Compound Interest

Average Error: 74.86% → 0.82%

Time: 21.2s

Precision: binary64

Cost: 21768

Math

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

↓

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq 1000000000:\\ \;\;\;\;n \cdot \frac{t_0 \cdot 100 + -100}{i}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

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 (pow (+ 1.0 (/ i n)) n)) (t_1 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_1 5e-310)
     (/ (* (expm1 (* n (log1p (/ i n)))) 100.0) (/ i n))
     (if (<= t_1 1000000000.0)
       (* n (/ (+ (* t_0 100.0) -100.0) i))
       (* 100.0 (/ n (+ 1.0 (* i (+ -0.5 (* i 0.08333333333333333))))))))))

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 = pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 5e-310) {
		tmp = (expm1((n * log1p((i / n)))) * 100.0) / (i / n);
	} else if (t_1 <= 1000000000.0) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (-0.5 + (i * 0.08333333333333333)))));
	}
	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 = Math.pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 5e-310) {
		tmp = (Math.expm1((n * Math.log1p((i / n)))) * 100.0) / (i / n);
	} else if (t_1 <= 1000000000.0) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = 100.0 * (n / (1.0 + (i * (-0.5 + (i * 0.08333333333333333)))));
	}
	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 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_1 <= 5e-310:
		tmp = (math.expm1((n * math.log1p((i / n)))) * 100.0) / (i / n)
	elif t_1 <= 1000000000.0:
		tmp = n * (((t_0 * 100.0) + -100.0) / i)
	else:
		tmp = 100.0 * (n / (1.0 + (i * (-0.5 + (i * 0.08333333333333333)))))
	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(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 5e-310)
		tmp = Float64(Float64(expm1(Float64(n * log1p(Float64(i / n)))) * 100.0) / Float64(i / n));
	elseif (t_1 <= 1000000000.0)
		tmp = Float64(n * Float64(Float64(Float64(t_0 * 100.0) + -100.0) / i));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * Float64(-0.5 + Float64(i * 0.08333333333333333))))));
	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[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision]}, Block[{t$95$1 = N[(N[(t$95$0 + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-310], N[(N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] * 100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1000000000.0], N[(n * N[(N[(N[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(i * N[(-0.5 + N[(i * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	74.86%
Target	74.94%
Herbie	0.82%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)) < 4.999999999999985e-310

   1. Initial program 72.39

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

   2. Applied egg-rr 0.46

      \[\leadsto \color{blue}{\frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot 100}{\frac{i}{n}}} \]

   if 4.999999999999985e-310 < (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)) < 1e9

   1. Initial program 5.57

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

   2. Simplified 5.42

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

      [Start] 5.57	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 5.54	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      associate-*r* [=>] 5.56	\[ \color{blue}{\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot n} \]
      *-lft-identity [<=] 5.56	\[ \left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot \color{blue}{\left(1 \cdot n\right)} \]
      associate-*r* [=>] 5.56	\[ \color{blue}{\left(\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot 1\right) \cdot n} \]
      *-commutative [=>] 5.56	\[ \color{blue}{n \cdot \left(\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \cdot 1\right)} \]
      *-commutative [=>] 5.56	\[ n \cdot \color{blue}{\left(1 \cdot \left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 5.56	\[ n \cdot \color{blue}{\left(100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      associate-*r/ [=>] 5.42	\[ n \cdot \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{i}} \]
      sub-neg [=>] 5.42	\[ n \cdot \frac{100 \cdot \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)\right)}}{i} \]
      distribute-lft-in [=>] 5.53	\[ n \cdot \frac{\color{blue}{100 \cdot {\left(1 + \frac{i}{n}\right)}^{n} + 100 \cdot \left(-1\right)}}{i} \]
      fma-def [=>] 5.42	\[ n \cdot \frac{\color{blue}{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \left(-1\right)\right)}}{i} \]
      metadata-eval [=>] 5.42	\[ n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, 100 \cdot \color{blue}{-1}\right)}{i} \]
      metadata-eval [=>] 5.42	\[ n \cdot \frac{\mathsf{fma}\left(100, {\left(1 + \frac{i}{n}\right)}^{n}, \color{blue}{-100}\right)}{i} \]

   3. Applied egg-rr 5.53

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

   if 1e9 < (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

   1. Initial program 99.11

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

   2. Taylor expanded in n around inf 97.63

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

   3. Simplified 21.92

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

      [Start] 97.63	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      *-commutative [=>] 97.63	\[ \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i} \cdot 100} \]
      associate-/l* [=>] 97.63	\[ \color{blue}{\frac{n}{\frac{i}{e^{i} - 1}}} \cdot 100 \]
      expm1-def [=>] 21.92	\[ \frac{n}{\frac{i}{\color{blue}{\mathsf{expm1}\left(i\right)}}} \cdot 100 \]

   4. Taylor expanded in i around 0 1.03

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

   5. Simplified 1.03

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

      [Start] 1.03	\[ \frac{n}{1 + \left(0.08333333333333333 \cdot {i}^{2} + -0.5 \cdot i\right)} \cdot 100 \]
      +-commutative [=>] 1.03	\[ \frac{n}{1 + \color{blue}{\left(-0.5 \cdot i + 0.08333333333333333 \cdot {i}^{2}\right)}} \cdot 100 \]
      *-commutative [=>] 1.03	\[ \frac{n}{1 + \left(\color{blue}{i \cdot -0.5} + 0.08333333333333333 \cdot {i}^{2}\right)} \cdot 100 \]
      *-commutative [=>] 1.03	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{{i}^{2} \cdot 0.08333333333333333}\right)} \cdot 100 \]
      unpow2 [=>] 1.03	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{\left(i \cdot i\right)} \cdot 0.08333333333333333\right)} \cdot 100 \]
      associate-*l* [=>] 1.03	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{i \cdot \left(i \cdot 0.08333333333333333\right)}\right)} \cdot 100 \]
      distribute-lft-out [=>] 1.03	\[ \frac{n}{1 + \color{blue}{i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}} \cdot 100 \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.82

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 5 \cdot 10^{-310}:\\ \;\;\;\;\frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot 100}{\frac{i}{n}}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 1000000000:\\ \;\;\;\;n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} \cdot 100 + -100}{i}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	1.95%
Cost	21768

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-310}:\\ \;\;\;\;n \cdot \left(\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;t_1 \leq 1000000000:\\ \;\;\;\;n \cdot \frac{t_0 \cdot 100 + -100}{i}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 2
Error	1.8%
Cost	21768

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-310}:\\ \;\;\;\;n \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{\frac{i}{100}}\\ \mathbf{elif}\;t_1 \leq 1000000000:\\ \;\;\;\;n \cdot \frac{t_0 \cdot 100 + -100}{i}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 3
Error	18.92%
Cost	7244

\[\begin{array}{l} t_0 := n \cdot \left(\frac{100}{i} \cdot \mathsf{expm1}\left(i\right)\right)\\ \mathbf{if}\;n \leq -8.5 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 9 \cdot 10^{+17}:\\ \;\;\;\;\frac{n \cdot 100}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	18.53%
Cost	7244

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.96 \cdot 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 7.2 \cdot 10^{-211}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{n \cdot 100}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	18.63%
Cost	7244

\[\begin{array}{l} t_0 := \frac{i}{\mathsf{expm1}\left(i\right)}\\ \mathbf{if}\;n \leq -1.96 \cdot 10^{-169}:\\ \;\;\;\;\frac{n \cdot 100}{t_0}\\ \mathbf{elif}\;n \leq 2.3 \cdot 10^{-219}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 2 \cdot 10^{+17}:\\ \;\;\;\;\frac{n \cdot 100}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{t_0}\\ \end{array} \]

Alternative 6
Error	21.21%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;i \leq -0.001:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 100}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 7
Error	21.44%
Cost	6980

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00068:\\ \;\;\;\;\mathsf{expm1}\left(i\right) \cdot \left(100 \cdot \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 100}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 8
Error	28.82%
Cost	1224

\[\begin{array}{l} \mathbf{if}\;n \leq -2.15 \cdot 10^{-169}:\\ \;\;\;\;n \cdot \frac{1}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(-100 + i \cdot -50\right) \cdot \frac{n}{-1 + i \cdot \left(i \cdot 0.25\right)}\\ \end{array} \]

Alternative 9
Error	28.9%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;n \leq -1.96 \cdot 10^{-169}:\\ \;\;\;\;n \cdot \frac{1}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 1.22 \cdot 10^{-216}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 10
Error	31%
Cost	972

\[\begin{array}{l} \mathbf{if}\;i \leq -0.000135:\\ \;\;\;\;-1 + \left(1 + \frac{n}{i} \cdot -200\right)\\ \mathbf{elif}\;i \leq 1.32 \cdot 10^{+71}:\\ \;\;\;\;n \cdot \left(100 + i \cdot \left(50 + i \cdot 16.666666666666668\right)\right)\\ \mathbf{elif}\;i \leq 6.2 \cdot 10^{+114}:\\ \;\;\;\;n \cdot \frac{-100}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 11
Error	29%
Cost	968

\[\begin{array}{l} \mathbf{if}\;n \leq -1.96 \cdot 10^{-169}:\\ \;\;\;\;n \cdot \frac{1}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 2.45 \cdot 10^{-222}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot \left(-0.005 + i \cdot 0.0008333333333333334\right)}\\ \end{array} \]

Alternative 12
Error	29.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;n \leq -1.96 \cdot 10^{-169} \lor \neg \left(n \leq 3.4 \cdot 10^{-222}\right):\\ \;\;\;\;n \cdot \frac{1}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 13
Error	29.7%
Cost	840

\[\begin{array}{l} \mathbf{if}\;n \leq -1.96 \cdot 10^{-169}:\\ \;\;\;\;n \cdot \frac{1}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 2.25 \cdot 10^{-222}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \]

Alternative 14
Error	29.7%
Cost	713

\[\begin{array}{l} \mathbf{if}\;n \leq -1.96 \cdot 10^{-169} \lor \neg \left(n \leq 6.6 \cdot 10^{-211}\right):\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 15
Error	33.06%
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq -1.6:\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+92}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-200}{\frac{i}{n}}\\ \end{array} \]

Alternative 16
Error	33.51%
Cost	585

\[\begin{array}{l} \mathbf{if}\;i \leq -2 \lor \neg \left(i \leq 1.35 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 17
Error	33.41%
Cost	584

\[\begin{array}{l} \mathbf{if}\;i \leq -2:\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+92}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;\frac{-200}{\frac{i}{n}}\\ \end{array} \]

Alternative 18
Error	32.86%
Cost	448

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

Alternative 19
Error	96.98%
Cost	192

\[i \cdot -50 \]

Alternative 20
Error	43.96%
Cost	192

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023089 
(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))))