Compound Interest

Average Accuracy: 24.7% → 81.7%

Time: 22.1s

Precision: binary64

Cost: 40596.00

Math

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

↓

\[\begin{array}{l} t_0 := \log i - \log n\\ t_1 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.86 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq -3.1 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \frac{n \cdot \left(100 \cdot \log \left(\frac{i}{n}\right)\right)}{i}\\ \mathbf{elif}\;n \leq -2.9 \cdot 10^{-166}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(\frac{-1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot t_0 + n \cdot \left(n \cdot \mathsf{fma}\left(0.5, {t_0}^{2}, \frac{1}{i}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))

↓

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (- (log i) (log n))) (t_1 (* 100.0 (/ n (/ i (expm1 i))))))
   (if (<= n -1.86e-31)
     t_1
     (if (<= n -3.1e-42)
       (* n (/ (* n (* 100.0 (log (/ i n)))) i))
       (if (<= n -2.9e-166)
         (* 100.0 (/ n (+ 1.0 (* 0.08333333333333333 (* i i)))))
         (if (<= n -4e-310)
           (/
            (* 100.0 (expm1 (* n (- (log (/ -1.0 n)) (log (/ -1.0 i))))))
            (/ i n))
           (if (<= n 6e-55)
             (*
              (/ n i)
              (*
               100.0
               (+ (* n t_0) (* n (* n (fma 0.5 (pow t_0 2.0) (/ 1.0 i)))))))
             t_1)))))))

C

double code(double i, double n) {
	return 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

↓

double code(double i, double n) {
	double t_0 = log(i) - log(n);
	double t_1 = 100.0 * (n / (i / expm1(i)));
	double tmp;
	if (n <= -1.86e-31) {
		tmp = t_1;
	} else if (n <= -3.1e-42) {
		tmp = n * ((n * (100.0 * log((i / n)))) / i);
	} else if (n <= -2.9e-166) {
		tmp = 100.0 * (n / (1.0 + (0.08333333333333333 * (i * i))));
	} else if (n <= -4e-310) {
		tmp = (100.0 * expm1((n * (log((-1.0 / n)) - log((-1.0 / i)))))) / (i / n);
	} else if (n <= 6e-55) {
		tmp = (n / i) * (100.0 * ((n * t_0) + (n * (n * fma(0.5, pow(t_0, 2.0), (1.0 / i))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(i, n)
	return Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
end

↓

function code(i, n)
	t_0 = Float64(log(i) - log(n))
	t_1 = Float64(100.0 * Float64(n / Float64(i / expm1(i))))
	tmp = 0.0
	if (n <= -1.86e-31)
		tmp = t_1;
	elseif (n <= -3.1e-42)
		tmp = Float64(n * Float64(Float64(n * Float64(100.0 * log(Float64(i / n)))) / i));
	elseif (n <= -2.9e-166)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(0.08333333333333333 * Float64(i * i)))));
	elseif (n <= -4e-310)
		tmp = Float64(Float64(100.0 * expm1(Float64(n * Float64(log(Float64(-1.0 / n)) - log(Float64(-1.0 / i)))))) / Float64(i / n));
	elseif (n <= 6e-55)
		tmp = Float64(Float64(n / i) * Float64(100.0 * Float64(Float64(n * t_0) + Float64(n * Float64(n * fma(0.5, (t_0 ^ 2.0), Float64(1.0 / i)))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[i_, n_] := N[(100.0 * N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[i_, n_] := Block[{t$95$0 = N[(N[Log[i], $MachinePrecision] - N[Log[n], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.86e-31], t$95$1, If[LessEqual[n, -3.1e-42], N[(n * N[(N[(n * N[(100.0 * N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, -2.9e-166], N[(100.0 * N[(n / N[(1.0 + N[(0.08333333333333333 * N[(i * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, -4e-310], N[(N[(100.0 * N[(Exp[N[(n * N[(N[Log[N[(-1.0 / n), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / i), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6e-55], N[(N[(n / i), $MachinePrecision] * N[(100.0 * N[(N[(n * t$95$0), $MachinePrecision] + N[(n * N[(n * N[(0.5 * N[Power[t$95$0, 2.0], $MachinePrecision] + N[(1.0 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Target

Original	24.7%
Target	25.7%
Herbie	81.7%

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

Derivation

1. Split input into 5 regimes

2. if n < -1.85999999999999995e-31 or 6.00000000000000033e-55 < n

   1. Initial program 18.2%

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

   2. Simplified 18.7%

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

      [Start] 18.2	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 18.7	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 18.7	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 18.7	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 18.7	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 18.7	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 18.7	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 18.7	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 26.2%

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

   4. Simplified 89.0%

      \[\leadsto \color{blue}{100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]
      Proof

      [Start] 26.2	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      associate-/l* [=>] 26.2	\[ 100 \cdot \color{blue}{\frac{n}{\frac{i}{e^{i} - 1}}} \]
      expm1-def [=>] 89.0	\[ 100 \cdot \frac{n}{\frac{i}{\color{blue}{\mathsf{expm1}\left(i\right)}}} \]

   if -1.85999999999999995e-31 < n < -3.1000000000000003e-42

   1. Initial program 7.2%

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

   2. Simplified 7.2%

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

      [Start] 7.2	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 7.2	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 7.2	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 7.2	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 7.2	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 7.2	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 7.2	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 7.2	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around 0 0.0%

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

   4. Simplified 0.0%

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

      [Start] 0.0	\[ 100 \cdot \frac{{n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)}{i} \]
      associate-/l* [=>] 0.0	\[ 100 \cdot \color{blue}{\frac{{n}^{2}}{\frac{i}{-1 \cdot \log n + \log i}}} \]
      associate-/r/ [=>] 0.0	\[ 100 \cdot \color{blue}{\left(\frac{{n}^{2}}{i} \cdot \left(-1 \cdot \log n + \log i\right)\right)} \]
      unpow2 [=>] 0.0	\[ 100 \cdot \left(\frac{\color{blue}{n \cdot n}}{i} \cdot \left(-1 \cdot \log n + \log i\right)\right) \]
      +-commutative [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \color{blue}{\left(\log i + -1 \cdot \log n\right)}\right) \]
      mul-1-neg [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i + \color{blue}{\left(-\log n\right)}\right)\right) \]
      unsub-neg [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \color{blue}{\left(\log i - \log n\right)}\right) \]

   5. Taylor expanded in n around inf 0.0%

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

   6. Simplified 41.5%

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

      [Start] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i - -1 \cdot \log \left(\frac{1}{n}\right)\right)\right) \]
      cancel-sign-sub-inv [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \color{blue}{\left(\log i + \left(--1\right) \cdot \log \left(\frac{1}{n}\right)\right)}\right) \]
      metadata-eval [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i + \color{blue}{1} \cdot \log \left(\frac{1}{n}\right)\right)\right) \]
      log-rec [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i + 1 \cdot \color{blue}{\left(-\log n\right)}\right)\right) \]
      *-commutative [<=] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i + \color{blue}{\left(-\log n\right) \cdot 1}\right)\right) \]
      *-rgt-identity [=>] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \left(\log i + \color{blue}{\left(-\log n\right)}\right)\right) \]
      sub-neg [<=] 0.0	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \color{blue}{\left(\log i - \log n\right)}\right) \]
      log-div [<=] 41.5	\[ 100 \cdot \left(\frac{n \cdot n}{i} \cdot \color{blue}{\log \left(\frac{i}{n}\right)}\right) \]

   7. Taylor expanded in n around 0 0.0%

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

   8. Simplified 40.9%

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

      [Start] 0.0	\[ 100 \cdot \frac{{n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)}{i} \]
      associate-*r/ [=>] 0.0	\[ \color{blue}{\frac{100 \cdot \left({n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)\right)}{i}} \]
      distribute-rgt-in [=>] 0.0	\[ \frac{100 \cdot \color{blue}{\left(\left(-1 \cdot \log n\right) \cdot {n}^{2} + \log i \cdot {n}^{2}\right)}}{i} \]
      log-pow [<=] 0.0	\[ \frac{100 \cdot \left(\color{blue}{\log \left({n}^{-1}\right)} \cdot {n}^{2} + \log i \cdot {n}^{2}\right)}{i} \]
      unpow-1 [=>] 0.0	\[ \frac{100 \cdot \left(\log \color{blue}{\left(\frac{1}{n}\right)} \cdot {n}^{2} + \log i \cdot {n}^{2}\right)}{i} \]
      distribute-rgt-in [<=] 0.0	\[ \frac{100 \cdot \color{blue}{\left({n}^{2} \cdot \left(\log \left(\frac{1}{n}\right) + \log i\right)\right)}}{i} \]

   9. Applied egg-rr 41.9%

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

   if -3.1000000000000003e-42 < n < -2.9e-166

   1. Initial program 28.1%

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

   2. Simplified 27.7%

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

      [Start] 28.1	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 27.7	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 27.7	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 27.7	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 27.7	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 27.7	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 27.7	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 27.7	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 17.1%

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

   4. Simplified 62.9%

      \[\leadsto \color{blue}{100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}} \]
      Proof

      [Start] 17.1	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      associate-/l* [=>] 17.1	\[ 100 \cdot \color{blue}{\frac{n}{\frac{i}{e^{i} - 1}}} \]
      expm1-def [=>] 62.9	\[ 100 \cdot \frac{n}{\frac{i}{\color{blue}{\mathsf{expm1}\left(i\right)}}} \]

   5. Taylor expanded in i around 0 71.1%

      \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + \left(0.08333333333333333 \cdot {i}^{2} + -0.5 \cdot i\right)}} \]

   6. Simplified 71.1%

      \[\leadsto 100 \cdot \frac{n}{\color{blue}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}} \]
      Proof

      [Start] 71.1	\[ 100 \cdot \frac{n}{1 + \left(0.08333333333333333 \cdot {i}^{2} + -0.5 \cdot i\right)} \]
      +-commutative [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \color{blue}{\left(-0.5 \cdot i + 0.08333333333333333 \cdot {i}^{2}\right)}} \]
      *-commutative [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \left(\color{blue}{i \cdot -0.5} + 0.08333333333333333 \cdot {i}^{2}\right)} \]
      *-commutative [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{{i}^{2} \cdot 0.08333333333333333}\right)} \]
      unpow2 [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{\left(i \cdot i\right)} \cdot 0.08333333333333333\right)} \]
      associate-*l* [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{i \cdot \left(i \cdot 0.08333333333333333\right)}\right)} \]
      distribute-lft-out [=>] 71.1	\[ 100 \cdot \frac{n}{1 + \color{blue}{i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}} \]

   7. Taylor expanded in i around inf 71.1%

      \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{0.08333333333333333 \cdot {i}^{2}}} \]

   8. Simplified 71.1%

      \[\leadsto 100 \cdot \frac{n}{1 + \color{blue}{0.08333333333333333 \cdot \left(i \cdot i\right)}} \]
      Proof

      [Start] 71.1	\[ 100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot {i}^{2}} \]
      unpow2 [=>] 71.1	\[ 100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \color{blue}{\left(i \cdot i\right)}} \]

   if -2.9e-166 < n < -3.999999999999988e-310

   1. Initial program 67.7%

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

   2. Simplified 67.7%

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

      [Start] 67.7	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-*r/ [=>] 67.7	\[ \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]
      sub-neg [=>] 67.7	\[ \frac{100 \cdot \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)\right)}}{\frac{i}{n}} \]
      metadata-eval [=>] 67.7	\[ \frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}\right)}{\frac{i}{n}} \]

   3. Taylor expanded in i around -inf 67.2%

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

   4. Simplified 77.2%

      \[\leadsto \frac{\color{blue}{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(\frac{-1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}}{\frac{i}{n}} \]
      Proof

      [Start] 67.2	\[ \frac{100 \cdot \left(e^{n \cdot \left(-1 \cdot \log \left(\frac{-1}{i}\right) + \log \left(-\frac{1}{n}\right)\right)} - 1\right)}{\frac{i}{n}} \]
      expm1-def [=>] 77.2	\[ \frac{100 \cdot \color{blue}{\mathsf{expm1}\left(n \cdot \left(-1 \cdot \log \left(\frac{-1}{i}\right) + \log \left(-\frac{1}{n}\right)\right)\right)}}{\frac{i}{n}} \]
      +-commutative [=>] 77.2	\[ \frac{100 \cdot \mathsf{expm1}\left(n \cdot \color{blue}{\left(\log \left(-\frac{1}{n}\right) + -1 \cdot \log \left(\frac{-1}{i}\right)\right)}\right)}{\frac{i}{n}} \]
      mul-1-neg [=>] 77.2	\[ \frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(-\frac{1}{n}\right) + \color{blue}{\left(-\log \left(\frac{-1}{i}\right)\right)}\right)\right)}{\frac{i}{n}} \]
      unsub-neg [=>] 77.2	\[ \frac{100 \cdot \mathsf{expm1}\left(n \cdot \color{blue}{\left(\log \left(-\frac{1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)}\right)}{\frac{i}{n}} \]
      distribute-neg-frac [=>] 77.2	\[ \frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \color{blue}{\left(\frac{-1}{n}\right)} - \log \left(\frac{-1}{i}\right)\right)\right)}{\frac{i}{n}} \]
      metadata-eval [=>] 77.2	\[ \frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(\frac{\color{blue}{-1}}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}{\frac{i}{n}} \]

   if -3.999999999999988e-310 < n < 6.00000000000000033e-55

   1. Initial program 25.0%

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

   2. Simplified 25.0%

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

      [Start] 25.0	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-*r/ [=>] 25.0	\[ \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]
      associate-/l* [<=] 25.0	\[ \color{blue}{\frac{\left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right) \cdot n}{i}} \]
      *-commutative [=>] 25.0	\[ \frac{\color{blue}{n \cdot \left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right)}}{i} \]
      associate-/l* [=>] 25.0	\[ \color{blue}{\frac{n}{\frac{i}{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}} \]
      associate-/r/ [=>] 25.0	\[ \color{blue}{\frac{n}{i} \cdot \left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right)} \]
      sub-neg [=>] 25.0	\[ \frac{n}{i} \cdot \left(100 \cdot \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)\right)}\right) \]
      distribute-lft-in [=>] 25.0	\[ \frac{n}{i} \cdot \color{blue}{\left(100 \cdot {\left(1 + \frac{i}{n}\right)}^{n} + 100 \cdot \left(-1\right)\right)} \]
      fma-def [=>] 25.0	\[ \frac{n}{i} \cdot \color{blue}{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \left(-1\right)\right)} \]
      metadata-eval [=>] 25.0	\[ \frac{n}{i} \cdot \mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \color{blue}{-1}\right) \]
      metadata-eval [=>] 25.0	\[ \frac{n}{i} \cdot \mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, \color{blue}{-100}\right) \]

   3. Taylor expanded in n around 0 66.2%

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

   4. Simplified 66.5%

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

      [Start] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \left({n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right) + 100 \cdot \left(n \cdot \left(-1 \cdot \log n + \log i\right)\right)\right) \]
      distribute-lft-out [=>] 66.2	\[ \frac{n}{i} \cdot \color{blue}{\left(100 \cdot \left({n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right) + n \cdot \left(-1 \cdot \log n + \log i\right)\right)\right)} \]
      +-commutative [=>] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \color{blue}{\left(n \cdot \left(-1 \cdot \log n + \log i\right) + {n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)}\right) \]
      +-commutative [=>] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \color{blue}{\left(\log i + -1 \cdot \log n\right)} + {n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)\right) \]
      mul-1-neg [=>] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i + \color{blue}{\left(-\log n\right)}\right) + {n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)\right) \]
      unsub-neg [=>] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \color{blue}{\left(\log i - \log n\right)} + {n}^{2} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)\right) \]
      unpow2 [=>] 66.2	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right) + \color{blue}{\left(n \cdot n\right)} \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)\right) \]
      associate-*l* [=>] 66.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right) + \color{blue}{n \cdot \left(n \cdot \left(0.5 \cdot {\left(-1 \cdot \log n + \log i\right)}^{2} + \frac{1}{i}\right)\right)}\right)\right) \]
      fma-def [=>] 66.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right) + n \cdot \left(n \cdot \color{blue}{\mathsf{fma}\left(0.5, {\left(-1 \cdot \log n + \log i\right)}^{2}, \frac{1}{i}\right)}\right)\right)\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -1.86 \cdot 10^{-31}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -3.1 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \frac{n \cdot \left(100 \cdot \log \left(\frac{i}{n}\right)\right)}{i}\\ \mathbf{elif}\;n \leq -2.9 \cdot 10^{-166}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(\frac{-1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right) + n \cdot \left(n \cdot \mathsf{fma}\left(0.5, {\left(\log i - \log n\right)}^{2}, \frac{1}{i}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	81.6%
Cost	20688.00

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.86 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -3.4 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \frac{n \cdot \left(100 \cdot \log \left(\frac{i}{n}\right)\right)}{i}\\ \mathbf{elif}\;n \leq -6.1 \cdot 10^{-167}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{100 \cdot \mathsf{expm1}\left(n \cdot \left(\log \left(\frac{-1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	81.8%
Cost	14164.00

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.86 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -1.05 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \frac{n \cdot \left(100 \cdot \log \left(\frac{i}{n}\right)\right)}{i}\\ \mathbf{elif}\;n \leq -1.7 \cdot 10^{-217}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{100 \cdot \left(\log \left(-i\right) - \log \left(-n\right)\right)}{\frac{\frac{i}{n}}{n}}\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-55}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	82.6%
Cost	7640.00

\[\begin{array}{l} \mathbf{if}\;n \leq -2.4 \cdot 10^{-31}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -3.4 \cdot 10^{-42}:\\ \;\;\;\;100 \cdot \left(\log \left(\frac{i}{n}\right) \cdot \left(n \cdot \frac{n}{i}\right)\right)\\ \mathbf{elif}\;n \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;100 \cdot \left(n + i \cdot -0.5\right)\\ \mathbf{elif}\;n \leq -2.6 \cdot 10^{-219}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 3 \cdot 10^{-243}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \frac{100 \cdot \mathsf{expm1}\left(i\right)}{i}\\ \end{array} \]

Alternative 4
Accuracy	82.7%
Cost	7640.00

\[\begin{array}{l} \mathbf{if}\;n \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -3.4 \cdot 10^{-42}:\\ \;\;\;\;100 \cdot \frac{n \cdot \log \left(\frac{i}{n}\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;100 \cdot \left(n + i \cdot -0.5\right)\\ \mathbf{elif}\;n \leq -1.1 \cdot 10^{-219}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 2.3 \cdot 10^{-237}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \frac{100 \cdot \mathsf{expm1}\left(i\right)}{i}\\ \end{array} \]

Alternative 5
Accuracy	82.7%
Cost	7640.00

\[\begin{array}{l} \mathbf{if}\;n \leq -7.2 \cdot 10^{-31}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -1.9 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \left(\log \left(\frac{i}{n}\right) \cdot \left(100 \cdot \frac{n}{i}\right)\right)\\ \mathbf{elif}\;n \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;100 \cdot \left(n + i \cdot -0.5\right)\\ \mathbf{elif}\;n \leq -1.2 \cdot 10^{-219}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 3.3 \cdot 10^{-237}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \frac{100 \cdot \mathsf{expm1}\left(i\right)}{i}\\ \end{array} \]

Alternative 6
Accuracy	82.9%
Cost	7508.00

\[\begin{array}{l} \mathbf{if}\;n \leq -1.86 \cdot 10^{-31}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -3.1 \cdot 10^{-42}:\\ \;\;\;\;n \cdot \frac{n \cdot \left(100 \cdot \log \left(\frac{i}{n}\right)\right)}{i}\\ \mathbf{elif}\;n \leq -1.55 \cdot 10^{-218}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 8.5 \cdot 10^{-237}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \frac{100 \cdot \mathsf{expm1}\left(i\right)}{i}\\ \end{array} \]

Alternative 7
Accuracy	83.1%
Cost	7376.00

\[\begin{array}{l} t_0 := 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{if}\;n \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -9.5 \cdot 10^{-221}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-236}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Accuracy	83.1%
Cost	7376.00

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.85 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Accuracy	83.1%
Cost	7376.00

\[\begin{array}{l} \mathbf{if}\;n \leq -1.25 \cdot 10^{-16}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -7 \cdot 10^{-220}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{elif}\;n \leq 2.7 \cdot 10^{-235}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 0.0115:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \frac{100 \cdot \mathsf{expm1}\left(i\right)}{i}\\ \end{array} \]

Alternative 10
Accuracy	69.2%
Cost	969.00

\[\begin{array}{l} \mathbf{if}\;n \leq -1.55 \cdot 10^{-220} \lor \neg \left(n \leq 1.7 \cdot 10^{-240}\right):\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 11
Accuracy	69.7%
Cost	968.00

\[\begin{array}{l} \mathbf{if}\;n \leq -5.1 \cdot 10^{-220}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{elif}\;n \leq 5.4 \cdot 10^{-236}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + 0.08333333333333333 \cdot \left(i \cdot i\right)}\\ \end{array} \]

Alternative 12
Accuracy	69.3%
Cost	841.00

\[\begin{array}{l} \mathbf{if}\;n \leq -2.4 \cdot 10^{-165} \lor \neg \left(n \leq 1.1 \cdot 10^{-233}\right):\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 13
Accuracy	63.7%
Cost	713.00

\[\begin{array}{l} \mathbf{if}\;i \leq -1.45 \lor \neg \left(i \leq 245\right):\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \]

Alternative 14
Accuracy	67.3%
Cost	713.00

\[\begin{array}{l} \mathbf{if}\;i \leq -1.85 \lor \neg \left(i \leq 165\right):\\ \;\;\;\;\frac{n}{i \cdot i} \cdot 1200\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \]

Alternative 15
Accuracy	66.9%
Cost	576.00

\[100 \cdot \frac{n}{1 + i \cdot -0.5} \]

Alternative 16
Accuracy	2.9%
Cost	192.00

\[i \cdot -50 \]

Alternative 17
Accuracy	56.0%
Cost	192.00

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023096 
(FPCore (i n)
  :name "Compound Interest"
  :precision binary64

  :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))))