Compound Interest

Average Error: 42.9 → 23.8

Time: 34.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;n \le -2.813114393619137495994961909777216500149 \cdot 10^{175}:\\ \;\;\;\;100 \cdot \frac{\left(\left(i \cdot i\right) \cdot \left(0.5 - \log 1 \cdot 0.5\right) + \left(i \cdot 1 + \log 1 \cdot n\right)\right) \cdot n}{i}\\ \mathbf{elif}\;n \le -1.421989441319127851613951560151701461699 \cdot 10^{58}:\\ \;\;\;\;\sqrt{100} \cdot \left(\left(n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right) \cdot \frac{\sqrt{100}}{i}\right)\\ \mathbf{elif}\;n \le -1.995072885870678103259479030384682118893:\\ \;\;\;\;\frac{\left(n \cdot n\right) \cdot \left(100 \cdot \log 1\right)}{i} + \left(50 \cdot \left(i \cdot n\right) + \left(100 \cdot n - \left(i \cdot n\right) \cdot \left(\log 1 \cdot 50\right)\right)\right)\\ \mathbf{elif}\;n \le -4.586926552796907742204996293991418623461 \cdot 10^{-267}:\\ \;\;\;\;\frac{100}{i} \cdot \frac{\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} \cdot {\left(1 + \frac{i}{n}\right)}^{n}\right) \cdot {\left(1 + \frac{i}{n}\right)}^{n} - 1 \cdot \left(1 \cdot 1\right)}{\left({\left(1 + \frac{i}{n}\right)}^{n} \cdot 1 + 1 \cdot 1\right) + {\left(1 + \frac{i}{n}\right)}^{n} \cdot {\left(1 + \frac{i}{n}\right)}^{n}}}{\frac{1}{n}}\\ \mathbf{elif}\;n \le 8.765996428721520261943646244564954658781 \cdot 10^{-223}:\\ \;\;\;\;100 \cdot \frac{\left(\left(i \cdot 1 + 1\right) + \log 1 \cdot n\right) - 1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(i \cdot i\right) \cdot \left(0.5 - \log 1 \cdot 0.5\right) + \left(i \cdot 1 + \log 1 \cdot n\right)\right) \cdot \frac{100}{i}}{\frac{1}{n}}\\ \end{array}\]

C

double f(double i, double n) {
        double r9903469 = 100.0;
        double r9903470 = 1.0;
        double r9903471 = i;
        double r9903472 = n;
        double r9903473 = r9903471 / r9903472;
        double r9903474 = r9903470 + r9903473;
        double r9903475 = pow(r9903474, r9903472);
        double r9903476 = r9903475 - r9903470;
        double r9903477 = r9903476 / r9903473;
        double r9903478 = r9903469 * r9903477;
        return r9903478;
}

↓

double f(double i, double n) {
        double r9903479 = n;
        double r9903480 = -2.8131143936191375e+175;
        bool r9903481 = r9903479 <= r9903480;
        double r9903482 = 100.0;
        double r9903483 = i;
        double r9903484 = r9903483 * r9903483;
        double r9903485 = 0.5;
        double r9903486 = 1.0;
        double r9903487 = log(r9903486);
        double r9903488 = r9903487 * r9903485;
        double r9903489 = r9903485 - r9903488;
        double r9903490 = r9903484 * r9903489;
        double r9903491 = r9903483 * r9903486;
        double r9903492 = r9903487 * r9903479;
        double r9903493 = r9903491 + r9903492;
        double r9903494 = r9903490 + r9903493;
        double r9903495 = r9903494 * r9903479;
        double r9903496 = r9903495 / r9903483;
        double r9903497 = r9903482 * r9903496;
        double r9903498 = -1.4219894413191279e+58;
        bool r9903499 = r9903479 <= r9903498;
        double r9903500 = sqrt(r9903482);
        double r9903501 = r9903483 / r9903479;
        double r9903502 = r9903486 + r9903501;
        double r9903503 = pow(r9903502, r9903479);
        double r9903504 = r9903503 - r9903486;
        double r9903505 = r9903479 * r9903504;
        double r9903506 = r9903500 / r9903483;
        double r9903507 = r9903505 * r9903506;
        double r9903508 = r9903500 * r9903507;
        double r9903509 = -1.995072885870678;
        bool r9903510 = r9903479 <= r9903509;
        double r9903511 = r9903479 * r9903479;
        double r9903512 = r9903482 * r9903487;
        double r9903513 = r9903511 * r9903512;
        double r9903514 = r9903513 / r9903483;
        double r9903515 = 50.0;
        double r9903516 = r9903483 * r9903479;
        double r9903517 = r9903515 * r9903516;
        double r9903518 = r9903482 * r9903479;
        double r9903519 = r9903487 * r9903515;
        double r9903520 = r9903516 * r9903519;
        double r9903521 = r9903518 - r9903520;
        double r9903522 = r9903517 + r9903521;
        double r9903523 = r9903514 + r9903522;
        double r9903524 = -4.586926552796908e-267;
        bool r9903525 = r9903479 <= r9903524;
        double r9903526 = r9903482 / r9903483;
        double r9903527 = r9903503 * r9903503;
        double r9903528 = r9903527 * r9903503;
        double r9903529 = r9903486 * r9903486;
        double r9903530 = r9903486 * r9903529;
        double r9903531 = r9903528 - r9903530;
        double r9903532 = r9903503 * r9903486;
        double r9903533 = r9903532 + r9903529;
        double r9903534 = r9903533 + r9903527;
        double r9903535 = r9903531 / r9903534;
        double r9903536 = 1.0;
        double r9903537 = r9903536 / r9903479;
        double r9903538 = r9903535 / r9903537;
        double r9903539 = r9903526 * r9903538;
        double r9903540 = 8.76599642872152e-223;
        bool r9903541 = r9903479 <= r9903540;
        double r9903542 = r9903491 + r9903536;
        double r9903543 = r9903542 + r9903492;
        double r9903544 = r9903543 - r9903486;
        double r9903545 = r9903544 / r9903501;
        double r9903546 = r9903482 * r9903545;
        double r9903547 = r9903494 * r9903526;
        double r9903548 = r9903547 / r9903537;
        double r9903549 = r9903541 ? r9903546 : r9903548;
        double r9903550 = r9903525 ? r9903539 : r9903549;
        double r9903551 = r9903510 ? r9903523 : r9903550;
        double r9903552 = r9903499 ? r9903508 : r9903551;
        double r9903553 = r9903481 ? r9903497 : r9903552;
        return r9903553;
}

Error

Bits error versus i

Bits error versus n

Target

Original	42.9
Target	42.9
Herbie	23.8

\[100 \cdot \frac{e^{n \cdot \begin{array}{l} \mathbf{if}\;1 + \frac{i}{n} = 1:\\ \;\;\;\;\frac{i}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{n} \cdot \log \left(1 + \frac{i}{n}\right)}{\left(\frac{i}{n} + 1\right) - 1}\\ \end{array}} - 1}{\frac{i}{n}}\]

Derivation

1. Split input into 6 regimes

2. if n < -2.8131143936191375e+175

   1. Initial program 53.6

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   2. Using strategy rm

   3. Applied div-inv 53.6

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

   4. Applied *-un-lft-identity 53.6

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

   5. Applied times-frac 53.1

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

   6. Applied associate-*r* 53.1

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

   7. Simplified 53.1

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

   8. Taylor expanded around 0 25.5

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\log 1 \cdot n + \left(1 \cdot i + 0.5 \cdot {i}^{2}\right)\right) - 0.5 \cdot \left(\log 1 \cdot {i}^{2}\right)}}{\frac{1}{n}}\]

   9. Simplified 25.5

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}}{\frac{1}{n}}\]
   10. Using strategy rm

   11. Applied div-inv 25.5

       \[\leadsto \color{blue}{\left(100 \cdot \frac{1}{i}\right)} \cdot \frac{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}{\frac{1}{n}}\]

   12. Applied associate-*l* 25.2

       \[\leadsto \color{blue}{100 \cdot \left(\frac{1}{i} \cdot \frac{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}{\frac{1}{n}}\right)}\]

   13. Simplified 25.1

       \[\leadsto 100 \cdot \color{blue}{\frac{\left(\left(n \cdot \log 1 + 1 \cdot i\right) + \left(i \cdot i\right) \cdot \left(0.5 - 0.5 \cdot \log 1\right)\right) \cdot n}{i}}\]

   if -2.8131143936191375e+175 < n < -1.4219894413191279e+58

   1. Initial program 41.0

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   2. Using strategy rm

   3. Applied div-inv 41.0

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

   4. Applied *-un-lft-identity 41.0

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

   5. Applied times-frac 40.7

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

   6. Applied associate-*r* 40.7

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

   7. Simplified 40.7

      \[\leadsto \color{blue}{\frac{100}{i}} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\]
   8. Using strategy rm

   9. Applied *-un-lft-identity 40.7

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

   10. Applied add-sqr-sqrt 40.7

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

   11. Applied times-frac 40.7

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

   12. Applied associate-*l* 40.7

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

   13. Simplified 40.7

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

   if -1.4219894413191279e+58 < n < -1.995072885870678

   1. Initial program 35.7

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   2. Using strategy rm

   3. Applied div-inv 35.7

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

   4. Applied *-un-lft-identity 35.7

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

   5. Applied times-frac 35.7

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

   6. Applied associate-*r* 35.7

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

   7. Simplified 35.7

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

   8. Taylor expanded around 0 28.8

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\log 1 \cdot n + \left(1 \cdot i + 0.5 \cdot {i}^{2}\right)\right) - 0.5 \cdot \left(\log 1 \cdot {i}^{2}\right)}}{\frac{1}{n}}\]

   9. Simplified 28.8

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}}{\frac{1}{n}}\]
   10. Using strategy rm

   11. Applied div-inv 28.8

       \[\leadsto \color{blue}{\left(100 \cdot \frac{1}{i}\right)} \cdot \frac{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}{\frac{1}{n}}\]

   12. Applied associate-*l* 28.4

       \[\leadsto \color{blue}{100 \cdot \left(\frac{1}{i} \cdot \frac{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}{\frac{1}{n}}\right)}\]

   13. Simplified 28.3

       \[\leadsto 100 \cdot \color{blue}{\frac{\left(\left(n \cdot \log 1 + 1 \cdot i\right) + \left(i \cdot i\right) \cdot \left(0.5 - 0.5 \cdot \log 1\right)\right) \cdot n}{i}}\]

   14. Taylor expanded around 0 28.1

       \[\leadsto \color{blue}{\left(100 \cdot n + \left(50 \cdot \left(i \cdot n\right) + 100 \cdot \frac{\log 1 \cdot {n}^{2}}{i}\right)\right) - 50 \cdot \left(\log 1 \cdot \left(i \cdot n\right)\right)}\]

   15. Simplified 28.1

       \[\leadsto \color{blue}{\frac{\left(100 \cdot \log 1\right) \cdot \left(n \cdot n\right)}{i} + \left(\left(i \cdot n\right) \cdot 50 + \left(n \cdot 100 - \left(50 \cdot \log 1\right) \cdot \left(i \cdot n\right)\right)\right)}\]

   if -1.995072885870678 < n < -4.586926552796908e-267

   1. Initial program 16.2

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   2. Using strategy rm

   3. Applied div-inv 16.2

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

   4. Applied *-un-lft-identity 16.2

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

   5. Applied times-frac 16.8

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

   6. Applied associate-*r* 17.0

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

   7. Simplified 17.0

      \[\leadsto \color{blue}{\frac{100}{i}} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{1}{n}}\]
   8. Using strategy rm

   9. Applied flip3-- 17.0

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\frac{{\left({\left(1 + \frac{i}{n}\right)}^{n}\right)}^{3} - {1}^{3}}{{\left(1 + \frac{i}{n}\right)}^{n} \cdot {\left(1 + \frac{i}{n}\right)}^{n} + \left(1 \cdot 1 + {\left(1 + \frac{i}{n}\right)}^{n} \cdot 1\right)}}}{\frac{1}{n}}\]

   10. Simplified 17.0

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

   if -4.586926552796908e-267 < n < 8.76599642872152e-223

   1. Initial program 29.9

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

   2. Taylor expanded around 0 14.8

      \[\leadsto 100 \cdot \frac{\color{blue}{\left(\log 1 \cdot n + \left(1 \cdot i + 1\right)\right)} - 1}{\frac{i}{n}}\]

   if 8.76599642872152e-223 < n

   1. Initial program 57.6

      \[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
   2. Using strategy rm

   3. Applied div-inv 57.6

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

   4. Applied *-un-lft-identity 57.6

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

   5. Applied times-frac 57.3

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

   6. Applied associate-*r* 57.3

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

   7. Simplified 57.3

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

   8. Taylor expanded around 0 27.7

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\log 1 \cdot n + \left(1 \cdot i + 0.5 \cdot {i}^{2}\right)\right) - 0.5 \cdot \left(\log 1 \cdot {i}^{2}\right)}}{\frac{1}{n}}\]

   9. Simplified 27.7

      \[\leadsto \frac{100}{i} \cdot \frac{\color{blue}{\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n}}{\frac{1}{n}}\]
   10. Using strategy rm

   11. Applied associate-*r/ 22.6

       \[\leadsto \color{blue}{\frac{\frac{100}{i} \cdot \left(\left(\left(i \cdot i\right) \cdot 0.5 + \left(1 \cdot i - \left(i \cdot i\right) \cdot \left(\log 1 \cdot 0.5\right)\right)\right) + \log 1 \cdot n\right)}{\frac{1}{n}}}\]

   12. Simplified 22.6

       \[\leadsto \frac{\color{blue}{\frac{100}{i} \cdot \left(\left(n \cdot \log 1 + 1 \cdot i\right) + \left(i \cdot i\right) \cdot \left(0.5 - 0.5 \cdot \log 1\right)\right)}}{\frac{1}{n}}\]
3. Recombined 6 regimes into one program.

4. Final simplification 23.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \le -2.813114393619137495994961909777216500149 \cdot 10^{175}:\\ \;\;\;\;100 \cdot \frac{\left(\left(i \cdot i\right) \cdot \left(0.5 - \log 1 \cdot 0.5\right) + \left(i \cdot 1 + \log 1 \cdot n\right)\right) \cdot n}{i}\\ \mathbf{elif}\;n \le -1.421989441319127851613951560151701461699 \cdot 10^{58}:\\ \;\;\;\;\sqrt{100} \cdot \left(\left(n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right) \cdot \frac{\sqrt{100}}{i}\right)\\ \mathbf{elif}\;n \le -1.995072885870678103259479030384682118893:\\ \;\;\;\;\frac{\left(n \cdot n\right) \cdot \left(100 \cdot \log 1\right)}{i} + \left(50 \cdot \left(i \cdot n\right) + \left(100 \cdot n - \left(i \cdot n\right) \cdot \left(\log 1 \cdot 50\right)\right)\right)\\ \mathbf{elif}\;n \le -4.586926552796907742204996293991418623461 \cdot 10^{-267}:\\ \;\;\;\;\frac{100}{i} \cdot \frac{\frac{\left({\left(1 + \frac{i}{n}\right)}^{n} \cdot {\left(1 + \frac{i}{n}\right)}^{n}\right) \cdot {\left(1 + \frac{i}{n}\right)}^{n} - 1 \cdot \left(1 \cdot 1\right)}{\left({\left(1 + \frac{i}{n}\right)}^{n} \cdot 1 + 1 \cdot 1\right) + {\left(1 + \frac{i}{n}\right)}^{n} \cdot {\left(1 + \frac{i}{n}\right)}^{n}}}{\frac{1}{n}}\\ \mathbf{elif}\;n \le 8.765996428721520261943646244564954658781 \cdot 10^{-223}:\\ \;\;\;\;100 \cdot \frac{\left(\left(i \cdot 1 + 1\right) + \log 1 \cdot n\right) - 1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(i \cdot i\right) \cdot \left(0.5 - \log 1 \cdot 0.5\right) + \left(i \cdot 1 + \log 1 \cdot n\right)\right) \cdot \frac{100}{i}}{\frac{1}{n}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(FPCore (i n)
  :name "Compound Interest"

  :herbie-target
  (* 100.0 (/ (- (exp (* n (if (== (+ 1.0 (/ i n)) 1.0) (/ i n) (/ (* (/ i n) (log (+ 1.0 (/ i n)))) (- (+ (/ i n) 1.0) 1.0))))) 1.0) (/ i n)))

  (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))