Compound Interest

Average Error: 47.2 → 11.8

Time: 16.6s

Precision: binary64

Cost: 13900

Math

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

↓

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -5 \cdot 10^{-310}:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(\log \left(\frac{n}{i}\right) \cdot \left(-n\right)\right)\right)\\ \mathbf{elif}\;n \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 (* 100.0 (/ n (/ i (expm1 i))))))
   (if (<= n -1.25e-167)
     t_0
     (if (<= n -5e-310)
       (* 100.0 (* (/ n i) (expm1 (* (log (/ n i)) (- n)))))
       (if (<= n 2.6e-63)
         (* (/ n i) (* 100.0 (* n (- (log i) (log n)))))
         t_0)))))

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 = 100.0 * (n / (i / expm1(i)));
	double tmp;
	if (n <= -1.25e-167) {
		tmp = t_0;
	} else if (n <= -5e-310) {
		tmp = 100.0 * ((n / i) * expm1((log((n / i)) * -n)));
	} else if (n <= 2.6e-63) {
		tmp = (n / i) * (100.0 * (n * (log(i) - log(n))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

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

↓

public static double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / Math.expm1(i)));
	double tmp;
	if (n <= -1.25e-167) {
		tmp = t_0;
	} else if (n <= -5e-310) {
		tmp = 100.0 * ((n / i) * Math.expm1((Math.log((n / i)) * -n)));
	} else if (n <= 2.6e-63) {
		tmp = (n / i) * (100.0 * (n * (Math.log(i) - Math.log(n))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	return 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))

↓

def code(i, n):
	t_0 = 100.0 * (n / (i / math.expm1(i)))
	tmp = 0
	if n <= -1.25e-167:
		tmp = t_0
	elif n <= -5e-310:
		tmp = 100.0 * ((n / i) * math.expm1((math.log((n / i)) * -n)))
	elif n <= 2.6e-63:
		tmp = (n / i) * (100.0 * (n * (math.log(i) - math.log(n))))
	else:
		tmp = t_0
	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(100.0 * Float64(n / Float64(i / expm1(i))))
	tmp = 0.0
	if (n <= -1.25e-167)
		tmp = t_0;
	elseif (n <= -5e-310)
		tmp = Float64(100.0 * Float64(Float64(n / i) * expm1(Float64(log(Float64(n / i)) * Float64(-n)))));
	elseif (n <= 2.6e-63)
		tmp = Float64(Float64(n / i) * Float64(100.0 * Float64(n * Float64(log(i) - log(n)))));
	else
		tmp = t_0;
	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[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.25e-167], t$95$0, If[LessEqual[n, -5e-310], N[(100.0 * N[(N[(n / i), $MachinePrecision] * N[(Exp[N[(N[Log[N[(n / i), $MachinePrecision]], $MachinePrecision] * (-n)), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.6e-63], N[(N[(n / i), $MachinePrecision] * N[(100.0 * N[(n * N[(N[Log[i], $MachinePrecision] - N[Log[n], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Target

Original	47.2
Target	47.2
Herbie	11.8

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

Derivation

1. Split input into 3 regimes

2. if n < -1.25000000000000005e-167 or 2.6000000000000001e-63 < n

   1. Initial program 51.4

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

   2. Simplified 51.2

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

      [Start] 51.4	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 51.2	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 51.2	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 51.2	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 51.2	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 51.2	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 51.2	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 51.2	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 48.2

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

   4. Simplified 9.3

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

      [Start] 48.2	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      associate-/l* [=>] 48.2	\[ 100 \cdot \color{blue}{\frac{n}{\frac{i}{e^{i} - 1}}} \]
      expm1-def [=>] 9.3	\[ 100 \cdot \frac{n}{\frac{i}{\color{blue}{\mathsf{expm1}\left(i\right)}}} \]

   if -1.25000000000000005e-167 < n < -4.999999999999985e-310

   1. Initial program 18.0

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

   2. Simplified 18.0

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

      [Start] 18.0	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-*r/ [=>] 18.0	\[ \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]
      sub-neg [=>] 18.0	\[ \frac{100 \cdot \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)\right)}}{\frac{i}{n}} \]
      metadata-eval [=>] 18.0	\[ \frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}\right)}{\frac{i}{n}} \]

   3. Taylor expanded in i around inf 64.0

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

   4. Simplified 12.5

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

      [Start] 64.0	\[ 100 \cdot \frac{n \cdot \left(e^{n \cdot \left(-1 \cdot \log \left(\frac{1}{i}\right) + \log \left(\frac{1}{n}\right)\right)} - 1\right)}{i} \]
      associate-/l* [=>] 64.0	\[ 100 \cdot \color{blue}{\frac{n}{\frac{i}{e^{n \cdot \left(-1 \cdot \log \left(\frac{1}{i}\right) + \log \left(\frac{1}{n}\right)\right)} - 1}}} \]
      associate-/r/ [=>] 64.0	\[ 100 \cdot \color{blue}{\left(\frac{n}{i} \cdot \left(e^{n \cdot \left(-1 \cdot \log \left(\frac{1}{i}\right) + \log \left(\frac{1}{n}\right)\right)} - 1\right)\right)} \]
      expm1-def [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \color{blue}{\mathsf{expm1}\left(n \cdot \left(-1 \cdot \log \left(\frac{1}{i}\right) + \log \left(\frac{1}{n}\right)\right)\right)}\right) \]
      mul-1-neg [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(\color{blue}{\left(-\log \left(\frac{1}{i}\right)\right)} + \log \left(\frac{1}{n}\right)\right)\right)\right) \]
      log-rec [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(\left(-\log \left(\frac{1}{i}\right)\right) + \color{blue}{\left(-\log n\right)}\right)\right)\right) \]
      distribute-neg-out [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \color{blue}{\left(-\left(\log \left(\frac{1}{i}\right) + \log n\right)\right)}\right)\right) \]
      +-commutative [<=] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\color{blue}{\left(\log n + \log \left(\frac{1}{i}\right)\right)}\right)\right)\right) \]
      /-rgt-identity [<=] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\log \color{blue}{\left(\frac{n}{1}\right)} + \log \left(\frac{1}{i}\right)\right)\right)\right)\right) \]
      log-div [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\color{blue}{\left(\log n - \log 1\right)} + \log \left(\frac{1}{i}\right)\right)\right)\right)\right) \]
      metadata-eval [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\left(\log n - \color{blue}{0}\right) + \log \left(\frac{1}{i}\right)\right)\right)\right)\right) \]
      associate-+l- [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\color{blue}{\left(\log n - \left(0 - \log \left(\frac{1}{i}\right)\right)\right)}\right)\right)\right) \]
      neg-sub0 [<=] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\log n - \color{blue}{\left(-\log \left(\frac{1}{i}\right)\right)}\right)\right)\right)\right) \]
      log-rec [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\log n - \left(-\color{blue}{\left(-\log i\right)}\right)\right)\right)\right)\right) \]
      remove-double-neg [=>] 64.0	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\left(\log n - \color{blue}{\log i}\right)\right)\right)\right) \]
      log-div [<=] 12.5	\[ 100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(n \cdot \left(-\color{blue}{\log \left(\frac{n}{i}\right)}\right)\right)\right) \]

   if -4.999999999999985e-310 < n < 2.6000000000000001e-63

   1. Initial program 46.4

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

   2. Simplified 46.4

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

      [Start] 46.4	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-*r/ [=>] 46.4	\[ \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]
      associate-/l* [<=] 46.4	\[ \color{blue}{\frac{\left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right) \cdot n}{i}} \]
      *-commutative [=>] 46.4	\[ \frac{\color{blue}{n \cdot \left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right)}}{i} \]
      associate-/l* [=>] 46.4	\[ \color{blue}{\frac{n}{\frac{i}{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}} \]
      associate-/r/ [=>] 46.4	\[ \color{blue}{\frac{n}{i} \cdot \left(100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)\right)} \]
      sub-neg [=>] 46.4	\[ \frac{n}{i} \cdot \left(100 \cdot \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)\right)}\right) \]
      distribute-lft-in [=>] 46.4	\[ \frac{n}{i} \cdot \color{blue}{\left(100 \cdot {\left(1 + \frac{i}{n}\right)}^{n} + 100 \cdot \left(-1\right)\right)} \]
      fma-def [=>] 46.4	\[ \frac{n}{i} \cdot \color{blue}{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \left(-1\right)\right)} \]
      metadata-eval [=>] 46.4	\[ \frac{n}{i} \cdot \mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \color{blue}{-1}\right) \]
      metadata-eval [=>] 46.4	\[ \frac{n}{i} \cdot \mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, \color{blue}{-100}\right) \]

   3. Taylor expanded in n around 0 21.5

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

   4. Simplified 21.5

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

      [Start] 21.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(-1 \cdot \log n + \log i\right)\right)\right) \]
      +-commutative [=>] 21.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \color{blue}{\left(\log i + -1 \cdot \log n\right)}\right)\right) \]
      mul-1-neg [=>] 21.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i + \color{blue}{\left(-\log n\right)}\right)\right)\right) \]
      unsub-neg [=>] 21.5	\[ \frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \color{blue}{\left(\log i - \log n\right)}\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 11.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -5 \cdot 10^{-310}:\\ \;\;\;\;100 \cdot \left(\frac{n}{i} \cdot \mathsf{expm1}\left(\log \left(\frac{n}{i}\right) \cdot \left(-n\right)\right)\right)\\ \mathbf{elif}\;n \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Error	12.3
Cost	13900

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -4.2 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -5 \cdot 10^{-308}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 2.6 \cdot 10^{-63}:\\ \;\;\;\;\frac{n}{i} \cdot \left(100 \cdot \left(n \cdot \left(\log i - \log n\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	13.8
Cost	7113

\[\begin{array}{l} \mathbf{if}\;n \leq -8 \cdot 10^{-189} \lor \neg \left(n \leq 2.6 \cdot 10^{-63}\right):\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 3
Error	18.5
Cost	1352

\[\begin{array}{l} \mathbf{if}\;n \leq -1.06 \cdot 10^{-188}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{elif}\;n \leq 1.14 \cdot 10^{-181}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + i \cdot 0.5\right) \cdot \left(n \cdot \frac{100}{1 + i \cdot \left(i \cdot -0.25\right)}\right)\\ \end{array} \]

Alternative 4
Error	18.4
Cost	1352

\[\begin{array}{l} t_0 := 1 + i \cdot 0.5\\ \mathbf{if}\;n \leq -9.6 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{100}{\frac{1 + \left(i \cdot i\right) \cdot -0.25}{n}}}{\frac{1}{t_0}}\\ \mathbf{elif}\;n \leq 1.14 \cdot 10^{-181}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(n \cdot \frac{100}{1 + i \cdot \left(i \cdot -0.25\right)}\right)\\ \end{array} \]

Alternative 5
Error	18.6
Cost	1096

\[\begin{array}{l} \mathbf{if}\;n \leq -4.4 \cdot 10^{-189}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{elif}\;n \leq 1.14 \cdot 10^{-181}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 6
Error	19.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;n \leq -1.6 \cdot 10^{-188} \lor \neg \left(n \leq 1.25 \cdot 10^{-181}\right):\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \end{array} \]

Alternative 7
Error	19.1
Cost	841

\[\begin{array}{l} \mathbf{if}\;n \leq -4.1 \cdot 10^{-189} \lor \neg \left(n \leq 1.14 \cdot 10^{-181}\right):\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 8
Error	21.2
Cost	713

\[\begin{array}{l} \mathbf{if}\;i \leq -1.6 \lor \neg \left(i \leq 2.3 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{n \cdot -200}{i}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \]

Alternative 9
Error	19.1
Cost	713

\[\begin{array}{l} \mathbf{if}\;n \leq -4.6 \cdot 10^{-189} \lor \neg \left(n \leq 1.14 \cdot 10^{-181}\right):\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \end{array} \]

Alternative 10
Error	21.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -2 \lor \neg \left(i \leq 8 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 11
Error	21.4
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -2 \lor \neg \left(i \leq 1.55 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{n \cdot -200}{i}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 12
Error	21.2
Cost	448

\[\frac{n}{0.01 + i \cdot -0.005} \]

Alternative 13
Error	62.1
Cost	192

\[i \cdot -50 \]

Alternative 14
Error	28.5
Cost	192

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023010 
(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))))