Compound Interest

Average Error: 75.07% → 21.45%

Time: 17.8s

Precision: binary64

Cost: 13768

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{100}{\frac{i}{n \cdot \mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq 3 \cdot 10^{-280}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \log \left(\frac{i}{n}\right)\right)}{i}\right)\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-42}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (i n)
 :precision binary64
 (if (<= n -5.5e-110)
   (/ 100.0 (/ i (* n (expm1 i))))
   (if (<= n 3e-280)
     (* 100.0 (* n (/ (expm1 (* n (log (/ i n)))) i)))
     (if (<= n 6e-42)
       (/ n (+ 0.01 (* i -0.005)))
       (* 100.0 (* n (/ (expm1 i) i)))))))

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 tmp;
	if (n <= -5.5e-110) {
		tmp = 100.0 / (i / (n * expm1(i)));
	} else if (n <= 3e-280) {
		tmp = 100.0 * (n * (expm1((n * log((i / n)))) / i));
	} else if (n <= 6e-42) {
		tmp = n / (0.01 + (i * -0.005));
	} else {
		tmp = 100.0 * (n * (expm1(i) / i));
	}
	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 tmp;
	if (n <= -5.5e-110) {
		tmp = 100.0 / (i / (n * Math.expm1(i)));
	} else if (n <= 3e-280) {
		tmp = 100.0 * (n * (Math.expm1((n * Math.log((i / n)))) / i));
	} else if (n <= 6e-42) {
		tmp = n / (0.01 + (i * -0.005));
	} else {
		tmp = 100.0 * (n * (Math.expm1(i) / i));
	}
	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):
	tmp = 0
	if n <= -5.5e-110:
		tmp = 100.0 / (i / (n * math.expm1(i)))
	elif n <= 3e-280:
		tmp = 100.0 * (n * (math.expm1((n * math.log((i / n)))) / i))
	elif n <= 6e-42:
		tmp = n / (0.01 + (i * -0.005))
	else:
		tmp = 100.0 * (n * (math.expm1(i) / i))
	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)
	tmp = 0.0
	if (n <= -5.5e-110)
		tmp = Float64(100.0 / Float64(i / Float64(n * expm1(i))));
	elseif (n <= 3e-280)
		tmp = Float64(100.0 * Float64(n * Float64(expm1(Float64(n * log(Float64(i / n)))) / i)));
	elseif (n <= 6e-42)
		tmp = Float64(n / Float64(0.01 + Float64(i * -0.005)));
	else
		tmp = Float64(100.0 * Float64(n * Float64(expm1(i) / i)));
	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_] := If[LessEqual[n, -5.5e-110], N[(100.0 / N[(i / N[(n * N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 3e-280], N[(100.0 * N[(n * N[(N[(Exp[N[(n * N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6e-42], N[(n / N[(0.01 + N[(i * -0.005), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n * N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	75.07%
Target	74.01%
Herbie	21.45%

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

Derivation

1. Split input into 4 regimes

2. if n < -5.4999999999999998e-110

   1. Initial program 72.95

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

   2. Simplified 72.72

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

      [Start] 72.95	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 72.72	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 72.72	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 72.72	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 72.72	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 72.72	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 72.72	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 72.72	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 71.96

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

   4. Simplified 19.75

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

      [Start] 71.96	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      associate-*r/ [=>] 72.04	\[ \color{blue}{\frac{100 \cdot \left(n \cdot \left(e^{i} - 1\right)\right)}{i}} \]
      associate-/l* [=>] 71.79	\[ \color{blue}{\frac{100}{\frac{i}{n \cdot \left(e^{i} - 1\right)}}} \]
      expm1-def [=>] 19.75	\[ \frac{100}{\frac{i}{n \cdot \color{blue}{\mathsf{expm1}\left(i\right)}}} \]

   if -5.4999999999999998e-110 < n < 2.99999999999999987e-280

   1. Initial program 44.36

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

   2. Simplified 45.28

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

      [Start] 44.36	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 45.28	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 45.28	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 45.28	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 45.28	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 45.28	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 45.28	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 45.28	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in i around -inf 50.82

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

   4. Simplified 39.52

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

      [Start] 50.82	\[ 100 \cdot \left(n \cdot \frac{e^{n \cdot \left(-1 \cdot \log \left(\frac{-1}{i}\right) + \log \left(-\frac{1}{n}\right)\right)} - 1}{i}\right) \]
      expm1-def [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{\mathsf{expm1}\left(n \cdot \left(-1 \cdot \log \left(\frac{-1}{i}\right) + \log \left(-\frac{1}{n}\right)\right)\right)}}{i}\right) \]
      +-commutative [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \color{blue}{\left(\log \left(-\frac{1}{n}\right) + -1 \cdot \log \left(\frac{-1}{i}\right)\right)}\right)}{i}\right) \]
      mul-1-neg [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \left(\log \left(-\frac{1}{n}\right) + \color{blue}{\left(-\log \left(\frac{-1}{i}\right)\right)}\right)\right)}{i}\right) \]
      unsub-neg [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \color{blue}{\left(\log \left(-\frac{1}{n}\right) - \log \left(\frac{-1}{i}\right)\right)}\right)}{i}\right) \]
      distribute-neg-frac [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \left(\log \color{blue}{\left(\frac{-1}{n}\right)} - \log \left(\frac{-1}{i}\right)\right)\right)}{i}\right) \]
      metadata-eval [=>] 39.52	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \left(\log \left(\frac{\color{blue}{-1}}{n}\right) - \log \left(\frac{-1}{i}\right)\right)\right)}{i}\right) \]

   5. Applied egg-rr 34.43

      \[\leadsto 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \color{blue}{\left(0 + \log \left(\frac{1}{n} \cdot i\right)\right)}\right)}{i}\right) \]

   6. Simplified 34.35

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

      [Start] 34.43	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \left(0 + \log \left(\frac{1}{n} \cdot i\right)\right)\right)}{i}\right) \]
      +-lft-identity [=>] 34.43	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \color{blue}{\log \left(\frac{1}{n} \cdot i\right)}\right)}{i}\right) \]
      associate-*l/ [=>] 34.35	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \log \color{blue}{\left(\frac{1 \cdot i}{n}\right)}\right)}{i}\right) \]
      *-lft-identity [=>] 34.35	\[ 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \log \left(\frac{\color{blue}{i}}{n}\right)\right)}{i}\right) \]

   if 2.99999999999999987e-280 < n < 6.00000000000000054e-42

   1. Initial program 77.21

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

   2. Simplified 77.21

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

      [Start] 77.21	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 77.21	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 77.21	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 77.21	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 77.21	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 77.21	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 77.21	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 77.21	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 90.42

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

   4. Simplified 58.82

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

      [Start] 90.42	\[ 100 \cdot \left(n \cdot \frac{e^{i} - 1}{i}\right) \]
      expm1-def [=>] 58.82	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{\mathsf{expm1}\left(i\right)}}{i}\right) \]

   5. Applied egg-rr 58.89

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

   6. Taylor expanded in i around 0 38.28

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

   7. Simplified 38.28

      \[\leadsto \frac{n}{\color{blue}{0.01 + i \cdot -0.005}} \]
      Proof

      [Start] 38.28	\[ \frac{n}{0.01 + -0.005 \cdot i} \]
      *-commutative [=>] 38.28	\[ \frac{n}{0.01 + \color{blue}{i \cdot -0.005}} \]

   if 6.00000000000000054e-42 < n

   1. Initial program 94.7

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

   2. Simplified 94.11

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

      [Start] 94.7	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 94.11	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 94.11	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 94.11	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 94.11	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 94.11	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 94.11	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 94.11	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Taylor expanded in n around inf 78.62

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

   4. Simplified 5.54

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

      [Start] 78.62	\[ 100 \cdot \left(n \cdot \frac{e^{i} - 1}{i}\right) \]
      expm1-def [=>] 5.54	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{\mathsf{expm1}\left(i\right)}}{i}\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 21.45

   \[\leadsto \begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{-110}:\\ \;\;\;\;\frac{100}{\frac{i}{n \cdot \mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq 3 \cdot 10^{-280}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \log \left(\frac{i}{n}\right)\right)}{i}\right)\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-42}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	17.83%
Cost	21768

\[\begin{array}{l} t_0 := {\left(\frac{i}{n} + 1\right)}^{n} + -1\\ t_1 := \frac{t_0}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{elif}\;t_1 \leq 10000000000:\\ \;\;\;\;\frac{n \cdot t_0}{\frac{i}{100}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \end{array} \]

Alternative 2
Error	17.91%
Cost	21640

\[\begin{array}{l} t_0 := \frac{{\left(\frac{i}{n} + 1\right)}^{n} + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{elif}\;t_0 \leq 10000000000:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{-1 + {\left(\frac{i}{n}\right)}^{n}}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \end{array} \]

Alternative 3
Error	19.59%
Cost	7244

\[\begin{array}{l} t_0 := 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{if}\;n \leq -1.95 \cdot 10^{-181}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6 \cdot 10^{-42}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	30.53%
Cost	836

\[\begin{array}{l} \mathbf{if}\;n \leq -1.95 \cdot 10^{-181}:\\ \;\;\;\;\frac{100}{\frac{1}{n} + \frac{i}{n} \cdot -0.5}\\ \mathbf{elif}\;n \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \end{array} \]

Alternative 5
Error	30.61%
Cost	713

\[\begin{array}{l} \mathbf{if}\;n \leq -2.3 \cdot 10^{-181} \lor \neg \left(n \leq 2 \cdot 10^{-265}\right):\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 6
Error	42.11%
Cost	712

\[\begin{array}{l} \mathbf{if}\;n \leq -2.7 \cdot 10^{-241}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 1.1 \cdot 10^{-265}:\\ \;\;\;\;n \cdot \left(\left(i \cdot i\right) \cdot 16.666666666666668\right)\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 7
Error	42.3%
Cost	712

\[\begin{array}{l} \mathbf{if}\;n \leq -1 \cdot 10^{-248}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 3.6 \cdot 10^{-265}:\\ \;\;\;\;n \cdot \left(\left(i \cdot i\right) \cdot 16.666666666666668\right)\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + i \cdot -50\\ \end{array} \]

Alternative 8
Error	42.42%
Cost	712

\[\begin{array}{l} \mathbf{if}\;n \leq -2.35 \cdot 10^{-276}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 3.1 \cdot 10^{-266}:\\ \;\;\;\;\frac{100}{\frac{i}{n \cdot i}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100 + i \cdot -50\\ \end{array} \]

Alternative 9
Error	42.34%
Cost	584

\[\begin{array}{l} \mathbf{if}\;n \leq -1.35 \cdot 10^{-277}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 2.7 \cdot 10^{-267}:\\ \;\;\;\;\left(n \cdot i\right) \cdot 50\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 10
Error	32.83%
Cost	448

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

Alternative 11
Error	43.56%
Cost	192

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023121 
(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))))