Compound Interest

Percentage Accurate: 27.3% → 97.9%

Time: 37.1s

Alternatives: 20

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: 27.3% 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: 97.9% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n)) (t_1 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_1 0.0)
     (/ (* (expm1 (* n (log1p (/ i n)))) (- 100.0)) (/ (- i) n))
     (if (<= t_1 INFINITY)
       (/ (+ (* t_0 100.0) -100.0) (/ i n))
       (* 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 tmp;
	if (t_1 <= 0.0) {
		tmp = (expm1((n * log1p((i / n)))) * -100.0) / (-i / n);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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 tmp;
	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 = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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)
	tmp = 0
	if t_1 <= 0.0:
		tmp = (math.expm1((n * math.log1p((i / n)))) * -100.0) / (-i / n)
	elif t_1 <= math.inf:
		tmp = ((t_0 * 100.0) + -100.0) / (i / n)
	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))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(expm1(Float64(n * log1p(Float64(i / n)))) * Float64(-100.0)) / Float64(Float64(-i) / n));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(t_0 * 100.0) + -100.0) / Float64(i / n));
	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]}, If[LessEqual[t$95$1, 0.0], N[(N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] * (-100.0)), $MachinePrecision] / N[((-i) / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], 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 2: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ t_1 := t_0 \cdot 100\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;\frac{100}{\frac{\frac{i}{\mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

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-287)
     t_1
     (if (<= t_0 0.0)
       (/ 100.0 (/ (/ i (expm1 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-287) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 / ((i / expm1(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-287) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 / ((i / Math.expm1(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-287:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 100.0 / ((i / math.expm1(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-287)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(100.0 / Float64(Float64(i / expm1(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-287], t$95$1, If[LessEqual[t$95$0, 0.0], N[(100.0 / N[(N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision] / n), $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 3: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ t_2 := \frac{t_0 \cdot 100 + -100}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-213}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{100}{\frac{\frac{i}{\mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

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 (/ (+ (* t_0 100.0) -100.0) (/ i n))))
   (if (<= t_1 -2e-213)
     t_2
     (if (<= t_1 0.0)
       (/ 100.0 (/ (/ i (expm1 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 = ((t_0 * 100.0) + -100.0) / (i / n);
	double tmp;
	if (t_1 <= -2e-213) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 / ((i / expm1(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 = ((t_0 * 100.0) + -100.0) / (i / n);
	double tmp;
	if (t_1 <= -2e-213) {
		tmp = t_2;
	} else if (t_1 <= 0.0) {
		tmp = 100.0 / ((i / Math.expm1(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 = ((t_0 * 100.0) + -100.0) / (i / n)
	tmp = 0
	if t_1 <= -2e-213:
		tmp = t_2
	elif t_1 <= 0.0:
		tmp = 100.0 / ((i / math.expm1(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(Float64(Float64(t_0 * 100.0) + -100.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= -2e-213)
		tmp = t_2;
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 / Float64(Float64(i / expm1(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[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-213], t$95$2, If[LessEqual[t$95$1, 0.0], N[(100.0 / N[(N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision] / n), $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 4: 84.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-287}:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{100}{\frac{\frac{i}{\mathsf{expm1}\left(i\right)}}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{t_0 \cdot 100 + -100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n)) (t_1 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_1 -1e-287)
     (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
     (if (<= t_1 0.0)
       (/ 100.0 (/ (/ i (expm1 i)) n))
       (if (<= t_1 INFINITY)
         (/ (+ (* t_0 100.0) -100.0) (/ i n))
         (* 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 tmp;
	if (t_1 <= -1e-287) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 / ((i / expm1(i)) / n);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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 tmp;
	if (t_1 <= -1e-287) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 / ((i / Math.expm1(i)) / n);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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)
	tmp = 0
	if t_1 <= -1e-287:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	elif t_1 <= 0.0:
		tmp = 100.0 / ((i / math.expm1(i)) / n)
	elif t_1 <= math.inf:
		tmp = ((t_0 * 100.0) + -100.0) / (i / n)
	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))
	tmp = 0.0
	if (t_1 <= -1e-287)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 / Float64(Float64(i / expm1(i)) / n));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(t_0 * 100.0) + -100.0) / Float64(i / n));
	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]}, If[LessEqual[t$95$1, -1e-287], N[(100.0 * N[(N[(t$95$0 * N[(n / i), $MachinePrecision]), $MachinePrecision] - N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(100.0 / N[(N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision] / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], 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 5: 96.3% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n)) (t_1 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_1 0.0)
     (* 100.0 (* (expm1 (* n (log1p (/ i n)))) (/ n i)))
     (if (<= t_1 INFINITY)
       (/ (+ (* t_0 100.0) -100.0) (/ i n))
       (* 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 tmp;
	if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1((n * log1p((i / n)))) * (n / i));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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 tmp;
	if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1((n * Math.log1p((i / n)))) * (n / i));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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)
	tmp = 0
	if t_1 <= 0.0:
		tmp = 100.0 * (math.expm1((n * math.log1p((i / n)))) * (n / i))
	elif t_1 <= math.inf:
		tmp = ((t_0 * 100.0) + -100.0) / (i / n)
	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))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) * Float64(n / i)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(t_0 * 100.0) + -100.0) / Float64(i / n));
	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]}, If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(N[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], 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: 96.3% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n)) (t_1 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_1 0.0)
     (* (expm1 (* n (log1p (/ i n)))) (/ 100.0 (/ i n)))
     (if (<= t_1 INFINITY)
       (/ (+ (* t_0 100.0) -100.0) (/ i n))
       (* 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 tmp;
	if (t_1 <= 0.0) {
		tmp = expm1((n * log1p((i / n)))) * (100.0 / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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 tmp;
	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 = ((t_0 * 100.0) + -100.0) / (i / n);
	} 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)
	tmp = 0
	if t_1 <= 0.0:
		tmp = math.expm1((n * math.log1p((i / n)))) * (100.0 / (i / n))
	elif t_1 <= math.inf:
		tmp = ((t_0 * 100.0) + -100.0) / (i / n)
	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))
	tmp = 0.0
	if (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(Float64(Float64(t_0 * 100.0) + -100.0) / Float64(i / n));
	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]}, 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[(N[(N[(t$95$0 * 100.0), $MachinePrecision] + -100.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], 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: 82.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{i}{\mathsf{expm1}\left(i\right)}\\ \mathbf{if}\;n \leq -1.45 \cdot 10^{-192}:\\ \;\;\;\;\frac{100}{\frac{t_0}{n}}\\ \mathbf{elif}\;n \leq 6.1 \cdot 10^{-183}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;\frac{n}{0.01 + \left(0.0008333333333333334 \cdot {i}^{2} + i \cdot -0.005\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{\frac{t_0}{100}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (/ i (expm1 i))))
   (if (<= n -1.45e-192)
     (/ 100.0 (/ t_0 n))
     (if (<= n 6.1e-183)
       (/ 0.0 (/ i n))
       (if (<= n 1.75e-32)
         (/ n (+ 0.01 (+ (* 0.0008333333333333334 (pow i 2.0)) (* i -0.005))))
         (/ n (/ t_0 100.0)))))))

C

double code(double i, double n) {
	double t_0 = i / expm1(i);
	double tmp;
	if (n <= -1.45e-192) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 6.1e-183) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = n / (0.01 + ((0.0008333333333333334 * pow(i, 2.0)) + (i * -0.005)));
	} else {
		tmp = n / (t_0 / 100.0);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = i / Math.expm1(i);
	double tmp;
	if (n <= -1.45e-192) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 6.1e-183) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = n / (0.01 + ((0.0008333333333333334 * Math.pow(i, 2.0)) + (i * -0.005)));
	} else {
		tmp = n / (t_0 / 100.0);
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = i / math.expm1(i)
	tmp = 0
	if n <= -1.45e-192:
		tmp = 100.0 / (t_0 / n)
	elif n <= 6.1e-183:
		tmp = 0.0 / (i / n)
	elif n <= 1.75e-32:
		tmp = n / (0.01 + ((0.0008333333333333334 * math.pow(i, 2.0)) + (i * -0.005)))
	else:
		tmp = n / (t_0 / 100.0)
	return tmp

Julia

function code(i, n)
	t_0 = Float64(i / expm1(i))
	tmp = 0.0
	if (n <= -1.45e-192)
		tmp = Float64(100.0 / Float64(t_0 / n));
	elseif (n <= 6.1e-183)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.75e-32)
		tmp = Float64(n / Float64(0.01 + Float64(Float64(0.0008333333333333334 * (i ^ 2.0)) + Float64(i * -0.005))));
	else
		tmp = Float64(n / Float64(t_0 / 100.0));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.45e-192], N[(100.0 / N[(t$95$0 / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.1e-183], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.75e-32], N[(n / N[(0.01 + N[(N[(0.0008333333333333334 * N[Power[i, 2.0], $MachinePrecision]), $MachinePrecision] + N[(i * -0.005), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n / N[(t$95$0 / 100.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -2.1 \cdot 10^{-193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ n (/ i (expm1 i))))))
   (if (<= n -2.1e-193)
     t_0
     (if (<= n 1.9e-175)
       (/ 0.0 (/ i n))
       (if (<= n 1.75e-32) (* 100.0 (/ n (+ 1.0 (* i -0.5)))) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / expm1(i)));
	double tmp;
	if (n <= -2.1e-193) {
		tmp = t_0;
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} 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 <= -2.1e-193) {
		tmp = t_0;
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (n / (i / math.expm1(i)))
	tmp = 0
	if n <= -2.1e-193:
		tmp = t_0
	elif n <= 1.9e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.75e-32:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	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 <= -2.1e-193)
		tmp = t_0;
	elseif (n <= 1.9e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.75e-32)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	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, -2.1e-193], t$95$0, If[LessEqual[n, 1.9e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.75e-32], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 9: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{i}{\mathsf{expm1}\left(i\right)}\\ \mathbf{if}\;n \leq -2.4 \cdot 10^{-198}:\\ \;\;\;\;\frac{100}{\frac{t_0}{n}}\\ \mathbf{elif}\;n \leq 2 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{n}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (/ i (expm1 i))))
   (if (<= n -2.4e-198)
     (/ 100.0 (/ t_0 n))
     (if (<= n 2e-175)
       (/ 0.0 (/ i n))
       (if (<= n 1.75e-32)
         (* 100.0 (/ n (+ 1.0 (* i -0.5))))
         (* 100.0 (/ n t_0)))))))

C

double code(double i, double n) {
	double t_0 = i / expm1(i);
	double tmp;
	if (n <= -2.4e-198) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 2e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = 100.0 * (n / t_0);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = i / Math.expm1(i);
	double tmp;
	if (n <= -2.4e-198) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 2e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = 100.0 * (n / t_0);
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = i / math.expm1(i)
	tmp = 0
	if n <= -2.4e-198:
		tmp = 100.0 / (t_0 / n)
	elif n <= 2e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.75e-32:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = 100.0 * (n / t_0)
	return tmp

Julia

function code(i, n)
	t_0 = Float64(i / expm1(i))
	tmp = 0.0
	if (n <= -2.4e-198)
		tmp = Float64(100.0 / Float64(t_0 / n));
	elseif (n <= 2e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.75e-32)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	else
		tmp = Float64(100.0 * Float64(n / t_0));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -2.4e-198], N[(100.0 / N[(t$95$0 / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.75e-32], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n / t$95$0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 10: 80.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{i}{\mathsf{expm1}\left(i\right)}\\ \mathbf{if}\;n \leq -1.25 \cdot 10^{-197}:\\ \;\;\;\;\frac{100}{\frac{t_0}{n}}\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.75 \cdot 10^{-32}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{n}{\frac{t_0}{100}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (/ i (expm1 i))))
   (if (<= n -1.25e-197)
     (/ 100.0 (/ t_0 n))
     (if (<= n 1.9e-175)
       (/ 0.0 (/ i n))
       (if (<= n 1.75e-32)
         (* 100.0 (/ n (+ 1.0 (* i -0.5))))
         (/ n (/ t_0 100.0)))))))

C

double code(double i, double n) {
	double t_0 = i / expm1(i);
	double tmp;
	if (n <= -1.25e-197) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = n / (t_0 / 100.0);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = i / Math.expm1(i);
	double tmp;
	if (n <= -1.25e-197) {
		tmp = 100.0 / (t_0 / n);
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.75e-32) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = n / (t_0 / 100.0);
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = i / math.expm1(i)
	tmp = 0
	if n <= -1.25e-197:
		tmp = 100.0 / (t_0 / n)
	elif n <= 1.9e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.75e-32:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = n / (t_0 / 100.0)
	return tmp

Julia

function code(i, n)
	t_0 = Float64(i / expm1(i))
	tmp = 0.0
	if (n <= -1.25e-197)
		tmp = Float64(100.0 / Float64(t_0 / n));
	elseif (n <= 1.9e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.75e-32)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	else
		tmp = Float64(n / Float64(t_0 / 100.0));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.25e-197], N[(100.0 / N[(t$95$0 / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.9e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.75e-32], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n / N[(t$95$0 / 100.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 11: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{-47} \lor \neg \left(i \leq 1.25 \cdot 10^{-22}\right):\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + 100 \cdot \left(i \cdot \left(0.5 - \frac{0.5}{n}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= i -2.1e-47) (not (<= i 1.25e-22)))
   (* 100.0 (/ (expm1 i) (/ i n)))
   (* n (+ 100.0 (* 100.0 (* i (- 0.5 (/ 0.5 n))))))))

C

double code(double i, double n) {
	double tmp;
	if ((i <= -2.1e-47) || !(i <= 1.25e-22)) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else {
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if ((i <= -2.1e-47) || !(i <= 1.25e-22)) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else {
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (i <= -2.1e-47) or not (i <= 1.25e-22):
		tmp = 100.0 * (math.expm1(i) / (i / n))
	else:
		tmp = n * (100.0 + (100.0 * (i * (0.5 - (0.5 / n)))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((i <= -2.1e-47) || !(i <= 1.25e-22))
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	else
		tmp = Float64(n * Float64(100.0 + Float64(100.0 * Float64(i * Float64(0.5 - Float64(0.5 / n))))));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[Or[LessEqual[i, -2.1e-47], N[Not[LessEqual[i, 1.25e-22]], $MachinePrecision]], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(100.0 * N[(i * N[(0.5 - N[(0.5 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 64.4% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{if}\;n \leq -1.05 \cdot 10^{+255}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -6 \cdot 10^{-197}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0)))))
   (if (<= n -1.05e+255)
     t_0
     (if (<= n -6e-197)
       (/ n (+ 0.01 (* i -0.005)))
       (if (<= n 1.9e-175)
         (/ 0.0 (/ i n))
         (if (<= n 1.85e+83) (* 100.0 (/ n (+ 1.0 (* i -0.5)))) t_0))))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double tmp;
	if (n <= -1.05e+255) {
		tmp = t_0;
	} else if (n <= -6e-197) {
		tmp = n / (0.01 + (i * -0.005));
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.85e+83) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

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 = n * (100.0d0 + (i * 50.0d0))
    if (n <= (-1.05d+255)) then
        tmp = t_0
    else if (n <= (-6d-197)) then
        tmp = n / (0.01d0 + (i * (-0.005d0)))
    else if (n <= 1.9d-175) then
        tmp = 0.0d0 / (i / n)
    else if (n <= 1.85d+83) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double tmp;
	if (n <= -1.05e+255) {
		tmp = t_0;
	} else if (n <= -6e-197) {
		tmp = n / (0.01 + (i * -0.005));
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.85e+83) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	tmp = 0
	if n <= -1.05e+255:
		tmp = t_0
	elif n <= -6e-197:
		tmp = n / (0.01 + (i * -0.005))
	elif n <= 1.9e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.85e+83:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(n * Float64(100.0 + Float64(i * 50.0)))
	tmp = 0.0
	if (n <= -1.05e+255)
		tmp = t_0;
	elseif (n <= -6e-197)
		tmp = Float64(n / Float64(0.01 + Float64(i * -0.005)));
	elseif (n <= 1.9e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.85e+83)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = n * (100.0 + (i * 50.0));
	tmp = 0.0;
	if (n <= -1.05e+255)
		tmp = t_0;
	elseif (n <= -6e-197)
		tmp = n / (0.01 + (i * -0.005));
	elseif (n <= 1.9e-175)
		tmp = 0.0 / (i / n);
	elseif (n <= 1.85e+83)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.05e+255], t$95$0, If[LessEqual[n, -6e-197], N[(n / N[(0.01 + N[(i * -0.005), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.9e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.85e+83], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

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

Alternative 13: 64.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.8 \cdot 10^{+251}:\\ \;\;\;\;\frac{n \cdot \left(i \cdot 100\right)}{i}\\ \mathbf{elif}\;n \leq -4.9 \cdot 10^{-197}:\\ \;\;\;\;\frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.65 \cdot 10^{+84}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -1.8e+251)
   (/ (* n (* i 100.0)) i)
   (if (<= n -4.9e-197)
     (/ n (+ 0.01 (* i -0.005)))
     (if (<= n 1.9e-175)
       (/ 0.0 (/ i n))
       (if (<= n 1.65e+84)
         (* 100.0 (/ n (+ 1.0 (* i -0.5))))
         (* n (+ 100.0 (* i 50.0))))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -1.8e+251) {
		tmp = (n * (i * 100.0)) / i;
	} else if (n <= -4.9e-197) {
		tmp = n / (0.01 + (i * -0.005));
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.65e+84) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} 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 <= (-1.8d+251)) then
        tmp = (n * (i * 100.0d0)) / i
    else if (n <= (-4.9d-197)) then
        tmp = n / (0.01d0 + (i * (-0.005d0)))
    else if (n <= 1.9d-175) then
        tmp = 0.0d0 / (i / n)
    else if (n <= 1.65d+84) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    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 <= -1.8e+251) {
		tmp = (n * (i * 100.0)) / i;
	} else if (n <= -4.9e-197) {
		tmp = n / (0.01 + (i * -0.005));
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.65e+84) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -1.8e+251:
		tmp = (n * (i * 100.0)) / i
	elif n <= -4.9e-197:
		tmp = n / (0.01 + (i * -0.005))
	elif n <= 1.9e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.65e+84:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -1.8e+251)
		tmp = Float64(Float64(n * Float64(i * 100.0)) / i);
	elseif (n <= -4.9e-197)
		tmp = Float64(n / Float64(0.01 + Float64(i * -0.005)));
	elseif (n <= 1.9e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.65e+84)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	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 <= -1.8e+251)
		tmp = (n * (i * 100.0)) / i;
	elseif (n <= -4.9e-197)
		tmp = n / (0.01 + (i * -0.005));
	elseif (n <= 1.9e-175)
		tmp = 0.0 / (i / n);
	elseif (n <= 1.65e+84)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -1.8e+251], N[(N[(n * N[(i * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, -4.9e-197], N[(n / N[(0.01 + N[(i * -0.005), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.9e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.65e+84], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 14: 64.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.8 \cdot 10^{+251}:\\ \;\;\;\;\frac{n \cdot \left(i \cdot 100\right)}{i}\\ \mathbf{elif}\;n \leq -9.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{100}{\frac{i}{n} \cdot -0.5 + \frac{1}{n}}\\ \mathbf{elif}\;n \leq 2.05 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.85 \cdot 10^{+83}:\\ \;\;\;\;100 \cdot \frac{n}{1 + i \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -1.8e+251)
   (/ (* n (* i 100.0)) i)
   (if (<= n -9.8e-200)
     (/ 100.0 (+ (* (/ i n) -0.5) (/ 1.0 n)))
     (if (<= n 2.05e-175)
       (/ 0.0 (/ i n))
       (if (<= n 1.85e+83)
         (* 100.0 (/ n (+ 1.0 (* i -0.5))))
         (* n (+ 100.0 (* i 50.0))))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -1.8e+251) {
		tmp = (n * (i * 100.0)) / i;
	} else if (n <= -9.8e-200) {
		tmp = 100.0 / (((i / n) * -0.5) + (1.0 / n));
	} else if (n <= 2.05e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.85e+83) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} 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 <= (-1.8d+251)) then
        tmp = (n * (i * 100.0d0)) / i
    else if (n <= (-9.8d-200)) then
        tmp = 100.0d0 / (((i / n) * (-0.5d0)) + (1.0d0 / n))
    else if (n <= 2.05d-175) then
        tmp = 0.0d0 / (i / n)
    else if (n <= 1.85d+83) then
        tmp = 100.0d0 * (n / (1.0d0 + (i * (-0.5d0))))
    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 <= -1.8e+251) {
		tmp = (n * (i * 100.0)) / i;
	} else if (n <= -9.8e-200) {
		tmp = 100.0 / (((i / n) * -0.5) + (1.0 / n));
	} else if (n <= 2.05e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.85e+83) {
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -1.8e+251:
		tmp = (n * (i * 100.0)) / i
	elif n <= -9.8e-200:
		tmp = 100.0 / (((i / n) * -0.5) + (1.0 / n))
	elif n <= 2.05e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.85e+83:
		tmp = 100.0 * (n / (1.0 + (i * -0.5)))
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -1.8e+251)
		tmp = Float64(Float64(n * Float64(i * 100.0)) / i);
	elseif (n <= -9.8e-200)
		tmp = Float64(100.0 / Float64(Float64(Float64(i / n) * -0.5) + Float64(1.0 / n)));
	elseif (n <= 2.05e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.85e+83)
		tmp = Float64(100.0 * Float64(n / Float64(1.0 + Float64(i * -0.5))));
	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 <= -1.8e+251)
		tmp = (n * (i * 100.0)) / i;
	elseif (n <= -9.8e-200)
		tmp = 100.0 / (((i / n) * -0.5) + (1.0 / n));
	elseif (n <= 2.05e-175)
		tmp = 0.0 / (i / n);
	elseif (n <= 1.85e+83)
		tmp = 100.0 * (n / (1.0 + (i * -0.5)));
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -1.8e+251], N[(N[(n * N[(i * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, -9.8e-200], N[(100.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.5), $MachinePrecision] + N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2.05e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.85e+83], N[(100.0 * N[(n / N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 15: 64.4% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ t_1 := \frac{n}{0.01 + i \cdot -0.005}\\ \mathbf{if}\;n \leq -4.6 \cdot 10^{+251}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -1.1 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{-175}:\\ \;\;\;\;\frac{0}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 1.9 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0)))) (t_1 (/ n (+ 0.01 (* i -0.005)))))
   (if (<= n -4.6e+251)
     t_0
     (if (<= n -1.1e-196)
       t_1
       (if (<= n 1.9e-175) (/ 0.0 (/ i n)) (if (<= n 1.9e+83) t_1 t_0))))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double t_1 = n / (0.01 + (i * -0.005));
	double tmp;
	if (n <= -4.6e+251) {
		tmp = t_0;
	} else if (n <= -1.1e-196) {
		tmp = t_1;
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.9e+83) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = n * (100.0d0 + (i * 50.0d0))
    t_1 = n / (0.01d0 + (i * (-0.005d0)))
    if (n <= (-4.6d+251)) then
        tmp = t_0
    else if (n <= (-1.1d-196)) then
        tmp = t_1
    else if (n <= 1.9d-175) then
        tmp = 0.0d0 / (i / n)
    else if (n <= 1.9d+83) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double t_1 = n / (0.01 + (i * -0.005));
	double tmp;
	if (n <= -4.6e+251) {
		tmp = t_0;
	} else if (n <= -1.1e-196) {
		tmp = t_1;
	} else if (n <= 1.9e-175) {
		tmp = 0.0 / (i / n);
	} else if (n <= 1.9e+83) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	t_1 = n / (0.01 + (i * -0.005))
	tmp = 0
	if n <= -4.6e+251:
		tmp = t_0
	elif n <= -1.1e-196:
		tmp = t_1
	elif n <= 1.9e-175:
		tmp = 0.0 / (i / n)
	elif n <= 1.9e+83:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(n * Float64(100.0 + Float64(i * 50.0)))
	t_1 = Float64(n / Float64(0.01 + Float64(i * -0.005)))
	tmp = 0.0
	if (n <= -4.6e+251)
		tmp = t_0;
	elseif (n <= -1.1e-196)
		tmp = t_1;
	elseif (n <= 1.9e-175)
		tmp = Float64(0.0 / Float64(i / n));
	elseif (n <= 1.9e+83)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	t_0 = n * (100.0 + (i * 50.0));
	t_1 = n / (0.01 + (i * -0.005));
	tmp = 0.0;
	if (n <= -4.6e+251)
		tmp = t_0;
	elseif (n <= -1.1e-196)
		tmp = t_1;
	elseif (n <= 1.9e-175)
		tmp = 0.0 / (i / n);
	elseif (n <= 1.9e+83)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(n / N[(0.01 + N[(i * -0.005), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -4.6e+251], t$95$0, If[LessEqual[n, -1.1e-196], t$95$1, If[LessEqual[n, 1.9e-175], N[(0.0 / N[(i / n), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 1.9e+83], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 16: 57.1% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2 \lor \neg \left(i \leq 1.2 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= i -2.0) (not (<= i 1.2e+154))) (* (/ n i) -200.0) (* n 100.0)))

C

double code(double i, double n) {
	double tmp;
	if ((i <= -2.0) || !(i <= 1.2e+154)) {
		tmp = (n / i) * -200.0;
	} else {
		tmp = n * 100.0;
	}
	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)) .or. (.not. (i <= 1.2d+154))) then
        tmp = (n / i) * (-200.0d0)
    else
        tmp = n * 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((i <= -2.0) || !(i <= 1.2e+154)) {
		tmp = (n / i) * -200.0;
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (i <= -2.0) or not (i <= 1.2e+154):
		tmp = (n / i) * -200.0
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((i <= -2.0) || !(i <= 1.2e+154))
		tmp = Float64(Float64(n / i) * -200.0);
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((i <= -2.0) || ~((i <= 1.2e+154)))
		tmp = (n / i) * -200.0;
	else
		tmp = n * 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[i, -2.0], N[Not[LessEqual[i, 1.2e+154]], $MachinePrecision]], N[(N[(n / i), $MachinePrecision] * -200.0), $MachinePrecision], N[(n * 100.0), $MachinePrecision]]

Derivation

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

Alternative 17: 59.9% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2:\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{+15}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;50 \cdot \left(i \cdot n\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -2.0)
   (* (/ n i) -200.0)
   (if (<= i 3.8e+15) (* n 100.0) (* 50.0 (* i n)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -2.0) {
		tmp = (n / i) * -200.0;
	} else if (i <= 3.8e+15) {
		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 / i) * (-200.0d0)
    else if (i <= 3.8d+15) 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 / i) * -200.0;
	} else if (i <= 3.8e+15) {
		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 / i) * -200.0
	elif i <= 3.8e+15:
		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(Float64(n / i) * -200.0);
	elseif (i <= 3.8e+15)
		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 / i) * -200.0;
	elseif (i <= 3.8e+15)
		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[(n / i), $MachinePrecision] * -200.0), $MachinePrecision], If[LessEqual[i, 3.8e+15], N[(n * 100.0), $MachinePrecision], N[(50.0 * N[(i * n), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 18: 60.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.62:\\ \;\;\;\;\frac{n}{i} \cdot -200\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -1.62) (* (/ n i) -200.0) (* n (+ 100.0 (* i 50.0)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -1.62) {
		tmp = (n / i) * -200.0;
	} 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 (i <= (-1.62d0)) then
        tmp = (n / i) * (-200.0d0)
    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 (i <= -1.62) {
		tmp = (n / i) * -200.0;
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -1.62:
		tmp = (n / i) * -200.0
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -1.62)
		tmp = Float64(Float64(n / i) * -200.0);
	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 (i <= -1.62)
		tmp = (n / i) * -200.0;
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -1.62], N[(N[(n / i), $MachinePrecision] * -200.0), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 19: 60.4% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.62:\\ \;\;\;\;\frac{100}{\frac{i}{n} \cdot -0.5}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -1.62) (/ 100.0 (* (/ i n) -0.5)) (* n (+ 100.0 (* i 50.0)))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -1.62) {
		tmp = 100.0 / ((i / n) * -0.5);
	} 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 (i <= (-1.62d0)) then
        tmp = 100.0d0 / ((i / n) * (-0.5d0))
    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 (i <= -1.62) {
		tmp = 100.0 / ((i / n) * -0.5);
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -1.62:
		tmp = 100.0 / ((i / n) * -0.5)
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -1.62)
		tmp = Float64(100.0 / Float64(Float64(i / n) * -0.5));
	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 (i <= -1.62)
		tmp = 100.0 / ((i / n) * -0.5);
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -1.62], N[(100.0 / N[(N[(i / n), $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 20: 49.6% 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: 33.7% 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 2023341 
(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))))