Compound Interest

Average Error: 48.1 → 11.1

Time: 24.3s

Precision: binary64

Cost: 20104

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 17:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\log i - \log n\right) \cdot \left(100 \cdot \frac{{n}^{2}}{i}\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (i n)
 :precision binary64
 (if (<= i -0.00175)
   (* 100.0 (/ (- (exp i) 1.0) (/ i n)))
   (if (<= i 17.0)
     (/
      (* n -100.0)
      (- (+ (* 0.5 i) (* -0.08333333333333333 (pow i 2.0))) 1.0))
     (* (- (log i) (log n)) (* 100.0 (/ (pow n 2.0) 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 (i <= -0.00175) {
		tmp = 100.0 * ((exp(i) - 1.0) / (i / n));
	} else if (i <= 17.0) {
		tmp = (n * -100.0) / (((0.5 * i) + (-0.08333333333333333 * pow(i, 2.0))) - 1.0);
	} else {
		tmp = (log(i) - log(n)) * (100.0 * (pow(n, 2.0) / i));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 100.0d0 * ((((1.0d0 + (i / n)) ** n) - 1.0d0) / (i / n))
end function

↓

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= (-0.00175d0)) then
        tmp = 100.0d0 * ((exp(i) - 1.0d0) / (i / n))
    else if (i <= 17.0d0) then
        tmp = (n * (-100.0d0)) / (((0.5d0 * i) + ((-0.08333333333333333d0) * (i ** 2.0d0))) - 1.0d0)
    else
        tmp = (log(i) - log(n)) * (100.0d0 * ((n ** 2.0d0) / i))
    end if
    code = tmp
end function

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 (i <= -0.00175) {
		tmp = 100.0 * ((Math.exp(i) - 1.0) / (i / n));
	} else if (i <= 17.0) {
		tmp = (n * -100.0) / (((0.5 * i) + (-0.08333333333333333 * Math.pow(i, 2.0))) - 1.0);
	} else {
		tmp = (Math.log(i) - Math.log(n)) * (100.0 * (Math.pow(n, 2.0) / 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 i <= -0.00175:
		tmp = 100.0 * ((math.exp(i) - 1.0) / (i / n))
	elif i <= 17.0:
		tmp = (n * -100.0) / (((0.5 * i) + (-0.08333333333333333 * math.pow(i, 2.0))) - 1.0)
	else:
		tmp = (math.log(i) - math.log(n)) * (100.0 * (math.pow(n, 2.0) / 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 (i <= -0.00175)
		tmp = Float64(100.0 * Float64(Float64(exp(i) - 1.0) / Float64(i / n)));
	elseif (i <= 17.0)
		tmp = Float64(Float64(n * -100.0) / Float64(Float64(Float64(0.5 * i) + Float64(-0.08333333333333333 * (i ^ 2.0))) - 1.0));
	else
		tmp = Float64(Float64(log(i) - log(n)) * Float64(100.0 * Float64((n ^ 2.0) / i)));
	end
	return tmp
end

MATLAB

function tmp = code(i, n)
	tmp = 100.0 * ((((1.0 + (i / n)) ^ n) - 1.0) / (i / n));
end

↓

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= -0.00175)
		tmp = 100.0 * ((exp(i) - 1.0) / (i / n));
	elseif (i <= 17.0)
		tmp = (n * -100.0) / (((0.5 * i) + (-0.08333333333333333 * (i ^ 2.0))) - 1.0);
	else
		tmp = (log(i) - log(n)) * (100.0 * ((n ^ 2.0) / i));
	end
	tmp_2 = 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[i, -0.00175], N[(100.0 * N[(N[(N[Exp[i], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 17.0], N[(N[(n * -100.0), $MachinePrecision] / N[(N[(N[(0.5 * i), $MachinePrecision] + N[(-0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[Log[i], $MachinePrecision] - N[Log[n], $MachinePrecision]), $MachinePrecision] * N[(100.0 * N[(N[Power[n, 2.0], $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	48.1
Target	47.5
Herbie	11.1

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

Derivation

1. Split input into 3 regimes

2. if i < -0.00175000000000000004

   1. Initial program 29.0

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

   2. Taylor expanded in n around inf 11.6

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

   if -0.00175000000000000004 < i < 17

   1. Initial program 58.4

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

   2. Taylor expanded in n around inf 57.5

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

   3. Simplified 57.5

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

      [Start] 57.5	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      rational.json-simplify-2 [=>] 57.5	\[ 100 \cdot \frac{\color{blue}{\left(e^{i} - 1\right) \cdot n}}{i} \]
      rational.json-simplify-49 [=>] 57.5	\[ 100 \cdot \color{blue}{\left(n \cdot \frac{e^{i} - 1}{i}\right)} \]
      rational.json-simplify-16 [=>] 57.5	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{e^{i} + -1}}{i}\right) \]
      rational.json-simplify-1 [=>] 57.5	\[ 100 \cdot \left(n \cdot \frac{\color{blue}{-1 + e^{i}}}{i}\right) \]

   4. Applied egg-rr 57.5

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

   5. Simplified 57.5

      \[\leadsto \color{blue}{\frac{n \cdot -100}{\frac{i}{1 - e^{i}}}} \]
      Proof

      [Start] 57.5	\[ \frac{-100 \cdot n}{-\frac{i}{-1 + e^{i}}} \]
      rational.json-simplify-10 [=>] 57.5	\[ \frac{\color{blue}{\frac{100 \cdot n}{-1}}}{-\frac{i}{-1 + e^{i}}} \]
      rational.json-simplify-49 [=>] 57.5	\[ \frac{\color{blue}{n \cdot \frac{100}{-1}}}{-\frac{i}{-1 + e^{i}}} \]
      metadata-eval [=>] 57.5	\[ \frac{n \cdot \color{blue}{-100}}{-\frac{i}{-1 + e^{i}}} \]
      rational.json-simplify-8 [=>] 57.5	\[ \frac{n \cdot -100}{\color{blue}{\frac{i}{-1 + e^{i}} \cdot -1}} \]
      rational.json-simplify-2 [=>] 57.5	\[ \frac{n \cdot -100}{\color{blue}{-1 \cdot \frac{i}{-1 + e^{i}}}} \]
      rational.json-simplify-49 [<=] 57.5	\[ \frac{n \cdot -100}{\color{blue}{\frac{i \cdot -1}{-1 + e^{i}}}} \]
      rational.json-simplify-8 [<=] 57.5	\[ \frac{n \cdot -100}{\frac{\color{blue}{-i}}{-1 + e^{i}}} \]
      rational.json-simplify-1 [=>] 57.5	\[ \frac{n \cdot -100}{\frac{-i}{\color{blue}{e^{i} + -1}}} \]
      rational.json-simplify-16 [<=] 57.5	\[ \frac{n \cdot -100}{\frac{-i}{\color{blue}{e^{i} - 1}}} \]
      rational.json-simplify-50 [<=] 57.5	\[ \frac{n \cdot -100}{\color{blue}{\frac{i}{1 - e^{i}}}} \]

   6. Taylor expanded in i around 0 8.8

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

   if 17 < i

   1. Initial program 32.2

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

   2. Simplified 32.2

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

      [Start] 32.2	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      rational.json-simplify-61 [=>] 32.2	\[ 100 \cdot \color{blue}{\frac{n}{\frac{i}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      rational.json-simplify-7 [<=] 32.2	\[ 100 \cdot \frac{\color{blue}{\frac{n}{1}}}{\frac{i}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}} \]
      rational.json-simplify-46 [<=] 32.2	\[ 100 \cdot \color{blue}{\frac{n}{1 \cdot \frac{i}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      rational.json-simplify-6 [=>] 32.2	\[ 100 \cdot \frac{n}{\color{blue}{\frac{i}{{\left(1 + \frac{i}{n}\right)}^{n} - 1}}} \]
      rational.json-simplify-16 [=>] 32.2	\[ 100 \cdot \frac{n}{\frac{i}{\color{blue}{{\left(1 + \frac{i}{n}\right)}^{n} + -1}}} \]

   3. Taylor expanded in n around 0 21.0

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

   4. Simplified 21.0

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

      [Start] 21.0	\[ 100 \cdot \frac{{n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)}{i} \]
      rational.json-simplify-2 [=>] 21.0	\[ 100 \cdot \frac{\color{blue}{\left(-1 \cdot \log n + \log i\right) \cdot {n}^{2}}}{i} \]
      rational.json-simplify-49 [=>] 21.0	\[ 100 \cdot \color{blue}{\left({n}^{2} \cdot \frac{-1 \cdot \log n + \log i}{i}\right)} \]
      rational.json-simplify-2 [=>] 21.0	\[ 100 \cdot \left({n}^{2} \cdot \frac{\color{blue}{\log n \cdot -1} + \log i}{i}\right) \]
      rational.json-simplify-9 [=>] 21.0	\[ 100 \cdot \left({n}^{2} \cdot \frac{\color{blue}{\left(-\log n\right)} + \log i}{i}\right) \]

   5. Taylor expanded in n around 0 21.0

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

   6. Simplified 21.2

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

      [Start] 21.0	\[ 100 \cdot \frac{\left(\log i - \log n\right) \cdot {n}^{2}}{i} \]
      rational.json-simplify-2 [=>] 21.0	\[ 100 \cdot \frac{\color{blue}{{n}^{2} \cdot \left(\log i - \log n\right)}}{i} \]
      rational.json-simplify-49 [=>] 21.2	\[ 100 \cdot \color{blue}{\left(\left(\log i - \log n\right) \cdot \frac{{n}^{2}}{i}\right)} \]
      rational.json-simplify-43 [=>] 21.2	\[ \color{blue}{\left(\log i - \log n\right) \cdot \left(\frac{{n}^{2}}{i} \cdot 100\right)} \]
      rational.json-simplify-2 [<=] 21.2	\[ \left(\log i - \log n\right) \cdot \color{blue}{\left(100 \cdot \frac{{n}^{2}}{i}\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 11.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 17:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\log i - \log n\right) \cdot \left(100 \cdot \frac{{n}^{2}}{i}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	11.1
Cost	20104

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 1:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left({n}^{2} \cdot \frac{\log i - \log n}{i}\right)\\ \end{array} \]

Alternative 2
Error	11.1
Cost	13832

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 0.41:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{n \cdot \left(\left(-\log n\right) + \log i\right)}}\\ \end{array} \]

Alternative 3
Error	11.1
Cost	13832

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 1.1:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n \cdot \left(\left(-\log n\right) + \log i\right)}{\frac{i}{n}}\\ \end{array} \]

Alternative 4
Error	12.4
Cost	7692

\[\begin{array}{l} \mathbf{if}\;i \leq -0.00175:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 0.072:\\ \;\;\;\;\frac{n \cdot -100}{\left(0.5 \cdot i + -0.08333333333333333 \cdot {i}^{2}\right) - 1}\\ \mathbf{elif}\;i \leq 3.6 \cdot 10^{+186}:\\ \;\;\;\;100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 5
Error	12.6
Cost	7560

\[\begin{array}{l} \mathbf{if}\;i \leq -0.000145:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 0.46:\\ \;\;\;\;\left(100 + \left({i}^{2} \cdot 16.666666666666668 + i \cdot 50\right)\right) \cdot n\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{{\left(1 + \frac{i}{n}\right)}^{n} + -1}}\\ \end{array} \]

Alternative 6
Error	12.6
Cost	7560

\[\begin{array}{l} \mathbf{if}\;i \leq -0.000145:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 1.35:\\ \;\;\;\;\left(100 + \left({i}^{2} \cdot 16.666666666666668 + i \cdot 50\right)\right) \cdot n\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \end{array} \]

Alternative 7
Error	12.3
Cost	7432

\[\begin{array}{l} \mathbf{if}\;i \leq -0.000145:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 7.5:\\ \;\;\;\;n \cdot \left({i}^{2} \cdot 16.666666666666668 + \left(100 + i \cdot 50\right)\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 8
Error	12.3
Cost	7432

\[\begin{array}{l} \mathbf{if}\;i \leq -0.000145:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 2.7:\\ \;\;\;\;\left(100 + \left({i}^{2} \cdot 16.666666666666668 + i \cdot 50\right)\right) \cdot n\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 9
Error	12.5
Cost	7108

\[\begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{-6}:\\ \;\;\;\;100 \cdot \left(n \cdot \frac{-1 + e^{i}}{i}\right)\\ \mathbf{elif}\;i \leq 0.065:\\ \;\;\;\;\frac{n \cdot -100}{0.5 \cdot i - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 10
Error	12.3
Cost	7108

\[\begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{-6}:\\ \;\;\;\;100 \cdot \frac{e^{i} - 1}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 0.25:\\ \;\;\;\;\frac{n \cdot -100}{0.5 \cdot i - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 11
Error	19.9
Cost	840

\[\begin{array}{l} \mathbf{if}\;i \leq -2.5 \cdot 10^{-12}:\\ \;\;\;\;100 \cdot \left(\left(n + -3\right) - -3\right)\\ \mathbf{elif}\;i \leq 0.82:\\ \;\;\;\;\frac{n \cdot -100}{0.5 \cdot i - 1}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 12
Error	19.6
Cost	712

\[\begin{array}{l} t_0 := 100 \cdot \left(\left(1 + n\right) - 1\right)\\ \mathbf{if}\;i \leq -1.65 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-35}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	19.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;100 \cdot \left(\left(n + -3\right) - -3\right)\\ \mathbf{elif}\;i \leq 7.8 \cdot 10^{-36}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(\left(1 + n\right) - 1\right)\\ \end{array} \]

Alternative 14
Error	19.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq -3.4 \cdot 10^{-12}:\\ \;\;\;\;100 \cdot \left(\left(n + -3\right) - -3\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-36}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(\left(1 + n\right) - 1\right)\\ \end{array} \]

Alternative 15
Error	19.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq -1.5 \cdot 10^{-12}:\\ \;\;\;\;100 \cdot \left(\left(n + -3\right) - -3\right)\\ \mathbf{elif}\;i \leq 9.5:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{0}{\frac{i}{n}}\\ \end{array} \]

Alternative 16
Error	62.1
Cost	192

\[-50 \cdot i \]

Alternative 17
Error	28.1
Cost	192

\[n \cdot 100 \]

Reproduce

herbie shell --seed 2023074 
(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))))