cdot \frac{1}{n}}}\]
8. Applied add-cube-cbrt14.1
  \[\leadsto 100 \cdot \frac{\color{blue}{\left(\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}} \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}\right) \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}}{1 \cdot \frac{1}{n}}\]
9. Applied times-frac14.1
  \[\leadsto 100 \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}} \cdot \sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{1} \cdot \frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{\frac{1}{n}}\right)}\]
10. Applied simplify14.1
  \[\leadsto 100 \cdot \left(\color{blue}{\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)}\right)} \cdot \frac{\sqrt[3]{\frac{\frac{1}{6} \cdot {i}^{3} + \left(\frac{1}{2} \cdot {i}^{2} + i\right)}{i}}}{\frac{1}{n}}\right)\]
11. Applied simplify14.0
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)}\right) \cdot \color{blue}{\left(n \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(1 + \frac{1}{2} \cdot i\right) + \left(i \cdot i\right) \cdot \frac{1}{6}\right)}\right)}\right)\]
12. Taylor expanded around 0 14.0
  \[\leadsto 100 \cdot \left(\left(\sqrt[3]{\frac{i}{i} \cdot \left(\left(i \cdot i\right) \cdot \frac{1}{6} + \left(\frac{1}{2} \cdot i + 1\right)\right)} \cdot \color{blue}{\left(\frac{1}{6} \cdot i + \left(\frac{1}{36} \cdot {i}^{2} + 1\right)\right)}\right) \cdot \left(n \cdot \sqrt[3]{\frac{i}{i} \cdot \left(\left(1 + \frac{1}{2} \cdot i\right) + \left(i \cdot i\right) \cdot \frac{1}{6}\right)}\right)\right)\]
13. Applied simplify14.0
  \[\leadsto \color{blue}{\left(\left(i \cdot \left(\frac{1}{36} \cdot i\right) + \left(\frac{1}{6} \cdot i + 1\right)\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right) \cdot \left(\left(100 \cdot n\right) \cdot \sqrt[3]{\left(1 + \frac{1}{2} \cdot i\right) + \frac{1}{6} \cdot \left(i \cdot i\right)}\right)}\]
if 1.5893655743611886e+306 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))))
1. Initial program 53.4
  \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
2. Taylor expanded around inf 29.2
  \[\leadsto 100 \cdot \color{blue}{\frac{\left(e^{\left(\log \left(\frac{1}{n}\right) - \log \left(\frac{1}{i}\right)\right) \cdot n} - 1\right) \cdot n}{i}}\]
3. Applied simplify32.2
  \[\leadsto \color{blue}{\left(\frac{100}{i} \cdot n\right) \cdot \left({\left(\frac{i}{n}\right)}^{n} - 1\right)}\]
Recombined 5 regimes into one program.

Error

Try it out

Target

Derivation

`if (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < -4.943788105127082e+295`

`if -4.943788105127082e+295 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < -3.185864819664644e-208`

`if -3.185864819664644e-208 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < 5.601788448279894e-249`

`if 5.601788448279894e-249 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i)))))) < 1.5893655743611886e+306`

`if 1.5893655743611886e+306 < (* (* (+ (* i (* 1/36 i)) (+ (* 1/6 i) 1)) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))) (* (* 100 n) (cbrt (+ (+ 1 (* 1/2 i)) (* 1/6 (* i i))))))`

Runtime

In
Out