Compound Interest

Average Error: 47.9 → 13.0

Time: 1.2min

Precision: binary64

Cost: 20564

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 12:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+204}:\\ \;\;\;\;{n}^{2} \cdot \left(\left(\left(-\log n\right) + \log i\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+272}:\\ \;\;\;\;\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right) \cdot \frac{100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

FPCore

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

↓

(FPCore (i n)
 :precision binary64
 (if (<= i -4.2e-9)
   (* n (* (+ -1.0 (exp i)) (/ 100.0 i)))
   (if (<= i 6.8e-98)
     (- (/ 76800.0 (/ 1024.0 n)) (/ 25600.0 (/ -1024.0 n)))
     (if (<= i 4.2e-22)
       (* 100.0 (* (/ i n) (/ 1.0 (/ i (* n n)))))
       (if (<= i 12.0)
         (* n (* 50.0 (+ i 2.0)))
         (if (<= i 1.75e+204)
           (* (pow n 2.0) (* (+ (- (log n)) (log i)) (/ 100.0 i)))
           (if (<= i 3.2e+272)
             (* (+ (pow (+ 1.0 (/ i n)) n) -1.0) (/ 100.0 (/ i n)))
             0.0)))))))

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 tmp;
	if (i <= -4.2e-9) {
		tmp = n * ((-1.0 + exp(i)) * (100.0 / i));
	} else if (i <= 6.8e-98) {
		tmp = (76800.0 / (1024.0 / n)) - (25600.0 / (-1024.0 / n));
	} else if (i <= 4.2e-22) {
		tmp = 100.0 * ((i / n) * (1.0 / (i / (n * n))));
	} else if (i <= 12.0) {
		tmp = n * (50.0 * (i + 2.0));
	} else if (i <= 1.75e+204) {
		tmp = pow(n, 2.0) * ((-log(n) + log(i)) * (100.0 / i));
	} else if (i <= 3.2e+272) {
		tmp = (pow((1.0 + (i / n)), n) + -1.0) * (100.0 / (i / n));
	} else {
		tmp = 0.0;
	}
	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 <= (-4.2d-9)) then
        tmp = n * (((-1.0d0) + exp(i)) * (100.0d0 / i))
    else if (i <= 6.8d-98) then
        tmp = (76800.0d0 / (1024.0d0 / n)) - (25600.0d0 / ((-1024.0d0) / n))
    else if (i <= 4.2d-22) then
        tmp = 100.0d0 * ((i / n) * (1.0d0 / (i / (n * n))))
    else if (i <= 12.0d0) then
        tmp = n * (50.0d0 * (i + 2.0d0))
    else if (i <= 1.75d+204) then
        tmp = (n ** 2.0d0) * ((-log(n) + log(i)) * (100.0d0 / i))
    else if (i <= 3.2d+272) then
        tmp = (((1.0d0 + (i / n)) ** n) + (-1.0d0)) * (100.0d0 / (i / n))
    else
        tmp = 0.0d0
    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 <= -4.2e-9) {
		tmp = n * ((-1.0 + Math.exp(i)) * (100.0 / i));
	} else if (i <= 6.8e-98) {
		tmp = (76800.0 / (1024.0 / n)) - (25600.0 / (-1024.0 / n));
	} else if (i <= 4.2e-22) {
		tmp = 100.0 * ((i / n) * (1.0 / (i / (n * n))));
	} else if (i <= 12.0) {
		tmp = n * (50.0 * (i + 2.0));
	} else if (i <= 1.75e+204) {
		tmp = Math.pow(n, 2.0) * ((-Math.log(n) + Math.log(i)) * (100.0 / i));
	} else if (i <= 3.2e+272) {
		tmp = (Math.pow((1.0 + (i / n)), n) + -1.0) * (100.0 / (i / n));
	} else {
		tmp = 0.0;
	}
	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):
	tmp = 0
	if i <= -4.2e-9:
		tmp = n * ((-1.0 + math.exp(i)) * (100.0 / i))
	elif i <= 6.8e-98:
		tmp = (76800.0 / (1024.0 / n)) - (25600.0 / (-1024.0 / n))
	elif i <= 4.2e-22:
		tmp = 100.0 * ((i / n) * (1.0 / (i / (n * n))))
	elif i <= 12.0:
		tmp = n * (50.0 * (i + 2.0))
	elif i <= 1.75e+204:
		tmp = math.pow(n, 2.0) * ((-math.log(n) + math.log(i)) * (100.0 / i))
	elif i <= 3.2e+272:
		tmp = (math.pow((1.0 + (i / n)), n) + -1.0) * (100.0 / (i / n))
	else:
		tmp = 0.0
	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)
	tmp = 0.0
	if (i <= -4.2e-9)
		tmp = Float64(n * Float64(Float64(-1.0 + exp(i)) * Float64(100.0 / i)));
	elseif (i <= 6.8e-98)
		tmp = Float64(Float64(76800.0 / Float64(1024.0 / n)) - Float64(25600.0 / Float64(-1024.0 / n)));
	elseif (i <= 4.2e-22)
		tmp = Float64(100.0 * Float64(Float64(i / n) * Float64(1.0 / Float64(i / Float64(n * n)))));
	elseif (i <= 12.0)
		tmp = Float64(n * Float64(50.0 * Float64(i + 2.0)));
	elseif (i <= 1.75e+204)
		tmp = Float64((n ^ 2.0) * Float64(Float64(Float64(-log(n)) + log(i)) * Float64(100.0 / i)));
	elseif (i <= 3.2e+272)
		tmp = Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) + -1.0) * Float64(100.0 / Float64(i / n)));
	else
		tmp = 0.0;
	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 <= -4.2e-9)
		tmp = n * ((-1.0 + exp(i)) * (100.0 / i));
	elseif (i <= 6.8e-98)
		tmp = (76800.0 / (1024.0 / n)) - (25600.0 / (-1024.0 / n));
	elseif (i <= 4.2e-22)
		tmp = 100.0 * ((i / n) * (1.0 / (i / (n * n))));
	elseif (i <= 12.0)
		tmp = n * (50.0 * (i + 2.0));
	elseif (i <= 1.75e+204)
		tmp = (n ^ 2.0) * ((-log(n) + log(i)) * (100.0 / i));
	elseif (i <= 3.2e+272)
		tmp = (((1.0 + (i / n)) ^ n) + -1.0) * (100.0 / (i / n));
	else
		tmp = 0.0;
	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, -4.2e-9], N[(n * N[(N[(-1.0 + N[Exp[i], $MachinePrecision]), $MachinePrecision] * N[(100.0 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e-98], N[(N[(76800.0 / N[(1024.0 / n), $MachinePrecision]), $MachinePrecision] - N[(25600.0 / N[(-1024.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.2e-22], N[(100.0 * N[(N[(i / n), $MachinePrecision] * N[(1.0 / N[(i / N[(n * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 12.0], N[(n * N[(50.0 * N[(i + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e+204], N[(N[Power[n, 2.0], $MachinePrecision] * N[(N[((-N[Log[n], $MachinePrecision]) + N[Log[i], $MachinePrecision]), $MachinePrecision] * N[(100.0 / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.2e+272], N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision] * N[(100.0 / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.0]]]]]]

Target

Original	47.9
Target	47.6
Herbie	13.0

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

Derivation

1. Split input into 7 regimes

2. if i < -4.20000000000000039e-9

   1. Initial program 29.4

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

   2. Simplified 29.3

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

      [Start] 29.4	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      rational_best-simplify-55 [=>] 29.3	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot \frac{100}{\frac{i}{n}}} \]
      rational_best-simplify-18 [=>] 29.3	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)} \cdot \frac{100}{\frac{i}{n}} \]

   3. Taylor expanded in n around inf 13.1

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

   4. Simplified 13.1

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

      [Start] 13.1	\[ 100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i} \]
      rational_best-simplify-55 [=>] 13.1	\[ \color{blue}{\left(n \cdot \left(e^{i} - 1\right)\right) \cdot \frac{100}{i}} \]
      rational_best-simplify-1 [=>] 13.1	\[ \color{blue}{\frac{100}{i} \cdot \left(n \cdot \left(e^{i} - 1\right)\right)} \]
      rational_best-simplify-1 [=>] 13.1	\[ \frac{100}{i} \cdot \color{blue}{\left(\left(e^{i} - 1\right) \cdot n\right)} \]
      rational_best-simplify-50 [=>] 13.1	\[ \color{blue}{n \cdot \left(\left(e^{i} - 1\right) \cdot \frac{100}{i}\right)} \]
      rational_best-simplify-18 [=>] 13.1	\[ n \cdot \left(\color{blue}{\left(e^{i} + -1\right)} \cdot \frac{100}{i}\right) \]
      rational_best-simplify-3 [=>] 13.1	\[ n \cdot \left(\color{blue}{\left(-1 + e^{i}\right)} \cdot \frac{100}{i}\right) \]

   if -4.20000000000000039e-9 < i < 6.8000000000000003e-98

   1. Initial program 58.9

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

   2. Taylor expanded in i around 0 27.9

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]

   3. Applied egg-rr 7.6

      \[\leadsto 100 \cdot \color{blue}{\left(\frac{1}{\frac{0.5}{n}} \cdot 0.5\right)} \]

   4. Simplified 7.6

      \[\leadsto 100 \cdot \color{blue}{\frac{2}{\frac{2}{n}}} \]
      Proof

      [Start] 7.6	\[ 100 \cdot \left(\frac{1}{\frac{0.5}{n}} \cdot 0.5\right) \]
      rational_best-simplify-1 [<=] 7.6	\[ 100 \cdot \color{blue}{\left(0.5 \cdot \frac{1}{\frac{0.5}{n}}\right)} \]
      rational_best-simplify-55 [=>] 7.6	\[ 100 \cdot \color{blue}{\left(1 \cdot \frac{0.5}{\frac{0.5}{n}}\right)} \]
      rational_best-simplify-1 [=>] 7.6	\[ 100 \cdot \color{blue}{\left(\frac{0.5}{\frac{0.5}{n}} \cdot 1\right)} \]
      rational_best-simplify-7 [=>] 7.6	\[ 100 \cdot \color{blue}{\frac{0.5}{\frac{0.5}{n}}} \]
      rational_best-simplify-108 [=>] 7.6	\[ 100 \cdot \color{blue}{\frac{0.5 + 0.5}{\frac{0.5}{n} + \frac{0.5}{n}}} \]
      metadata-eval [=>] 7.6	\[ 100 \cdot \frac{\color{blue}{1}}{\frac{0.5}{n} + \frac{0.5}{n}} \]
      rational_best-simplify-108 [=>] 7.6	\[ 100 \cdot \color{blue}{\frac{1 + 1}{\left(\frac{0.5}{n} + \frac{0.5}{n}\right) + \left(\frac{0.5}{n} + \frac{0.5}{n}\right)}} \]
      metadata-eval [=>] 7.6	\[ 100 \cdot \frac{\color{blue}{2}}{\left(\frac{0.5}{n} + \frac{0.5}{n}\right) + \left(\frac{0.5}{n} + \frac{0.5}{n}\right)} \]
      rational_best-simplify-64 [=>] 7.6	\[ 100 \cdot \frac{2}{\color{blue}{\frac{0.5 + 0.5}{n}} + \left(\frac{0.5}{n} + \frac{0.5}{n}\right)} \]
      metadata-eval [=>] 7.6	\[ 100 \cdot \frac{2}{\frac{\color{blue}{1}}{n} + \left(\frac{0.5}{n} + \frac{0.5}{n}\right)} \]
      rational_best-simplify-64 [=>] 7.6	\[ 100 \cdot \frac{2}{\frac{1}{n} + \color{blue}{\frac{0.5 + 0.5}{n}}} \]
      metadata-eval [=>] 7.6	\[ 100 \cdot \frac{2}{\frac{1}{n} + \frac{\color{blue}{1}}{n}} \]
      rational_best-simplify-64 [=>] 7.6	\[ 100 \cdot \frac{2}{\color{blue}{\frac{1 + 1}{n}}} \]
      metadata-eval [=>] 7.6	\[ 100 \cdot \frac{2}{\frac{\color{blue}{2}}{n}} \]

   5. Applied egg-rr 7.7

      \[\leadsto \color{blue}{\frac{100}{\frac{1}{n}} + 0} \]

   6. Simplified 7.6

      \[\leadsto \color{blue}{\frac{12800}{\frac{128}{n}}} \]
      Proof

      [Start] 7.7	\[ \frac{100}{\frac{1}{n}} + 0 \]
      rational_best-simplify-3 [<=] 7.7	\[ \color{blue}{0 + \frac{100}{\frac{1}{n}}} \]
      rational_best-simplify-6 [=>] 7.7	\[ \color{blue}{\frac{100}{\frac{1}{n}}} \]
      metadata-eval [<=] 7.7	\[ \frac{\color{blue}{\frac{200}{2}}}{\frac{1}{n}} \]
      rational_best-simplify-54 [<=] 7.7	\[ \color{blue}{\frac{200}{2 \cdot \frac{1}{n}}} \]
      rational_best-simplify-55 [=>] 7.7	\[ \frac{200}{\color{blue}{1 \cdot \frac{2}{n}}} \]
      rational_best-simplify-1 [<=] 7.7	\[ \frac{200}{\color{blue}{\frac{2}{n} \cdot 1}} \]
      rational_best-simplify-7 [=>] 7.7	\[ \frac{200}{\color{blue}{\frac{2}{n}}} \]
      rational_best-simplify-108 [=>] 7.7	\[ \color{blue}{\frac{200 + 200}{\frac{2}{n} + \frac{2}{n}}} \]
      metadata-eval [=>] 7.7	\[ \frac{\color{blue}{400}}{\frac{2}{n} + \frac{2}{n}} \]
      rational_best-simplify-64 [=>] 7.7	\[ \frac{400}{\color{blue}{\frac{2 + 2}{n}}} \]
      metadata-eval [=>] 7.7	\[ \frac{400}{\frac{\color{blue}{4}}{n}} \]
      rational_best-simplify-108 [=>] 7.7	\[ \color{blue}{\frac{400 + 400}{\frac{4}{n} + \frac{4}{n}}} \]
      metadata-eval [=>] 7.7	\[ \frac{\color{blue}{800}}{\frac{4}{n} + \frac{4}{n}} \]
      rational_best-simplify-64 [=>] 7.7	\[ \frac{800}{\color{blue}{\frac{4 + 4}{n}}} \]
      metadata-eval [=>] 7.7	\[ \frac{800}{\frac{\color{blue}{8}}{n}} \]
      rational_best-simplify-108 [=>] 7.6	\[ \color{blue}{\frac{800 + 800}{\frac{8}{n} + \frac{8}{n}}} \]
      metadata-eval [=>] 7.6	\[ \frac{\color{blue}{1600}}{\frac{8}{n} + \frac{8}{n}} \]
      rational_best-simplify-64 [=>] 7.6	\[ \frac{1600}{\color{blue}{\frac{8 + 8}{n}}} \]
      metadata-eval [=>] 7.6	\[ \frac{1600}{\frac{\color{blue}{16}}{n}} \]
      rational_best-simplify-108 [=>] 7.6	\[ \color{blue}{\frac{1600 + 1600}{\frac{16}{n} + \frac{16}{n}}} \]
      rational_best-simplify-108 [=>] 7.6	\[ \color{blue}{\frac{\left(1600 + 1600\right) + \left(1600 + 1600\right)}{\left(\frac{16}{n} + \frac{16}{n}\right) + \left(\frac{16}{n} + \frac{16}{n}\right)}} \]
      rational_best-simplify-108 [=>] 7.6	\[ \color{blue}{\frac{\left(\left(1600 + 1600\right) + \left(1600 + 1600\right)\right) + \left(\left(1600 + 1600\right) + \left(1600 + 1600\right)\right)}{\left(\left(\frac{16}{n} + \frac{16}{n}\right) + \left(\frac{16}{n} + \frac{16}{n}\right)\right) + \left(\left(\frac{16}{n} + \frac{16}{n}\right) + \left(\frac{16}{n} + \frac{16}{n}\right)\right)}} \]

   7. Applied egg-rr 7.7

      \[\leadsto \color{blue}{\frac{\frac{307200}{\frac{1024}{n}}}{4} - \frac{\frac{12800}{\frac{-128}{n}}}{4}} \]

   8. Simplified 7.6

      \[\leadsto \color{blue}{\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}} \]
      Proof

      [Start] 7.7	\[ \frac{\frac{307200}{\frac{1024}{n}}}{4} - \frac{\frac{12800}{\frac{-128}{n}}}{4} \]
      rational_best-simplify-49 [=>] 7.6	\[ \color{blue}{\frac{\frac{307200}{4}}{\frac{1024}{n}}} - \frac{\frac{12800}{\frac{-128}{n}}}{4} \]
      metadata-eval [=>] 7.6	\[ \frac{\color{blue}{76800}}{\frac{1024}{n}} - \frac{\frac{12800}{\frac{-128}{n}}}{4} \]
      rational_best-simplify-108 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\color{blue}{\frac{12800 + 12800}{\frac{-128}{n} + \frac{-128}{n}}}}{4} \]
      metadata-eval [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\frac{\color{blue}{25600}}{\frac{-128}{n} + \frac{-128}{n}}}{4} \]
      rational_best-simplify-108 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\color{blue}{\frac{25600 + 25600}{\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)}}}{4} \]
      metadata-eval [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\frac{\color{blue}{51200}}{\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)}}{4} \]
      rational_best-simplify-108 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\color{blue}{\frac{51200 + 51200}{\left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)}}}{4} \]
      metadata-eval [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\frac{\color{blue}{102400}}{\left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)}}{4} \]
      rational_best-simplify-49 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \color{blue}{\frac{\frac{102400}{4}}{\left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)}} \]
      metadata-eval [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{\color{blue}{25600}}{\left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)} \]
      rational_best-simplify-64 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{25600}{\left(\color{blue}{\frac{-128 + -128}{n}} + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)} \]
      rational_best-simplify-64 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{25600}{\left(\frac{-128 + -128}{n} + \color{blue}{\frac{-128 + -128}{n}}\right) + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)} \]
      rational_best-simplify-64 [=>] 7.6	\[ \frac{76800}{\frac{1024}{n}} - \frac{25600}{\color{blue}{\frac{\left(-128 + -128\right) + \left(-128 + -128\right)}{n}} + \left(\left(\frac{-128}{n} + \frac{-128}{n}\right) + \left(\frac{-128}{n} + \frac{-128}{n}\right)\right)} \]

   if 6.8000000000000003e-98 < i < 4.20000000000000016e-22

   1. Initial program 54.8

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

   2. Taylor expanded in i around 0 21.8

      \[\leadsto 100 \cdot \frac{\color{blue}{i}}{\frac{i}{n}} \]

   3. Applied egg-rr 22.7

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

   4. Simplified 31.3

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

      [Start] 22.7	\[ 100 \cdot \left(\frac{0.5}{\frac{i}{n}} \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{0.5}{n}}\right)\right) \]
      rational_best-simplify-1 [<=] 22.7	\[ 100 \cdot \color{blue}{\left(\left(\frac{i}{n} \cdot \frac{1}{\frac{0.5}{n}}\right) \cdot \frac{0.5}{\frac{i}{n}}\right)} \]
      rational_best-simplify-81 [=>] 21.4	\[ 100 \cdot \color{blue}{\frac{\frac{1}{\frac{0.5}{n}} \cdot 0.5}{\frac{\frac{i}{n}}{\frac{i}{n}}}} \]
      rational_best-simplify-1 [<=] 21.4	\[ 100 \cdot \frac{\color{blue}{0.5 \cdot \frac{1}{\frac{0.5}{n}}}}{\frac{\frac{i}{n}}{\frac{i}{n}}} \]
      rational_best-simplify-55 [=>] 21.4	\[ 100 \cdot \frac{\color{blue}{1 \cdot \frac{0.5}{\frac{0.5}{n}}}}{\frac{\frac{i}{n}}{\frac{i}{n}}} \]
      rational_best-simplify-82 [=>] 31.4	\[ 100 \cdot \color{blue}{\left(\left(\frac{i}{n} \cdot 1\right) \cdot \frac{\frac{0.5}{\frac{0.5}{n}}}{\frac{i}{n}}\right)} \]
      rational_best-simplify-7 [=>] 31.4	\[ 100 \cdot \left(\color{blue}{\frac{i}{n}} \cdot \frac{\frac{0.5}{\frac{0.5}{n}}}{\frac{i}{n}}\right) \]
      rational_best-simplify-108 [=>] 31.4	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{\color{blue}{\frac{0.5 + 0.5}{\frac{0.5}{n} + \frac{0.5}{n}}}}{\frac{i}{n}}\right) \]
      metadata-eval [=>] 31.4	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{\frac{\color{blue}{1}}{\frac{0.5}{n} + \frac{0.5}{n}}}{\frac{i}{n}}\right) \]
      rational_best-simplify-53 [=>] 31.4	\[ 100 \cdot \left(\frac{i}{n} \cdot \color{blue}{\frac{1}{\left(\frac{0.5}{n} + \frac{0.5}{n}\right) \cdot \frac{i}{n}}}\right) \]
      rational_best-simplify-64 [=>] 31.4	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\color{blue}{\frac{0.5 + 0.5}{n}} \cdot \frac{i}{n}}\right) \]
      metadata-eval [=>] 31.4	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{\color{blue}{1}}{n} \cdot \frac{i}{n}}\right) \]
      rational_best-simplify-79 [=>] 31.3	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\color{blue}{\frac{1 \cdot i}{n \cdot n}}}\right) \]
      rational_best-simplify-1 [<=] 31.3	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{\color{blue}{i \cdot 1}}{n \cdot n}}\right) \]
      rational_best-simplify-7 [=>] 31.3	\[ 100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{\color{blue}{i}}{n \cdot n}}\right) \]

   if 4.20000000000000016e-22 < i < 12

   1. Initial program 53.0

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

   2. Taylor expanded in i around 0 26.6

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

   3. Applied egg-rr 26.7

      \[\leadsto \color{blue}{\frac{\left(n \cdot \left(i \cdot \frac{n + -1}{n} + 2\right)\right) \cdot 400}{8}} \]

   4. Simplified 26.7

      \[\leadsto \color{blue}{\frac{n \cdot \left(\left(\left(i - -2\right) - \frac{i}{n}\right) \cdot 400\right)}{8}} \]
      Proof

      [Start] 26.7	\[ \frac{\left(n \cdot \left(i \cdot \frac{n + -1}{n} + 2\right)\right) \cdot 400}{8} \]
      rational_best-simplify-1 [=>] 26.7	\[ \frac{\color{blue}{400 \cdot \left(n \cdot \left(i \cdot \frac{n + -1}{n} + 2\right)\right)}}{8} \]
      rational_best-simplify-1 [=>] 26.7	\[ \frac{400 \cdot \color{blue}{\left(\left(i \cdot \frac{n + -1}{n} + 2\right) \cdot n\right)}}{8} \]
      rational_best-simplify-50 [=>] 26.7	\[ \frac{\color{blue}{n \cdot \left(\left(i \cdot \frac{n + -1}{n} + 2\right) \cdot 400\right)}}{8} \]
      rational_best-simplify-3 [=>] 26.7	\[ \frac{n \cdot \left(\color{blue}{\left(2 + i \cdot \frac{n + -1}{n}\right)} \cdot 400\right)}{8} \]
      rational_best-simplify-59 [=>] 26.7	\[ \frac{n \cdot \left(\color{blue}{\left(i \cdot \frac{n + -1}{n} - \left(-2\right)\right)} \cdot 400\right)}{8} \]
      rational_best-simplify-55 [=>] 26.7	\[ \frac{n \cdot \left(\left(\color{blue}{\left(n + -1\right) \cdot \frac{i}{n}} - \left(-2\right)\right) \cdot 400\right)}{8} \]
      rational_best-simplify-46 [=>] 26.7	\[ \frac{n \cdot \left(\left(\color{blue}{\left(i - \frac{i}{n}\right)} - \left(-2\right)\right) \cdot 400\right)}{8} \]
      metadata-eval [=>] 26.7	\[ \frac{n \cdot \left(\left(\left(i - \frac{i}{n}\right) - \color{blue}{-2}\right) \cdot 400\right)}{8} \]
      rational_best-simplify-48 [=>] 26.7	\[ \frac{n \cdot \left(\color{blue}{\left(\left(i - -2\right) - \frac{i}{n}\right)} \cdot 400\right)}{8} \]

   5. Taylor expanded in n around inf 25.9

      \[\leadsto \color{blue}{50 \cdot \left(n \cdot \left(2 + i\right)\right)} \]

   6. Simplified 25.9

      \[\leadsto \color{blue}{n \cdot \left(50 \cdot \left(i + 2\right)\right)} \]
      Proof

      [Start] 25.9	\[ 50 \cdot \left(n \cdot \left(2 + i\right)\right) \]
      rational_best-simplify-1 [=>] 25.9	\[ 50 \cdot \color{blue}{\left(\left(2 + i\right) \cdot n\right)} \]
      rational_best-simplify-3 [=>] 25.9	\[ 50 \cdot \left(\color{blue}{\left(i + 2\right)} \cdot n\right) \]
      rational_best-simplify-50 [=>] 25.9	\[ \color{blue}{n \cdot \left(\left(i + 2\right) \cdot 50\right)} \]
      rational_best-simplify-1 [=>] 25.9	\[ n \cdot \color{blue}{\left(50 \cdot \left(i + 2\right)\right)} \]

   if 12 < i < 1.74999999999999995e204

   1. Initial program 29.5

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

   2. Simplified 29.5

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

      [Start] 29.5	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      rational_best-simplify-55 [=>] 29.5	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot \frac{100}{\frac{i}{n}}} \]
      rational_best-simplify-18 [=>] 29.5	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)} \cdot \frac{100}{\frac{i}{n}} \]

   3. Taylor expanded in n around 0 17.8

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

   4. Simplified 17.7

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

      [Start] 17.8	\[ 100 \cdot \frac{{n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)}{i} \]
      rational_best-simplify-55 [=>] 17.7	\[ \color{blue}{\left({n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)\right) \cdot \frac{100}{i}} \]
      rational_best-simplify-1 [=>] 17.7	\[ \color{blue}{\frac{100}{i} \cdot \left({n}^{2} \cdot \left(-1 \cdot \log n + \log i\right)\right)} \]
      rational_best-simplify-1 [=>] 17.7	\[ \frac{100}{i} \cdot \color{blue}{\left(\left(-1 \cdot \log n + \log i\right) \cdot {n}^{2}\right)} \]
      rational_best-simplify-50 [=>] 17.7	\[ \color{blue}{{n}^{2} \cdot \left(\left(-1 \cdot \log n + \log i\right) \cdot \frac{100}{i}\right)} \]
      rational_best-simplify-1 [=>] 17.7	\[ {n}^{2} \cdot \left(\left(\color{blue}{\log n \cdot -1} + \log i\right) \cdot \frac{100}{i}\right) \]
      rational_best-simplify-10 [=>] 17.7	\[ {n}^{2} \cdot \left(\left(\color{blue}{\left(-\log n\right)} + \log i\right) \cdot \frac{100}{i}\right) \]

   if 1.74999999999999995e204 < i < 3.19999999999999985e272

   1. Initial program 32.6

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

   2. Simplified 32.5

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

      [Start] 32.6	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      rational_best-simplify-55 [=>] 32.5	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot \frac{100}{\frac{i}{n}}} \]
      rational_best-simplify-18 [=>] 32.5	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)} \cdot \frac{100}{\frac{i}{n}} \]

   if 3.19999999999999985e272 < i

   1. Initial program 33.0

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

   2. Simplified 32.9

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

      [Start] 33.0	\[ 100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \]
      rational_best-simplify-55 [=>] 32.9	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} - 1\right) \cdot \frac{100}{\frac{i}{n}}} \]
      rational_best-simplify-18 [=>] 32.9	\[ \color{blue}{\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right)} \cdot \frac{100}{\frac{i}{n}} \]

   3. Taylor expanded in i around 0 29.7

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

   4. Taylor expanded in i around 0 29.7

      \[\leadsto \color{blue}{0} \]
3. Recombined 7 regimes into one program.

4. Final simplification 13.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 12:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{+204}:\\ \;\;\;\;{n}^{2} \cdot \left(\left(\left(-\log n\right) + \log i\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{+272}:\\ \;\;\;\;\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right) \cdot \frac{100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternatives

Alternative 1
Error	13.0
Cost	14228

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 12:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{+204}:\\ \;\;\;\;100 \cdot \frac{n \cdot \left(\left(-\log n\right) + \log i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 1.25 \cdot 10^{+272}:\\ \;\;\;\;\left({\left(1 + \frac{i}{n}\right)}^{n} + -1\right) \cdot \frac{100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 2
Error	14.2
Cost	8468

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 2.3:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{elif}\;i \leq 5.4 \cdot 10^{+269}:\\ \;\;\;\;100 \cdot \left(2 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n}}{i \cdot \frac{2}{n}} + \frac{-1}{\frac{i}{n}}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 3
Error	14.0
Cost	7956

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 3.15 \cdot 10^{-99}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 0.95:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+271}:\\ \;\;\;\;100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 4
Error	14.0
Cost	7108

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;100 \cdot \frac{n \cdot \left(e^{i} - 1\right)}{i}\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 14.2:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 5
Error	14.0
Cost	7108

\[\begin{array}{l} \mathbf{if}\;i \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;n \cdot \left(\left(-1 + e^{i}\right) \cdot \frac{100}{i}\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 36:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 6
Error	21.3
Cost	1228

\[\begin{array}{l} \mathbf{if}\;i \leq -9.8 \cdot 10^{+23}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{-98}:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{-22}:\\ \;\;\;\;100 \cdot \left(\frac{i}{n} \cdot \frac{1}{\frac{i}{n \cdot n}}\right)\\ \mathbf{elif}\;i \leq 63:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i + 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 7
Error	19.8
Cost	968

\[\begin{array}{l} \mathbf{if}\;i \leq -0.105:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 12:\\ \;\;\;\;n \cdot \left(50 \cdot \left(i - \left(\frac{i}{n} - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 8
Error	20.3
Cost	968

\[\begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 12.2:\\ \;\;\;\;\frac{76800}{\frac{1024}{n}} - \frac{25600}{\frac{-1024}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 9
Error	20.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;i \leq -9.4 \cdot 10^{+23}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 21:\\ \;\;\;\;100 \cdot \left(n + -0.5 \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 10
Error	20.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{+26}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 32:\\ \;\;\;\;\frac{12800}{\frac{128}{n}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 11
Error	20.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+24}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 17:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \]

Alternative 12
Error	51.1
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023099 
(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))))