Compound Interest

Percentage Accurate: 29.2% → 98.6%

Time: 22.0s

Alternatives: 21

Speedup: 38.0×

• could not determine a ground truth

  1. i = -2.0000000000000001e231
  2. n = 1.99999999999999997e77

Specification

Math

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

FPCore

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

C

double code(double i, double n) {
	return 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

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

Java

public static double code(double i, double n) {
	return 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Python

def code(i, n):
	return 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))

Julia

function code(i, n)
	return Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
end

MATLAB

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

Initial Program: 29.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double i, double n) {
	return 100.0 * ((pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

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

Java

public static double code(double i, double n) {
	return 100.0 * ((Math.pow((1.0 + (i / n)), n) - 1.0) / (i / n));
}

Python

def code(i, n):
	return 100.0 * ((math.pow((1.0 + (i / n)), n) - 1.0) / (i / n))

Julia

function code(i, n)
	return Float64(100.0 * Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) - 1.0) / Float64(i / n)))
end

MATLAB

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

Alternative 1: 98.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t_1 \cdot 100\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;n \cdot \left(100 \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{i}\right)\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(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 -1e-64)
     (* t_1 100.0)
     (if (<= t_1 0.0)
       (* n (* 100.0 (/ (expm1 (* n (log1p (/ i n)))) i)))
       (if (<= t_1 INFINITY)
         (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 <= -1e-64) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = n * (100.0 * (expm1((n * log1p((i / n)))) / i));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 <= -1e-64) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = n * (100.0 * (Math.expm1((n * Math.log1p((i / n)))) / i));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

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 <= -1e-64:
		tmp = t_1 * 100.0
	elif t_1 <= 0.0:
		tmp = n * (100.0 * (math.expm1((n * math.log1p((i / n)))) / i))
	elif t_1 <= math.inf:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

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 <= -1e-64)
		tmp = Float64(t_1 * 100.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(n * Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / i)));
	elseif (t_1 <= Inf)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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, -1e-64], N[(t$95$1 * 100.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(n * N[(100.0 * N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(100.0 * N[(N[(t$95$0 * N[(n / i), $MachinePrecision]), $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;\frac{-100 + t_0 \cdot 100}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(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 -1e-273)
     (/ (+ -100.0 (* t_0 100.0)) (/ i n))
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 i) (/ i n)))
       (if (<= t_1 INFINITY)
         (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 <= -1e-273) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 <= -1e-273) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

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 <= -1e-273:
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n)
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif t_1 <= math.inf:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

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 <= -1e-273)
		tmp = Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / Float64(i / n));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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, -1e-273], N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(100.0 * N[(N[(t$95$0 * N[(n / i), $MachinePrecision]), $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-64}:\\ \;\;\;\;t_1 \cdot 100\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot \left(100 \cdot \frac{n}{i}\right)\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(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 -1e-64)
     (* t_1 100.0)
     (if (<= t_1 0.0)
       (* (expm1 (* n (log1p (/ i n)))) (* 100.0 (/ n i)))
       (if (<= t_1 INFINITY)
         (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 <= -1e-64) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = expm1((n * log1p((i / n)))) * (100.0 * (n / i));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 <= -1e-64) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = Math.expm1((n * Math.log1p((i / n)))) * (100.0 * (n / i));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

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 <= -1e-64:
		tmp = t_1 * 100.0
	elif t_1 <= 0.0:
		tmp = math.expm1((n * math.log1p((i / n)))) * (100.0 * (n / i))
	elif t_1 <= math.inf:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

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 <= -1e-64)
		tmp = Float64(t_1 * 100.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(expm1(Float64(n * log1p(Float64(i / n)))) * Float64(100.0 * Float64(n / i)));
	elseif (t_1 <= Inf)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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, -1e-64], N[(t$95$1 * 100.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] * N[(100.0 * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(100.0 * N[(N[(t$95$0 * N[(n / i), $MachinePrecision]), $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 98.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-12}:\\ \;\;\;\;t_1 \cdot 100\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right) \cdot \frac{100}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(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 -1e-12)
     (* t_1 100.0)
     (if (<= t_1 0.0)
       (* (expm1 (* n (log1p (/ i n)))) (/ 100.0 (/ i n)))
       (if (<= t_1 INFINITY)
         (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 <= -1e-12) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = expm1((n * log1p((i / n)))) * (100.0 / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 <= -1e-12) {
		tmp = t_1 * 100.0;
	} else if (t_1 <= 0.0) {
		tmp = Math.expm1((n * Math.log1p((i / n)))) * (100.0 / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

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 <= -1e-12:
		tmp = t_1 * 100.0
	elif t_1 <= 0.0:
		tmp = math.expm1((n * math.log1p((i / n)))) * (100.0 / (i / n))
	elif t_1 <= math.inf:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

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 <= -1e-12)
		tmp = Float64(t_1 * 100.0);
	elseif (t_1 <= 0.0)
		tmp = Float64(expm1(Float64(n * log1p(Float64(i / n)))) * Float64(100.0 / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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, -1e-12], N[(t$95$1 * 100.0), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] * N[(100.0 / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(100.0 * N[(N[(t$95$0 * N[(n / i), $MachinePrecision]), $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ t_1 := t_0 \cdot 100\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (/ (+ (pow (+ 1.0 (/ i n)) n) -1.0) (/ i n))) (t_1 (* t_0 100.0)))
   (if (<= t_0 -1e-273)
     t_1
     (if (<= t_0 0.0)
       (* 100.0 (/ (expm1 i) (/ i n)))
       (if (<= t_0 INFINITY) t_1 (* 100.0 (/ n (+ 1.0 (* i -0.5)))))))))

C

double code(double i, double n) {
	double t_0 = (pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double t_1 = t_0 * 100.0;
	double tmp;
	if (t_0 <= -1e-273) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = (Math.pow((1.0 + (i / n)), n) + -1.0) / (i / n);
	double t_1 = t_0 * 100.0;
	double tmp;
	if (t_0 <= -1e-273) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = (math.pow((1.0 + (i / n)), n) + -1.0) / (i / n)
	t_1 = t_0 * 100.0
	tmp = 0
	if t_0 <= -1e-273:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif t_0 <= math.inf:
		tmp = t_1
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(Float64((Float64(1.0 + Float64(i / n)) ^ n) + -1.0) / Float64(i / n))
	t_1 = Float64(t_0 * 100.0)
	tmp = 0.0
	if (t_0 <= -1e-273)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (t_0 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(N[Power[N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision], n], $MachinePrecision] + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 * 100.0), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-273], t$95$1, If[LessEqual[t$95$0, 0.0], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, Infinity], t$95$1, N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ t_2 := n \cdot \frac{-100 + t_0 \cdot 100}{i}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n))
        (t_1 (/ (+ t_0 -1.0) (/ i n)))
        (t_2 (* n (/ (+ -100.0 (* t_0 100.0)) i))))
   (if (<= t_1 -1e-273)
     t_2
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 i) (/ i n)))
       (if (<= t_1 INFINITY) t_2 (* 100.0 (/ n (+ 1.0 (* i -0.5)))))))))

C

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 t_2 = n * ((-100.0 + (t_0 * 100.0)) / i);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Java

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 t_2 = n * ((-100.0 + (t_0 * 100.0)) / i);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	t_2 = n * ((-100.0 + (t_0 * 100.0)) / i)
	tmp = 0
	if t_1 <= -1e-273:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	t_2 = Float64(n * Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / i))
	tmp = 0.0
	if (t_1 <= -1e-273)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

Wolfram

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]}, Block[{t$95$2 = N[(n * N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-273], t$95$2, If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ t_2 := n \cdot \frac{-100 + t_0 \cdot 100}{i}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n))
        (t_1 (/ (+ t_0 -1.0) (/ i n)))
        (t_2 (* n (/ (+ -100.0 (* t_0 100.0)) i))))
   (if (<= t_1 -1e-273)
     t_2
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 i) (/ i n)))
       (if (<= t_1 INFINITY)
         t_2
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 t_2 = n * ((-100.0 + (t_0 * 100.0)) / i);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 t_2 = n * ((-100.0 + (t_0 * 100.0)) / i);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	t_2 = n * ((-100.0 + (t_0 * 100.0)) / i)
	tmp = 0
	if t_1 <= -1e-273:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	t_2 = Float64(n * Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / i))
	tmp = 0.0
	if (t_1 <= -1e-273)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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]}, Block[{t$95$2 = N[(n * N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-273], t$95$2, If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ t_2 := \frac{-100 + t_0 \cdot 100}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-273}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + \left(i \cdot -0.5 + 0.08333333333333333 \cdot {i}^{2}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n))
        (t_1 (/ (+ t_0 -1.0) (/ i n)))
        (t_2 (/ (+ -100.0 (* t_0 100.0)) (/ i n))))
   (if (<= t_1 -1e-273)
     t_2
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 i) (/ i n)))
       (if (<= t_1 INFINITY)
         t_2
         (*
          100.0
          (/
           n
           (+ 1.0 (+ (* i -0.5) (* 0.08333333333333333 (pow i 2.0)))))))))))

C

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 t_2 = (-100.0 + (t_0 * 100.0)) / (i / n);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * pow(i, 2.0)))));
	}
	return tmp;
}

Java

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 t_2 = (-100.0 + (t_0 * 100.0)) / (i / n);
	double tmp;
	if (t_1 <= -1e-273) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * Math.pow(i, 2.0)))));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	t_2 = (-100.0 + (t_0 * 100.0)) / (i / n)
	tmp = 0
	if t_1 <= -1e-273:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif t_1 <= math.inf:
		tmp = t_2
	else:
		tmp = 100.0 * (n / (1.0 + ((i * -0.5) + (0.08333333333333333 * math.pow(i, 2.0)))))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	t_2 = Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= -1e-273)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(Float64(i * -0.5) + Float64(0.08333333333333333 * (i ^ 2.0))))));
	end
	return tmp
end

Wolfram

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]}, Block[{t$95$2 = N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-273], t$95$2, If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(100.0 * N[(n / N[(1.0 + N[(N[(i * -0.5), $MachinePrecision] + N[(0.08333333333333333 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{if}\;i \leq -1.3 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-13}:\\ \;\;\;\;n \cdot \left(100 + 100 \cdot \left(i \cdot \left(0.5 - \frac{0.5}{n}\right)\right)\right)\\ \mathbf{elif}\;i \leq 8 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (expm1 i) (/ i n)))))
   (if (<= i -1.3e-45)
     t_0
     (if (<= i 3.8e-13)
       (* n (+ 100.0 (* 100.0 (* i (- 0.5 (/ 0.5 n))))))
       (if (<= i 8e+251) t_0 (* 100.0 (/ n (+ 1.0 (* i -0.5)))))))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (expm1(i) / (i / n));
	double tmp;
	if (i <= -1.3e-45) {
		tmp = t_0;
	} else if (i <= 3.8e-13) {
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))));
	} else if (i <= 8e+251) {
		tmp = t_0;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * (Math.expm1(i) / (i / n));
	double tmp;
	if (i <= -1.3e-45) {
		tmp = t_0;
	} else if (i <= 3.8e-13) {
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))));
	} else if (i <= 8e+251) {
		tmp = t_0;
	} else {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (math.expm1(i) / (i / n))
	tmp = 0
	if i <= -1.3e-45:
		tmp = t_0
	elif i <= 3.8e-13:
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))))
	elif i <= 8e+251:
		tmp = t_0
	else:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(expm1(i) / Float64(i / n)))
	tmp = 0.0
	if (i <= -1.3e-45)
		tmp = t_0;
	elseif (i <= 3.8e-13)
		tmp = Float64(n * Float64(100.0 + Float64(100.0 * Float64(i * Float64(0.5 - Float64(0.5 / n))))));
	elseif (i <= 8e+251)
		tmp = t_0;
	else
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.3e-45], t$95$0, If[LessEqual[i, 3.8e-13], N[(n * N[(100.0 + N[(100.0 * N[(i * N[(0.5 - N[(0.5 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8e+251], t$95$0, N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 80.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \left(n \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\right)\\ \mathbf{if}\;n \leq -8.6 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 8.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (* n (/ (expm1 i) i)))))
   (if (<= n -8.6e-132)
     t_0
     (if (<= n 8.4e-151)
       (/ 0.0 (/ i n))
       (if (<= n 6.5e-18) (* 100.0 (/ i (/ i n))) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (n * (expm1(i) / i));
	double tmp;
	if (n <= -8.6e-132) {
		tmp = t_0;
	} else if (n <= 8.4e-151) {
		tmp = 0.0 / (i / n);
	} else if (n <= 6.5e-18) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * (n * (Math.expm1(i) / i));
	double tmp;
	if (n <= -8.6e-132) {
		tmp = t_0;
	} else if (n <= 8.4e-151) {
		tmp = 0.0 / (i / n);
	} else if (n <= 6.5e-18) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (n * (math.expm1(i) / i))
	tmp = 0
	if n <= -8.6e-132:
		tmp = t_0
	elif n <= 8.4e-151:
		tmp = 0.0 / (i / n)
	elif n <= 6.5e-18:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(n * Float64(expm1(i) / i)))
	tmp = 0.0
	if (n <= -8.6e-132)
		tmp = t_0;
	elseif (n <= 8.4e-151)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 6.5e-18)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(n * N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -8.6e-132], t$95$0, If[LessEqual[n, 8.4e-151], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.5e-18], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 80.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -8.6 \cdot 10^{-132}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 1.16 \cdot 10^{-150}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6.5 \cdot 10^{-18}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ n (/ i (expm1 i))))))
   (if (<= n -8.6e-132)
     t_0
     (if (<= n 1.16e-150)
       (/ 0.0 (/ i n))
       (if (<= n 6.5e-18) (* 100.0 (/ i (/ i n))) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / expm1(i)));
	double tmp;
	if (n <= -8.6e-132) {
		tmp = t_0;
	} else if (n <= 1.16e-150) {
		tmp = 0.0 / (i / n);
	} else if (n <= 6.5e-18) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / Math.expm1(i)));
	double tmp;
	if (n <= -8.6e-132) {
		tmp = t_0;
	} else if (n <= 1.16e-150) {
		tmp = 0.0 / (i / n);
	} else if (n <= 6.5e-18) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (n / (i / math.expm1(i)))
	tmp = 0
	if n <= -8.6e-132:
		tmp = t_0
	elif n <= 1.16e-150:
		tmp = 0.0 / (i / n)
	elif n <= 6.5e-18:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(n / Float64(i / expm1(i))))
	tmp = 0.0
	if (n <= -8.6e-132)
		tmp = t_0;
	elseif (n <= 1.16e-150)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 6.5e-18)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -8.6e-132], t$95$0, If[LessEqual[n, 1.16e-150], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.5e-18], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 63.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -6.8 \cdot 10^{+222}:\\ \;\;\;\;100 \cdot \left(n + 0.5 \cdot \left(i \cdot n\right)\right)\\ \mathbf{elif}\;n \leq -9.5 \cdot 10^{-132}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{elif}\;n \leq 1.95 \cdot 10^{-150}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;i \cdot -50 + n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -6.8e+222)
   (* 100.0 (+ n (* 0.5 (* i n))))
   (if (<= n -9.5e-132)
     (* 100.0 (/ n (+ 1.0 (* i -0.5))))
     (if (<= n 1.95e-150)
       (/ 0.0 (/ i n))
       (+ (* i -50.0) (* n (+ 100.0 (* i 50.0))))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -6.8e+222) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= -9.5e-132) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else if (n <= 1.95e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = (i * -50.0) + (n * (100.0 + (i * 50.0)));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-6.8d+222)) then
        tmp = 100.0d0 * (n + (0.5d0 * (i * n)))
    else if (n <= (-9.5d-132)) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    else if (n <= 1.95d-150) then
        tmp = 0.0d0 / (i / n)
    else
        tmp = (i * (-50.0d0)) + (n * (100.0d0 + (i * 50.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -6.8e+222) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= -9.5e-132) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else if (n <= 1.95e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = (i * -50.0) + (n * (100.0 + (i * 50.0)));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -6.8e+222:
		tmp = 100.0 * (n + (0.5 * (i * n)))
	elif n <= -9.5e-132:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	elif n <= 1.95e-150:
		tmp = 0.0 / (i / n)
	else:
		tmp = (i * -50.0) + (n * (100.0 + (i * 50.0)))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -6.8e+222)
		tmp = Float64(100.0 * Float64(n + Float64(0.5 * Float64(i * n))));
	elseif (n <= -9.5e-132)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	elseif (n <= 1.95e-150)
		tmp = Float64(0.0 / Float64(i / n));
	else
		tmp = Float64(Float64(i * -50.0) + Float64(n * Float64(100.0 + Float64(i * 50.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -6.8e+222)
		tmp = 100.0 * (n + (0.5 * (i * n)));
	elseif (n <= -9.5e-132)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	elseif (n <= 1.95e-150)
		tmp = 0.0 / (i / n);
	else
		tmp = (i * -50.0) + (n * (100.0 + (i * 50.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -6.8e+222], N[(100.0 * N[(n + N[(0.5 * N[(i * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, -9.5e-132], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.95e-150], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(N[(i * -50.0), $MachinePrecision] + N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 63.8% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -6.6 \cdot 10^{+224}:\\ \;\;\;\;100 \cdot \left(n + 0.5 \cdot \left(i \cdot n\right)\right)\\ \mathbf{elif}\;n \leq -8.6 \cdot 10^{-132}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{elif}\;n \leq 1.25 \cdot 10^{-150}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -6.6e+224)
   (* 100.0 (+ n (* 0.5 (* i n))))
   (if (<= n -8.6e-132)
     (* 100.0 (/ n (+ 1.0 (* i -0.5))))
     (if (<= n 1.25e-150) (/ 0.0 (/ i n)) (* n (+ 100.0 (* i 50.0)))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -6.6e+224) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= -8.6e-132) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else if (n <= 1.25e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-6.6d+224)) then
        tmp = 100.0d0 * (n + (0.5d0 * (i * n)))
    else if (n <= (-8.6d-132)) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    else if (n <= 1.25d-150) then
        tmp = 0.0d0 / (i / n)
    else
        tmp = n * (100.0d0 + (i * 50.0d0))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -6.6e+224) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= -8.6e-132) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else if (n <= 1.25e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -6.6e+224:
		tmp = 100.0 * (n + (0.5 * (i * n)))
	elif n <= -8.6e-132:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	elif n <= 1.25e-150:
		tmp = 0.0 / (i / n)
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -6.6e+224)
		tmp = Float64(100.0 * Float64(n + Float64(0.5 * Float64(i * n))));
	elseif (n <= -8.6e-132)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	elseif (n <= 1.25e-150)
		tmp = Float64(0.0 / Float64(i / n));
	else
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -6.6e+224)
		tmp = 100.0 * (n + (0.5 * (i * n)));
	elseif (n <= -8.6e-132)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	elseif (n <= 1.25e-150)
		tmp = 0.0 / (i / n);
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -6.6e+224], N[(100.0 * N[(n + N[(0.5 * N[(i * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, -8.6e-132], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.25e-150], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 62.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -7.4 \cdot 10^{+17} \lor \neg \left(n \leq 6.2 \cdot 10^{-18}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -7.4e+17) (not (<= n 6.2e-18)))
   (* n (+ 100.0 (* i 50.0)))
   (* 100.0 (/ i (/ i n)))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -7.4e+17) || !(n <= 6.2e-18)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 100.0 * (i / (i / n));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-7.4d+17)) .or. (.not. (n <= 6.2d-18))) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else
        tmp = 100.0d0 * (i / (i / n))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -7.4e+17) || !(n <= 6.2e-18)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 100.0 * (i / (i / n));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -7.4e+17) or not (n <= 6.2e-18):
		tmp = n * (100.0 + (i * 50.0))
	else:
		tmp = 100.0 * (i / (i / n))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -7.4e+17) || !(n <= 6.2e-18))
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	else
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -7.4e+17) || ~((n <= 6.2e-18)))
		tmp = n * (100.0 + (i * 50.0));
	else
		tmp = 100.0 * (i / (i / n));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -7.4e+17], N[Not[LessEqual[n, 6.2e-18]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 61.7% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -8.6 \cdot 10^{-132} \lor \neg \left(n \leq 8.4 \cdot 10^{-151}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -8.6e-132) (not (<= n 8.4e-151)))
   (* n (+ 100.0 (* i 50.0)))
   (/ 0.0 (/ i n))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -8.6e-132) || !(n <= 8.4e-151)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 0.0 / (i / n);
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((n <= (-8.6d-132)) .or. (.not. (n <= 8.4d-151))) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else
        tmp = 0.0d0 / (i / n)
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((n <= -8.6e-132) || !(n <= 8.4e-151)) {
		tmp = n * (100.0 + (i * 50.0));
	} else {
		tmp = 0.0 / (i / n);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (n <= -8.6e-132) or not (n <= 8.4e-151):
		tmp = n * (100.0 + (i * 50.0))
	else:
		tmp = 0.0 / (i / n)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((n <= -8.6e-132) || !(n <= 8.4e-151))
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	else
		tmp = Float64(0.0 / Float64(i / n));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((n <= -8.6e-132) || ~((n <= 8.4e-151)))
		tmp = n * (100.0 + (i * 50.0));
	else
		tmp = 0.0 / (i / n);
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[n, -8.6e-132], N[Not[LessEqual[n, 8.4e-151]], $MachinePrecision]], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 61.7% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.2 \cdot 10^{-131}:\\ \;\;\;\;100 \cdot \left(n + 0.5 \cdot \left(i \cdot n\right)\right)\\ \mathbf{elif}\;n \leq 3 \cdot 10^{-150}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -1.2e-131)
   (* 100.0 (+ n (* 0.5 (* i n))))
   (if (<= n 3e-150) (/ 0.0 (/ i n)) (* n (+ 100.0 (* i 50.0))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -1.2e-131) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= 3e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-1.2d-131)) then
        tmp = 100.0d0 * (n + (0.5d0 * (i * n)))
    else if (n <= 3d-150) then
        tmp = 0.0d0 / (i / n)
    else
        tmp = n * (100.0d0 + (i * 50.0d0))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -1.2e-131) {
		tmp = 100.0 * (n + (0.5 * (i * n)));
	} else if (n <= 3e-150) {
		tmp = 0.0 / (i / n);
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -1.2e-131:
		tmp = 100.0 * (n + (0.5 * (i * n)))
	elif n <= 3e-150:
		tmp = 0.0 / (i / n)
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -1.2e-131)
		tmp = Float64(100.0 * Float64(n + Float64(0.5 * Float64(i * n))));
	elseif (n <= 3e-150)
		tmp = Float64(0.0 / Float64(i / n));
	else
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -1.2e-131)
		tmp = 100.0 * (n + (0.5 * (i * n)));
	elseif (n <= 3e-150)
		tmp = 0.0 / (i / n);
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -1.2e-131], N[(100.0 * N[(n + N[(0.5 * N[(i * n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 3e-150], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 17: 57.3% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2 \cdot 10^{+87}:\\ \;\;\;\;100 \cdot \left(i \cdot \frac{n}{i}\right)\\ \mathbf{elif}\;i \leq 2:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -2e+87)
   (* 100.0 (* i (/ n i)))
   (if (<= i 2.0) (* n 100.0) (* 50.0 (* i n)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -2e+87) {
		tmp = 100.0 * (i * (n / i));
	} else if (i <= 2.0) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= (-2d+87)) then
        tmp = 100.0d0 * (i * (n / i))
    else if (i <= 2.0d0) then
        tmp = n * 100.0d0
    else
        tmp = 50.0d0 * (i * n)
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= -2e+87) {
		tmp = 100.0 * (i * (n / i));
	} else if (i <= 2.0) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -2e+87:
		tmp = 100.0 * (i * (n / i))
	elif i <= 2.0:
		tmp = n * 100.0
	else:
		tmp = 50.0 * (i * n)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -2e+87)
		tmp = Float64(100.0 * Float64(i * Float64(n / i)));
	elseif (i <= 2.0)
		tmp = Float64(n * 100.0);
	else
		tmp = Float64(50.0 * Float64(i * n));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= -2e+87)
		tmp = 100.0 * (i * (n / i));
	elseif (i <= 2.0)
		tmp = n * 100.0;
	else
		tmp = 50.0 * (i * n);
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -2e+87], N[(100.0 * N[(i * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.0], N[(n * 100.0), $MachinePrecision], N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 18: 57.7% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5 \cdot 10^{+87}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq 1.8:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -5e+87)
   (* 100.0 (/ i (/ i n)))
   (if (<= i 1.8) (* n 100.0) (* 50.0 (* i n)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -5e+87) {
		tmp = 100.0 * (i / (i / n));
	} else if (i <= 1.8) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= (-5d+87)) then
        tmp = 100.0d0 * (i / (i / n))
    else if (i <= 1.8d0) then
        tmp = n * 100.0d0
    else
        tmp = 50.0d0 * (i * n)
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= -5e+87) {
		tmp = 100.0 * (i / (i / n));
	} else if (i <= 1.8) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -5e+87:
		tmp = 100.0 * (i / (i / n))
	elif i <= 1.8:
		tmp = n * 100.0
	else:
		tmp = 50.0 * (i * n)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -5e+87)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	elseif (i <= 1.8)
		tmp = Float64(n * 100.0);
	else
		tmp = Float64(50.0 * Float64(i * n));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= -5e+87)
		tmp = 100.0 * (i / (i / n));
	elseif (i <= 1.8)
		tmp = n * 100.0;
	else
		tmp = 50.0 * (i * n);
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -5e+87], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8], N[(n * 100.0), $MachinePrecision], N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 19: 54.2% accurate, 16.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 2:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n) :precision binary64 (if (<= i 2.0) (* n 100.0) (* 50.0 (* i n))))

C

double code(double i, double n) {
	double tmp;
	if (i <= 2.0) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= 2.0d0) then
        tmp = n * 100.0d0
    else
        tmp = 50.0d0 * (i * n)
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= 2.0) {
		tmp = n * 100.0;
	} else {
		tmp = 50.0 * (i * n);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= 2.0:
		tmp = n * 100.0
	else:
		tmp = 50.0 * (i * n)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= 2.0)
		tmp = Float64(n * 100.0);
	else
		tmp = Float64(50.0 * Float64(i * n));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= 2.0)
		tmp = n * 100.0;
	else
		tmp = 50.0 * (i * n);
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, 2.0], N[(n * 100.0), $MachinePrecision], N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 20: 2.8% accurate, 38.0× speedup

Math

\[\begin{array}{l} \\ i \cdot -50 \end{array} \]

FPCore

(FPCore (i n) :precision binary64 (* i -50.0))

C

double code(double i, double n) {
	return i * -50.0;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = i * (-50.0d0)
end function

Java

public static double code(double i, double n) {
	return i * -50.0;
}

Python

def code(i, n):
	return i * -50.0

Julia

function code(i, n)
	return Float64(i * -50.0)
end

MATLAB

function tmp = code(i, n)
	tmp = i * -50.0;
end

Wolfram

code[i_, n_] := N[(i * -50.0), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 21: 48.8% accurate, 38.0× speedup

Math

\[\begin{array}{l} \\ n \cdot 100 \end{array} \]

FPCore

(FPCore (i n) :precision binary64 (* n 100.0))

C

double code(double i, double n) {
	return n * 100.0;
}

Fortran

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

Java

public static double code(double i, double n) {
	return n * 100.0;
}

Python

def code(i, n):
	return n * 100.0

Julia

function code(i, n)
	return Float64(n * 100.0)
end

MATLAB

function tmp = code(i, n)
	tmp = n * 100.0;
end

Wolfram

code[i_, n_] := N[(n * 100.0), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 34.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{i}{n}\\ 100 \cdot \frac{e^{n \cdot \begin{array}{l} \mathbf{if}\;t_0 = 1:\\ \;\;\;\;\frac{i}{n}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{i}{n} \cdot \log t_0}{\left(\frac{i}{n} + 1\right) - 1}\\ \end{array}} - 1}{\frac{i}{n}} \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ i n))))
   (*
    100.0
    (/
     (-
      (exp
       (*
        n
        (if (== t_0 1.0)
          (/ i n)
          (/ (* (/ i n) (log t_0)) (- (+ (/ i n) 1.0) 1.0)))))
      1.0)
     (/ i n)))))

C

double code(double i, double n) {
	double t_0 = 1.0 + (i / n);
	double tmp;
	if (t_0 == 1.0) {
		tmp = i / n;
	} else {
		tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0) - 1.0);
	}
	return 100.0 * ((exp((n * tmp)) - 1.0) / (i / n));
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (i / n)
    if (t_0 == 1.0d0) then
        tmp = i / n
    else
        tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0d0) - 1.0d0)
    end if
    code = 100.0d0 * ((exp((n * tmp)) - 1.0d0) / (i / n))
end function

Java

public static double code(double i, double n) {
	double t_0 = 1.0 + (i / n);
	double tmp;
	if (t_0 == 1.0) {
		tmp = i / n;
	} else {
		tmp = ((i / n) * Math.log(t_0)) / (((i / n) + 1.0) - 1.0);
	}
	return 100.0 * ((Math.exp((n * tmp)) - 1.0) / (i / n));
}

Python

def code(i, n):
	t_0 = 1.0 + (i / n)
	tmp = 0
	if t_0 == 1.0:
		tmp = i / n
	else:
		tmp = ((i / n) * math.log(t_0)) / (((i / n) + 1.0) - 1.0)
	return 100.0 * ((math.exp((n * tmp)) - 1.0) / (i / n))

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n))
	tmp = 0.0
	if (t_0 == 1.0)
		tmp = Float64(i / n);
	else
		tmp = Float64(Float64(Float64(i / n) * log(t_0)) / Float64(Float64(Float64(i / n) + 1.0) - 1.0));
	end
	return Float64(100.0 * Float64(Float64(exp(Float64(n * tmp)) - 1.0) / Float64(i / n)))
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = 1.0 + (i / n);
	tmp = 0.0;
	if (t_0 == 1.0)
		tmp = i / n;
	else
		tmp = ((i / n) * log(t_0)) / (((i / n) + 1.0) - 1.0);
	end
	tmp_2 = 100.0 * ((exp((n * tmp)) - 1.0) / (i / n));
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(1.0 + N[(i / n), $MachinePrecision]), $MachinePrecision]}, N[(100.0 * N[(N[(N[Exp[N[(n * If[Equal[t$95$0, 1.0], N[(i / n), $MachinePrecision], N[(N[(N[(i / n), $MachinePrecision] * N[Log[t$95$0], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(i / n), $MachinePrecision] + 1.0), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]], $MachinePrecision] - 1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023350 
(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))))