Error

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Target

Derivation

1. Split input into 3 regimes

2. if n < -6.946497033310484e+191 or -4.056551695566858e+130 < n < -4.0276202651907404e-09 or 9.658195263911622e-134 < n

   1. Initial program 51.9

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

   3. Applied div-sub51.9

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

   4. Taylor expanded around 0 22.1

      \[\leadsto 100 \cdot \color{blue}{\left(\frac{1}{6} \cdot \left({i}^{2} \cdot n\right) + \left(n + \frac{1}{2} \cdot \left(i \cdot n\right)\right)\right)}\]

   5. Simplified21.9

      \[\leadsto 100 \cdot \color{blue}{\left(n + \left(i \cdot n\right) \cdot \left(\frac{1}{6} \cdot i + \frac{1}{2}\right)\right)}\]

   6. Taylor expanded around 0 22.1

      \[\leadsto \color{blue}{\frac{50}{3} \cdot \left({i}^{2} \cdot n\right) + \left(100 \cdot n + 50 \cdot \left(i \cdot n\right)\right)}\]

   7. Simplified21.9

      \[\leadsto \color{blue}{\left(i \cdot n\right) \cdot \left(50 + \frac{50}{3} \cdot i\right) + 100 \cdot n}\]

   if -6.946497033310484e+191 < n < -4.056551695566858e+130

   1. Initial program 42.7

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

   3. Applied div-inv42.7

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

   4. Applied associate-/r*42.4

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

   if -4.0276202651907404e-09 < n < 9.658195263911622e-134

   1. Initial program 24.7

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

   2. Taylor expanded around 0 18.1

      \[\leadsto \color{blue}{0}\]
3. Recombined 3 regimes into one program.

4. Final simplification21.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \le -6.946497033310484 \cdot 10^{+191}:\\ \;\;\;\;n \cdot 100 + \left(i \cdot n\right) \cdot \left(50 + i \cdot \frac{50}{3}\right)\\ \mathbf{elif}\;n \le -4.056551695566858 \cdot 10^{+130}:\\ \;\;\;\;100 \cdot \frac{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}{\frac{1}{n}}\\ \mathbf{elif}\;n \le -4.0276202651907404 \cdot 10^{-09} \lor \neg \left(n \le 9.658195263911622 \cdot 10^{-134}\right):\\ \;\;\;\;n \cdot 100 + \left(i \cdot n\right) \cdot \left(50 + i \cdot \frac{50}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (i n)
  :name "Compound Interest"

  :herbie-target
  (* 100 (/ (- (exp (* n (if (== (+ 1 (/ i n)) 1) (/ i n) (/ (* (/ i n) (log (+ 1 (/ i n)))) (- (+ (/ i n) 1) 1))))) 1) (/ i n)))

  (* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))))

Details

Time bar (total: 19.1s)Debug log