Compound Interest

Average Accuracy: 25.5% → 98.3%

Time: 24.3s

Precision: binary64

Cost: 21768

Math

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

↓

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n} + -1\\ t_1 := \frac{t_0}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-173}:\\ \;\;\;\;\frac{100}{\frac{\frac{i}{n}}{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}}\\ \mathbf{elif}\;t_1 \leq 20000000000:\\ \;\;\;\;\frac{n \cdot t_0}{\frac{i}{100}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

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) -1.0)) (t_1 (/ t_0 (/ i n))))
   (if (<= t_1 5e-173)
     (/ 100.0 (/ (/ i n) (expm1 (* n (log1p (/ i n))))))
     (if (<= t_1 20000000000.0)
       (/ (* n t_0) (/ i 100.0))
       (* 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) + -1.0;
	double t_1 = t_0 / (i / n);
	double tmp;
	if (t_1 <= 5e-173) {
		tmp = 100.0 / ((i / n) / expm1((n * log1p((i / n)))));
	} else if (t_1 <= 20000000000.0) {
		tmp = (n * t_0) / (i / 100.0);
	} 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) + -1.0;
	double t_1 = t_0 / (i / n);
	double tmp;
	if (t_1 <= 5e-173) {
		tmp = 100.0 / ((i / n) / Math.expm1((n * Math.log1p((i / n)))));
	} else if (t_1 <= 20000000000.0) {
		tmp = (n * t_0) / (i / 100.0);
	} 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) + -1.0
	t_1 = t_0 / (i / n)
	tmp = 0
	if t_1 <= 5e-173:
		tmp = 100.0 / ((i / n) / math.expm1((n * math.log1p((i / n)))))
	elif t_1 <= 20000000000.0:
		tmp = (n * t_0) / (i / 100.0)
	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((Float64(1.0 + Float64(i / n)) ^ n) + -1.0)
	t_1 = Float64(t_0 / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 5e-173)
		tmp = Float64(100.0 / Float64(Float64(i / n) / expm1(Float64(n * log1p(Float64(i / n))))));
	elseif (t_1 <= 20000000000.0)
		tmp = Float64(Float64(n * t_0) / Float64(i / 100.0));
	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[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-173], N[(100.0 / N[(N[(i / n), $MachinePrecision] / N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 20000000000.0], N[(N[(n * t$95$0), $MachinePrecision] / N[(i / 100.0), $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	25.5%
Target	25.7%
Herbie	98.3%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)) < 5.0000000000000002e-173

   1. Initial program 28.6%

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

   2. Applied egg-rr 98.1%

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

      [Start] 28.6	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-*r/ [=>] 28.6	\[ \color{blue}{\frac{100 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}{\frac{i}{n}}} \]
      associate-/l* [=>] 28.6	\[ \color{blue}{\frac{100}{\frac{\frac{i}{n}}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      *-un-lft-identity [=>] 28.6	\[ \frac{100}{\frac{\frac{i}{n}}{\color{blue}{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}} \]
      associate-/r* [=>] 28.6	\[ \frac{100}{\color{blue}{\frac{\frac{\frac{i}{n}}{1}}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      associate-/r* [<=] 28.6	\[ \frac{100}{\color{blue}{\frac{\frac{i}{n}}{1 \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right)}}} \]
      *-un-lft-identity [<=] 28.6	\[ \frac{100}{\frac{\frac{i}{n}}{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      pow-to-exp [=>] 27.7	\[ \frac{100}{\frac{\frac{i}{n}}{\color{blue}{e^{\log \left(1 + \frac{i}{n}\right) \cdot n}} - 1}} \]
      expm1-def [=>] 39.0	\[ \frac{100}{\frac{\frac{i}{n}}{\color{blue}{\mathsf{expm1}\left(\log \left(1 + \frac{i}{n}\right) \cdot n\right)}}} \]
      *-commutative [=>] 39.0	\[ \frac{100}{\frac{\frac{i}{n}}{\mathsf{expm1}\left(\color{blue}{n \cdot \log \left(1 + \frac{i}{n}\right)}\right)}} \]
      log1p-def [=>] 98.1	\[ \frac{100}{\frac{\frac{i}{n}}{\mathsf{expm1}\left(n \cdot \color{blue}{\mathsf{log1p}\left(\frac{i}{n}\right)}\right)}} \]

   if 5.0000000000000002e-173 < (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)) < 2e10

   1. Initial program 97.0%

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

   2. Simplified 97.0%

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

      [Start] 97.0	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      associate-/r/ [=>] 97.0	\[ 100 \cdot \color{blue}{\left(\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i} \cdot n\right)} \]
      *-commutative [=>] 97.0	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)} \]
      *-rgt-identity [<=] 97.0	\[ 100 \cdot \left(\color{blue}{\left(n \cdot 1\right)} \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right) \]
      associate-*l* [=>] 97.0	\[ 100 \cdot \color{blue}{\left(n \cdot \left(1 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}\right)\right)} \]
      *-lft-identity [=>] 97.0	\[ 100 \cdot \left(n \cdot \color{blue}{\frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{i}}\right) \]
      sub-neg [=>] 97.0	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + \left(-1\right)}}{i}\right) \]
      metadata-eval [=>] 97.0	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + \color{blue}{-1}}{i}\right) \]

   3. Applied egg-rr 97.2%

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

      [Start] 97.0	\[ 100 \cdot \left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{i}\right) \]
      *-commutative [=>] 97.0	\[ \color{blue}{\left(n \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{i}\right) \cdot 100} \]
      associate-*r/ [=>] 97.1	\[ \color{blue}{\frac{n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)}{i}} \cdot 100 \]
      associate-*l/ [=>] 97.2	\[ \color{blue}{\frac{\left(n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)\right) \cdot 100}{i}} \]
      associate-/l* [=>] 97.2	\[ \color{blue}{\frac{n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)}{\frac{i}{100}}} \]

   if 2e10 < (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

   1. Initial program 0.6%

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

   2. Taylor expanded in n around inf 2.2%

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

   3. Simplified 78.3%

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

      [Start] 2.2	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      *-commutative [=>] 2.2	\[ \color{blue}{\frac{n \cdot \left(e^{i} - 1\right)}{i} \cdot 100} \]
      associate-/l* [=>] 2.2	\[ \color{blue}{\frac{n}{\frac{i}{e^{i} - 1}}} \cdot 100 \]
      expm1-def [=>] 78.3	\[ \frac{n}{\frac{i}{\color{blue}{\mathsf{expm1}\left(i\right)}}} \cdot 100 \]

   4. Taylor expanded in i around 0 99.3%

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

   5. Simplified 99.3%

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

      [Start] 99.3	\[ \frac{n}{1 + \left(0.08333333333333333 \cdot {i}^{2} + -0.5 \cdot i\right)} \cdot 100 \]
      +-commutative [=>] 99.3	\[ \frac{n}{1 + \color{blue}{\left(-0.5 \cdot i + 0.08333333333333333 \cdot {i}^{2}\right)}} \cdot 100 \]
      *-commutative [=>] 99.3	\[ \frac{n}{1 + \left(\color{blue}{i \cdot -0.5} + 0.08333333333333333 \cdot {i}^{2}\right)} \cdot 100 \]
      *-commutative [=>] 99.3	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{{i}^{2} \cdot 0.08333333333333333}\right)} \cdot 100 \]
      unpow2 [=>] 99.3	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{\left(i \cdot i\right)} \cdot 0.08333333333333333\right)} \cdot 100 \]
      associate-*l* [=>] 99.3	\[ \frac{n}{1 + \left(i \cdot -0.5 + \color{blue}{i \cdot \left(i \cdot 0.08333333333333333\right)}\right)} \cdot 100 \]
      distribute-lft-out [=>] 99.3	\[ \frac{n}{1 + \color{blue}{i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}} \cdot 100 \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 5 \cdot 10^{-173}:\\ \;\;\;\;\frac{100}{\frac{\frac{i}{n}}{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}}\\ \mathbf{elif}\;\frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}} \leq 20000000000:\\ \;\;\;\;\frac{n \cdot \left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)}{\frac{i}{100}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.7%
Cost	22408

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{\frac{i}{100 \cdot \mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_1 \leq 20000000000:\\ \;\;\;\;100 \cdot \left(\frac{\frac{i}{n} \cdot t_0 - \frac{i}{n}}{\frac{i}{n}} \cdot \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 2
Accuracy	82.7%
Cost	21832

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{\frac{i}{100 \cdot \mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_1 \leq 20000000000:\\ \;\;\;\;\frac{n \cdot \left(100 + t_0 \cdot -100\right)}{-i}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 3
Accuracy	82.7%
Cost	21768

\[\begin{array}{l} t_0 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{1}{\frac{\frac{i}{100 \cdot \mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_0 \leq 20000000000:\\ \;\;\;\;t_0 \cdot 100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 4
Accuracy	82.7%
Cost	21768

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n} + -1\\ t_1 := \frac{t_0}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{\frac{\frac{i}{100 \cdot \mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_1 \leq 20000000000:\\ \;\;\;\;\frac{n \cdot t_0}{\frac{i}{100}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 5
Accuracy	97.7%
Cost	21768

\[\begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n} + -1\\ t_1 := \frac{t_0}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{-173}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{i}\right)\\ \mathbf{elif}\;t_1 \leq 20000000000:\\ \;\;\;\;\frac{n \cdot t_0}{\frac{i}{100}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \end{array} \]

Alternative 6
Accuracy	82.2%
Cost	7244

\[\begin{array}{l} t_0 := 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{if}\;n \leq -2.1 \cdot 10^{-202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 5.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Accuracy	82.3%
Cost	7244

\[\begin{array}{l} t_0 := \frac{\mathsf{expm1}\left(i\right)}{i}\\ \mathbf{if}\;n \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;100 \cdot \left(n \cdot t_0\right)\\ \mathbf{elif}\;n \leq 3 \cdot 10^{-240}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 \cdot t_0\right)\\ \end{array} \]

Alternative 8
Accuracy	82.2%
Cost	7244

\[\begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 6.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Accuracy	82.2%
Cost	7244

\[\begin{array}{l} \mathbf{if}\;n \leq -6 \cdot 10^{-203}:\\ \;\;\;\;\frac{1}{\frac{\frac{i}{100 \cdot \mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;n \leq 2.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot \left(-0.5 + i \cdot 0.08333333333333333\right)}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \end{array} \]

Alternative 10
Accuracy	69.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;\frac{1}{\frac{0.01 + i \cdot -0.005}{n}}\\ \mathbf{elif}\;n \leq 5.2 \cdot 10^{-242}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.01}{n} + \frac{i}{n} \cdot -0.005}\\ \end{array} \]

Alternative 11
Accuracy	69.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;n \leq -1.9 \cdot 10^{-202}:\\ \;\;\;\;\frac{1}{\frac{0.01 + i \cdot -0.005}{n}}\\ \mathbf{elif}\;n \leq 5.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{0.01}{n} + \frac{-0.005}{\frac{n}{i}}}\\ \end{array} \]

Alternative 12
Accuracy	69.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;n \leq -1.25 \cdot 10^{-202} \lor \neg \left(n \leq 6 \cdot 10^{-240}\right):\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \end{array} \]

Alternative 13
Accuracy	69.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;n \leq -2.6 \cdot 10^{-202} \lor \neg \left(n \leq 9.4 \cdot 10^{-242}\right):\\ \;\;\;\;\frac{1}{\frac{0.01 + i \cdot -0.005}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \end{array} \]

Alternative 14
Accuracy	64.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+115} \lor \neg \left(i \leq 10^{-48}\right):\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 15
Accuracy	65.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;i \leq -1.45 \lor \neg \left(i \leq 180\right):\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \]

Alternative 16
Accuracy	68.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;i \leq -0.5 \lor \neg \left(i \leq 1.05 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \]

Alternative 17
Accuracy	57.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;n \leq -4.4 \cdot 10^{-256}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 1.38 \cdot 10^{-241}:\\ \;\;\;\;i \cdot \left(n \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \]

Alternative 18
Accuracy	3.0%
Cost	192

\[i \cdot -50 \]

Alternative 19
Accuracy	55.9%
Cost	192

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023135 
(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))))