Compound Interest

Percentage Accurate: 28.1% → 99.4%

Time: 24.7s

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: 28.1% 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: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-151}:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{n \cdot \mathsf{fma}\left(t_0, 100, -100\right)}{i}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

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 -5e-151)
     (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
       (if (<= t_1 INFINITY)
         (/ (* n (fma t_0 100.0 -100.0)) i)
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

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 <= -5e-151) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1((n * log1p((i / n)))) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (n * fma(t_0, 100.0, -100.0)) / i;
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -5e-151)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(n * fma(t_0, 100.0, -100.0)) / i);
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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, -5e-151], 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[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(n * N[(t$95$0 * 100.0 + -100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{{\left(1 + \frac{i}{n}\right)}^{n} + -1}{\frac{i}{n}}\\ t_1 := t_0 \cdot 100\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;t_0 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

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 -2e-101)
     t_1
     (if (<= t_0 0.0)
       (* 100.0 (/ n (/ i (expm1 i))))
       (if (<= t_0 INFINITY)
         t_1
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

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 <= -2e-101) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (t_0 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -2e-101) {
		tmp = t_1;
	} else if (t_0 <= 0.0) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (t_0 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -2e-101:
		tmp = t_1
	elif t_0 <= 0.0:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif t_0 <= math.inf:
		tmp = t_1
	else:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	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 <= -2e-101)
		tmp = t_1;
	elseif (t_0 <= 0.0)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (t_0 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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, -2e-101], t$95$1, If[LessEqual[t$95$0, 0.0], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, Infinity], t$95$1, N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 3: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-162}:\\ \;\;\;\;n \cdot \frac{-100 + t_0 \cdot 100}{i}\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_1 \cdot 100\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

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-162)
     (* n (/ (+ -100.0 (* t_0 100.0)) i))
     (if (<= t_1 0.0)
       (* 100.0 (/ n (/ i (expm1 i))))
       (if (<= t_1 INFINITY)
         (* t_1 100.0)
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

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-162) {
		tmp = n * ((-100.0 + (t_0 * 100.0)) / i);
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_1 * 100.0;
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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-162) {
		tmp = n * ((-100.0 + (t_0 * 100.0)) / i);
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 * 100.0;
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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-162:
		tmp = n * ((-100.0 + (t_0 * 100.0)) / i)
	elif t_1 <= 0.0:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif t_1 <= math.inf:
		tmp = t_1 * 100.0
	else:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	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-162)
		tmp = Float64(n * Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / i));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (t_1 <= Inf)
		tmp = Float64(t_1 * 100.0);
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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-162], N[(n * N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(t$95$1 * 100.0), $MachinePrecision], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := -100 + t_0 \cdot 100\\ t_2 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{-162}:\\ \;\;\;\;n \cdot \frac{t_1}{i}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;\frac{t_1}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (pow (+ 1.0 (/ i n)) n))
        (t_1 (+ -100.0 (* t_0 100.0)))
        (t_2 (/ (+ t_0 -1.0) (/ i n))))
   (if (<= t_2 -1e-162)
     (* n (/ t_1 i))
     (if (<= t_2 0.0)
       (* 100.0 (/ n (/ i (expm1 i))))
       (if (<= t_2 INFINITY)
         (/ t_1 (/ i n))
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

C

double code(double i, double n) {
	double t_0 = pow((1.0 + (i / n)), n);
	double t_1 = -100.0 + (t_0 * 100.0);
	double t_2 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_2 <= -1e-162) {
		tmp = n * (t_1 / i);
	} else if (t_2 <= 0.0) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1 / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((1.0 + (i / n)), n);
	double t_1 = -100.0 + (t_0 * 100.0);
	double t_2 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_2 <= -1e-162) {
		tmp = n * (t_1 / i);
	} else if (t_2 <= 0.0) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1 / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = -100.0 + (t_0 * 100.0)
	t_2 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_2 <= -1e-162:
		tmp = n * (t_1 / i)
	elif t_2 <= 0.0:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif t_2 <= math.inf:
		tmp = t_1 / (i / n)
	else:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(-100.0 + Float64(t_0 * 100.0))
	t_2 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_2 <= -1e-162)
		tmp = Float64(n * Float64(t_1 / i));
	elseif (t_2 <= 0.0)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (t_2 <= Inf)
		tmp = Float64(t_1 / Float64(i / n));
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$0 + -1.0), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-162], N[(n * N[(t$95$1 / i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], N[(t$95$1 / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-101}:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{-100 + t_0 \cdot 100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

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 -2e-101)
     (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
     (if (<= t_1 0.0)
       (* 100.0 (/ n (/ i (expm1 i))))
       (if (<= t_1 INFINITY)
         (/ (+ -100.0 (* t_0 100.0)) (/ i n))
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

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 <= -2e-101) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -2e-101) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -2e-101:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	elif t_1 <= 0.0:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif t_1 <= math.inf:
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n)
	else:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	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 <= -2e-101)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / Float64(i / n));
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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, -2e-101], 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 / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 6: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(1 + \frac{i}{n}\right)}^{n}\\ t_1 := \frac{t_0 + -1}{\frac{i}{n}}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-151}:\\ \;\;\;\;100 \cdot \left(t_0 \cdot \frac{n}{i} - \frac{n}{i}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(n \cdot \mathsf{log1p}\left(\frac{i}{n}\right)\right)}{\frac{i}{n}}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{-100 + t_0 \cdot 100}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \end{array} \end{array} \]

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 -5e-151)
     (* 100.0 (- (* t_0 (/ n i)) (/ n i)))
     (if (<= t_1 0.0)
       (* 100.0 (/ (expm1 (* n (log1p (/ i n)))) (/ i n)))
       (if (<= t_1 INFINITY)
         (/ (+ -100.0 (* t_0 100.0)) (/ i n))
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n)))))))))

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 <= -5e-151) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (expm1((n * log1p((i / n)))) / (i / n));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -5e-151) {
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i));
	} else if (t_1 <= 0.0) {
		tmp = 100.0 * (Math.expm1((n * Math.log1p((i / n)))) / (i / n));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n);
	} else {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	}
	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 <= -5e-151:
		tmp = 100.0 * ((t_0 * (n / i)) - (n / i))
	elif t_1 <= 0.0:
		tmp = 100.0 * (math.expm1((n * math.log1p((i / n)))) / (i / n))
	elif t_1 <= math.inf:
		tmp = (-100.0 + (t_0 * 100.0)) / (i / n)
	else:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	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 <= -5e-151)
		tmp = Float64(100.0 * Float64(Float64(t_0 * Float64(n / i)) - Float64(n / i)));
	elseif (t_1 <= 0.0)
		tmp = Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / Float64(i / n)));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(-100.0 + Float64(t_0 * 100.0)) / Float64(i / n));
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	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, -5e-151], 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[(Exp[N[(n * N[Log[1 + N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(-100.0 + N[(t$95$0 * 100.0), $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 7: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ t_1 := 100 \cdot \left(i \cdot -0.5\right)\\ \mathbf{if}\;n \leq -7.4 \cdot 10^{-211}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 1.55 \cdot 10^{-169}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \mathbf{elif}\;n \leq 8 \cdot 10^{+41}:\\ \;\;\;\;\frac{\left(n \cdot 100\right) \cdot \left(n \cdot 100\right) + t_1 \cdot \left(100 \cdot \left(\left(i \cdot n\right) \cdot \left(\frac{0.5}{n} - 0.5\right)\right)\right)}{n \cdot 100 - t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ n (/ i (expm1 i))))) (t_1 (* 100.0 (* i -0.5))))
   (if (<= n -7.4e-211)
     t_0
     (if (<= n 1.55e-169)
       (/ (* n 0.0) i)
       (if (<= n 1.35e-34)
         (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n))))
         (if (<= n 8e+41)
           (/
            (+
             (* (* n 100.0) (* n 100.0))
             (* t_1 (* 100.0 (* (* i n) (- (/ 0.5 n) 0.5)))))
            (- (* n 100.0) t_1))
           t_0))))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / expm1(i)));
	double t_1 = 100.0 * (i * -0.5);
	double tmp;
	if (n <= -7.4e-211) {
		tmp = t_0;
	} else if (n <= 1.55e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.35e-34) {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	} else if (n <= 8e+41) {
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - t_1);
	} 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 t_1 = 100.0 * (i * -0.5);
	double tmp;
	if (n <= -7.4e-211) {
		tmp = t_0;
	} else if (n <= 1.55e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.35e-34) {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	} else if (n <= 8e+41) {
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - t_1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (n / (i / math.expm1(i)))
	t_1 = 100.0 * (i * -0.5)
	tmp = 0
	if n <= -7.4e-211:
		tmp = t_0
	elif n <= 1.55e-169:
		tmp = (n * 0.0) / i
	elif n <= 1.35e-34:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	elif n <= 8e+41:
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - t_1)
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(n / Float64(i / expm1(i))))
	t_1 = Float64(100.0 * Float64(i * -0.5))
	tmp = 0.0
	if (n <= -7.4e-211)
		tmp = t_0;
	elseif (n <= 1.55e-169)
		tmp = Float64(Float64(n * 0.0) / i);
	elseif (n <= 1.35e-34)
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	elseif (n <= 8e+41)
		tmp = Float64(Float64(Float64(Float64(n * 100.0) * Float64(n * 100.0)) + Float64(t_1 * Float64(100.0 * Float64(Float64(i * n) * Float64(Float64(0.5 / n) - 0.5))))) / Float64(Float64(n * 100.0) - t_1));
	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]}, Block[{t$95$1 = N[(100.0 * N[(i * -0.5), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -7.4e-211], t$95$0, If[LessEqual[n, 1.55e-169], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, 1.35e-34], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 8e+41], N[(N[(N[(N[(n * 100.0), $MachinePrecision] * N[(n * 100.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(100.0 * N[(N[(i * n), $MachinePrecision] * N[(N[(0.5 / n), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(n * 100.0), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

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

Alternative 8: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{if}\;i \leq -1.2 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq -1.15 \cdot 10^{-207}:\\ \;\;\;\;\frac{100 \cdot \left(i \cdot n\right)}{i}\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-6}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (expm1 i) (/ i n)))))
   (if (<= i -1.2e-34)
     t_0
     (if (<= i -1.15e-207)
       (/ (* 100.0 (* i n)) i)
       (if (<= i 1.3e-6) (* n 100.0) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (expm1(i) / (i / n));
	double tmp;
	if (i <= -1.2e-34) {
		tmp = t_0;
	} else if (i <= -1.15e-207) {
		tmp = (100.0 * (i * n)) / i;
	} else if (i <= 1.3e-6) {
		tmp = n * 100.0;
	} else {
		tmp = t_0;
	}
	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 <= -1.2e-34) {
		tmp = t_0;
	} else if (i <= -1.15e-207) {
		tmp = (100.0 * (i * n)) / i;
	} else if (i <= 1.3e-6) {
		tmp = n * 100.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (math.expm1(i) / (i / n))
	tmp = 0
	if i <= -1.2e-34:
		tmp = t_0
	elif i <= -1.15e-207:
		tmp = (100.0 * (i * n)) / i
	elif i <= 1.3e-6:
		tmp = n * 100.0
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(expm1(i) / Float64(i / n)))
	tmp = 0.0
	if (i <= -1.2e-34)
		tmp = t_0;
	elseif (i <= -1.15e-207)
		tmp = Float64(Float64(100.0 * Float64(i * n)) / i);
	elseif (i <= 1.3e-6)
		tmp = Float64(n * 100.0);
	else
		tmp = t_0;
	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, -1.2e-34], t$95$0, If[LessEqual[i, -1.15e-207], N[(N[(100.0 * N[(i * n), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[i, 1.3e-6], N[(n * 100.0), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 9: 75.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6.7 \cdot 10^{-32}:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{elif}\;i \leq -6.6 \cdot 10^{-205}:\\ \;\;\;\;\frac{100 \cdot \left(i \cdot n\right)}{i}\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{-6}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;\mathsf{expm1}\left(i\right) \cdot \left(100 \cdot \frac{n}{i}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -6.7e-32)
   (* 100.0 (/ (expm1 i) (/ i n)))
   (if (<= i -6.6e-205)
     (/ (* 100.0 (* i n)) i)
     (if (<= i 1.3e-6) (* n 100.0) (* (expm1 i) (* 100.0 (/ n i)))))))

C

double code(double i, double n) {
	double tmp;
	if (i <= -6.7e-32) {
		tmp = 100.0 * (expm1(i) / (i / n));
	} else if (i <= -6.6e-205) {
		tmp = (100.0 * (i * n)) / i;
	} else if (i <= 1.3e-6) {
		tmp = n * 100.0;
	} else {
		tmp = expm1(i) * (100.0 * (n / i));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= -6.7e-32) {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	} else if (i <= -6.6e-205) {
		tmp = (100.0 * (i * n)) / i;
	} else if (i <= 1.3e-6) {
		tmp = n * 100.0;
	} else {
		tmp = Math.expm1(i) * (100.0 * (n / i));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -6.7e-32:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	elif i <= -6.6e-205:
		tmp = (100.0 * (i * n)) / i
	elif i <= 1.3e-6:
		tmp = n * 100.0
	else:
		tmp = math.expm1(i) * (100.0 * (n / i))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -6.7e-32)
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	elseif (i <= -6.6e-205)
		tmp = Float64(Float64(100.0 * Float64(i * n)) / i);
	elseif (i <= 1.3e-6)
		tmp = Float64(n * 100.0);
	else
		tmp = Float64(expm1(i) * Float64(100.0 * Float64(n / i)));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[i, -6.7e-32], N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -6.6e-205], N[(N[(100.0 * N[(i * n), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[i, 1.3e-6], N[(n * 100.0), $MachinePrecision], N[(N[(Exp[i] - 1), $MachinePrecision] * N[(100.0 * N[(n / i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 10: 67.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ t_1 := \frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \mathbf{if}\;n \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -7.2 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 1.8 \cdot 10^{-169}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 4.2 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 1.18 \cdot 10^{+89}:\\ \;\;\;\;\frac{\left(100 \cdot \left(n + \left(i \cdot n\right) \cdot \left(\frac{0.5}{n} + -0.5\right)\right)\right) \cdot \left(100 \cdot \left(n \cdot \left(1 + i \cdot \left(0.5 + \frac{-0.5}{n}\right)\right)\right)\right)}{n \cdot 100 + 100 \cdot \left(\left(i \cdot n\right) \cdot \left(\frac{0.5}{n} - 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0))))
        (t_1 (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n))))))
   (if (<= n -3.7e+191)
     t_0
     (if (<= n -7.2e-211)
       t_1
       (if (<= n 1.8e-169)
         (/ (* n 0.0) i)
         (if (<= n 4.2e-35)
           t_1
           (if (<= n 1.18e+89)
             (/
              (*
               (* 100.0 (+ n (* (* i n) (+ (/ 0.5 n) -0.5))))
               (* 100.0 (* n (+ 1.0 (* i (+ 0.5 (/ -0.5 n)))))))
              (+ (* n 100.0) (* 100.0 (* (* i n) (- (/ 0.5 n) 0.5)))))
             t_0)))))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.7e+191) {
		tmp = t_0;
	} else if (n <= -7.2e-211) {
		tmp = t_1;
	} else if (n <= 1.8e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 4.2e-35) {
		tmp = t_1;
	} else if (n <= 1.18e+89) {
		tmp = ((100.0 * (n + ((i * n) * ((0.5 / n) + -0.5)))) * (100.0 * (n * (1.0 + (i * (0.5 + (-0.5 / n))))))) / ((n * 100.0) + (100.0 * ((i * n) * ((0.5 / n) - 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) :: t_1
    real(8) :: tmp
    t_0 = n * (100.0d0 + (i * 50.0d0))
    t_1 = 1.0d0 / (((i / n) * (-0.005d0)) + (0.01d0 * (1.0d0 / n)))
    if (n <= (-3.7d+191)) then
        tmp = t_0
    else if (n <= (-7.2d-211)) then
        tmp = t_1
    else if (n <= 1.8d-169) then
        tmp = (n * 0.0d0) / i
    else if (n <= 4.2d-35) then
        tmp = t_1
    else if (n <= 1.18d+89) then
        tmp = ((100.0d0 * (n + ((i * n) * ((0.5d0 / n) + (-0.5d0))))) * (100.0d0 * (n * (1.0d0 + (i * (0.5d0 + ((-0.5d0) / n))))))) / ((n * 100.0d0) + (100.0d0 * ((i * n) * ((0.5d0 / n) - 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 t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.7e+191) {
		tmp = t_0;
	} else if (n <= -7.2e-211) {
		tmp = t_1;
	} else if (n <= 1.8e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 4.2e-35) {
		tmp = t_1;
	} else if (n <= 1.18e+89) {
		tmp = ((100.0 * (n + ((i * n) * ((0.5 / n) + -0.5)))) * (100.0 * (n * (1.0 + (i * (0.5 + (-0.5 / n))))))) / ((n * 100.0) + (100.0 * ((i * n) * ((0.5 / n) - 0.5))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	tmp = 0
	if n <= -3.7e+191:
		tmp = t_0
	elif n <= -7.2e-211:
		tmp = t_1
	elif n <= 1.8e-169:
		tmp = (n * 0.0) / i
	elif n <= 4.2e-35:
		tmp = t_1
	elif n <= 1.18e+89:
		tmp = ((100.0 * (n + ((i * n) * ((0.5 / n) + -0.5)))) * (100.0 * (n * (1.0 + (i * (0.5 + (-0.5 / n))))))) / ((n * 100.0) + (100.0 * ((i * n) * ((0.5 / n) - 0.5))))
	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(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))))
	tmp = 0.0
	if (n <= -3.7e+191)
		tmp = t_0;
	elseif (n <= -7.2e-211)
		tmp = t_1;
	elseif (n <= 1.8e-169)
		tmp = Float64(Float64(n * 0.0) / i);
	elseif (n <= 4.2e-35)
		tmp = t_1;
	elseif (n <= 1.18e+89)
		tmp = Float64(Float64(Float64(100.0 * Float64(n + Float64(Float64(i * n) * Float64(Float64(0.5 / n) + -0.5)))) * Float64(100.0 * Float64(n * Float64(1.0 + Float64(i * Float64(0.5 + Float64(-0.5 / n))))))) / Float64(Float64(n * 100.0) + Float64(100.0 * Float64(Float64(i * n) * Float64(Float64(0.5 / n) - 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));
	t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	tmp = 0.0;
	if (n <= -3.7e+191)
		tmp = t_0;
	elseif (n <= -7.2e-211)
		tmp = t_1;
	elseif (n <= 1.8e-169)
		tmp = (n * 0.0) / i;
	elseif (n <= 4.2e-35)
		tmp = t_1;
	elseif (n <= 1.18e+89)
		tmp = ((100.0 * (n + ((i * n) * ((0.5 / n) + -0.5)))) * (100.0 * (n * (1.0 + (i * (0.5 + (-0.5 / n))))))) / ((n * 100.0) + (100.0 * ((i * n) * ((0.5 / n) - 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]}, Block[{t$95$1 = N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -3.7e+191], t$95$0, If[LessEqual[n, -7.2e-211], t$95$1, If[LessEqual[n, 1.8e-169], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, 4.2e-35], t$95$1, If[LessEqual[n, 1.18e+89], N[(N[(N[(100.0 * N[(n + N[(N[(i * n), $MachinePrecision] * N[(N[(0.5 / n), $MachinePrecision] + -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(100.0 * N[(n * N[(1.0 + N[(i * N[(0.5 + N[(-0.5 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(n * 100.0), $MachinePrecision] + N[(100.0 * N[(N[(i * n), $MachinePrecision] * N[(N[(0.5 / n), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 11: 67.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ t_1 := \frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \mathbf{if}\;n \leq -3.4 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -7.4 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 4.7 \cdot 10^{-169}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;n \leq 8 \cdot 10^{+88}:\\ \;\;\;\;\frac{\left(n \cdot 100\right) \cdot \left(n \cdot 100\right) + \left(100 \cdot \left(\left(i \cdot n\right) \cdot \left(0.5 - \frac{0.5}{n}\right)\right)\right) \cdot \left(100 \cdot \left(\left(i \cdot n\right) \cdot \left(\frac{0.5}{n} - 0.5\right)\right)\right)}{n \cdot \left(100 - i \cdot 50\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0))))
        (t_1 (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n))))))
   (if (<= n -3.4e+191)
     t_0
     (if (<= n -7.4e-211)
       t_1
       (if (<= n 4.7e-169)
         (/ (* n 0.0) i)
         (if (<= n 1.35e-34)
           t_1
           (if (<= n 8e+88)
             (/
              (+
               (* (* n 100.0) (* n 100.0))
               (*
                (* 100.0 (* (* i n) (- 0.5 (/ 0.5 n))))
                (* 100.0 (* (* i n) (- (/ 0.5 n) 0.5)))))
              (* n (- 100.0 (* i 50.0))))
             t_0)))))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.4e+191) {
		tmp = t_0;
	} else if (n <= -7.4e-211) {
		tmp = t_1;
	} else if (n <= 4.7e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.35e-34) {
		tmp = t_1;
	} else if (n <= 8e+88) {
		tmp = (((n * 100.0) * (n * 100.0)) + ((100.0 * ((i * n) * (0.5 - (0.5 / n)))) * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / (n * (100.0 - (i * 50.0)));
	} 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 = 1.0d0 / (((i / n) * (-0.005d0)) + (0.01d0 * (1.0d0 / n)))
    if (n <= (-3.4d+191)) then
        tmp = t_0
    else if (n <= (-7.4d-211)) then
        tmp = t_1
    else if (n <= 4.7d-169) then
        tmp = (n * 0.0d0) / i
    else if (n <= 1.35d-34) then
        tmp = t_1
    else if (n <= 8d+88) then
        tmp = (((n * 100.0d0) * (n * 100.0d0)) + ((100.0d0 * ((i * n) * (0.5d0 - (0.5d0 / n)))) * (100.0d0 * ((i * n) * ((0.5d0 / n) - 0.5d0))))) / (n * (100.0d0 - (i * 50.0d0)))
    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 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.4e+191) {
		tmp = t_0;
	} else if (n <= -7.4e-211) {
		tmp = t_1;
	} else if (n <= 4.7e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.35e-34) {
		tmp = t_1;
	} else if (n <= 8e+88) {
		tmp = (((n * 100.0) * (n * 100.0)) + ((100.0 * ((i * n) * (0.5 - (0.5 / n)))) * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / (n * (100.0 - (i * 50.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	t_1 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	tmp = 0
	if n <= -3.4e+191:
		tmp = t_0
	elif n <= -7.4e-211:
		tmp = t_1
	elif n <= 4.7e-169:
		tmp = (n * 0.0) / i
	elif n <= 1.35e-34:
		tmp = t_1
	elif n <= 8e+88:
		tmp = (((n * 100.0) * (n * 100.0)) + ((100.0 * ((i * n) * (0.5 - (0.5 / n)))) * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / (n * (100.0 - (i * 50.0)))
	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(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))))
	tmp = 0.0
	if (n <= -3.4e+191)
		tmp = t_0;
	elseif (n <= -7.4e-211)
		tmp = t_1;
	elseif (n <= 4.7e-169)
		tmp = Float64(Float64(n * 0.0) / i);
	elseif (n <= 1.35e-34)
		tmp = t_1;
	elseif (n <= 8e+88)
		tmp = Float64(Float64(Float64(Float64(n * 100.0) * Float64(n * 100.0)) + Float64(Float64(100.0 * Float64(Float64(i * n) * Float64(0.5 - Float64(0.5 / n)))) * Float64(100.0 * Float64(Float64(i * n) * Float64(Float64(0.5 / n) - 0.5))))) / Float64(n * Float64(100.0 - Float64(i * 50.0))));
	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 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	tmp = 0.0;
	if (n <= -3.4e+191)
		tmp = t_0;
	elseif (n <= -7.4e-211)
		tmp = t_1;
	elseif (n <= 4.7e-169)
		tmp = (n * 0.0) / i;
	elseif (n <= 1.35e-34)
		tmp = t_1;
	elseif (n <= 8e+88)
		tmp = (((n * 100.0) * (n * 100.0)) + ((100.0 * ((i * n) * (0.5 - (0.5 / n)))) * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / (n * (100.0 - (i * 50.0)));
	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[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -3.4e+191], t$95$0, If[LessEqual[n, -7.4e-211], t$95$1, If[LessEqual[n, 4.7e-169], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, 1.35e-34], t$95$1, If[LessEqual[n, 8e+88], N[(N[(N[(N[(n * 100.0), $MachinePrecision] * N[(n * 100.0), $MachinePrecision]), $MachinePrecision] + N[(N[(100.0 * N[(N[(i * n), $MachinePrecision] * N[(0.5 - N[(0.5 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(100.0 * N[(N[(i * n), $MachinePrecision] * N[(N[(0.5 / n), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(n * N[(100.0 - N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 12: 67.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ t_1 := 100 \cdot \left(i \cdot -0.5\right)\\ t_2 := \frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \mathbf{if}\;n \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -4.5 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;n \leq 2.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{elif}\;n \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;n \leq 2.8 \cdot 10^{+149}:\\ \;\;\;\;\frac{\left(n \cdot 100\right) \cdot \left(n \cdot 100\right) + t_1 \cdot \left(100 \cdot \left(\left(i \cdot n\right) \cdot \left(\frac{0.5}{n} - 0.5\right)\right)\right)}{n \cdot 100 - t_1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0))))
        (t_1 (* 100.0 (* i -0.5)))
        (t_2 (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n))))))
   (if (<= n -3.7e+191)
     t_0
     (if (<= n -4.5e-211)
       t_2
       (if (<= n 2.2e-169)
         (/ (* n 0.0) i)
         (if (<= n 1.15e-34)
           t_2
           (if (<= n 2.8e+149)
             (/
              (+
               (* (* n 100.0) (* n 100.0))
               (* t_1 (* 100.0 (* (* i n) (- (/ 0.5 n) 0.5)))))
              (- (* n 100.0) t_1))
             t_0)))))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double t_1 = 100.0 * (i * -0.5);
	double t_2 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.7e+191) {
		tmp = t_0;
	} else if (n <= -4.5e-211) {
		tmp = t_2;
	} else if (n <= 2.2e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.15e-34) {
		tmp = t_2;
	} else if (n <= 2.8e+149) {
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - 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) :: t_2
    real(8) :: tmp
    t_0 = n * (100.0d0 + (i * 50.0d0))
    t_1 = 100.0d0 * (i * (-0.5d0))
    t_2 = 1.0d0 / (((i / n) * (-0.005d0)) + (0.01d0 * (1.0d0 / n)))
    if (n <= (-3.7d+191)) then
        tmp = t_0
    else if (n <= (-4.5d-211)) then
        tmp = t_2
    else if (n <= 2.2d-169) then
        tmp = (n * 0.0d0) / i
    else if (n <= 1.15d-34) then
        tmp = t_2
    else if (n <= 2.8d+149) then
        tmp = (((n * 100.0d0) * (n * 100.0d0)) + (t_1 * (100.0d0 * ((i * n) * ((0.5d0 / n) - 0.5d0))))) / ((n * 100.0d0) - 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 = 100.0 * (i * -0.5);
	double t_2 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	double tmp;
	if (n <= -3.7e+191) {
		tmp = t_0;
	} else if (n <= -4.5e-211) {
		tmp = t_2;
	} else if (n <= 2.2e-169) {
		tmp = (n * 0.0) / i;
	} else if (n <= 1.15e-34) {
		tmp = t_2;
	} else if (n <= 2.8e+149) {
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - t_1);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	t_1 = 100.0 * (i * -0.5)
	t_2 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	tmp = 0
	if n <= -3.7e+191:
		tmp = t_0
	elif n <= -4.5e-211:
		tmp = t_2
	elif n <= 2.2e-169:
		tmp = (n * 0.0) / i
	elif n <= 1.15e-34:
		tmp = t_2
	elif n <= 2.8e+149:
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - 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(100.0 * Float64(i * -0.5))
	t_2 = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))))
	tmp = 0.0
	if (n <= -3.7e+191)
		tmp = t_0;
	elseif (n <= -4.5e-211)
		tmp = t_2;
	elseif (n <= 2.2e-169)
		tmp = Float64(Float64(n * 0.0) / i);
	elseif (n <= 1.15e-34)
		tmp = t_2;
	elseif (n <= 2.8e+149)
		tmp = Float64(Float64(Float64(Float64(n * 100.0) * Float64(n * 100.0)) + Float64(t_1 * Float64(100.0 * Float64(Float64(i * n) * Float64(Float64(0.5 / n) - 0.5))))) / Float64(Float64(n * 100.0) - 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 = 100.0 * (i * -0.5);
	t_2 = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	tmp = 0.0;
	if (n <= -3.7e+191)
		tmp = t_0;
	elseif (n <= -4.5e-211)
		tmp = t_2;
	elseif (n <= 2.2e-169)
		tmp = (n * 0.0) / i;
	elseif (n <= 1.15e-34)
		tmp = t_2;
	elseif (n <= 2.8e+149)
		tmp = (((n * 100.0) * (n * 100.0)) + (t_1 * (100.0 * ((i * n) * ((0.5 / n) - 0.5))))) / ((n * 100.0) - 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[(100.0 * N[(i * -0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -3.7e+191], t$95$0, If[LessEqual[n, -4.5e-211], t$95$2, If[LessEqual[n, 2.2e-169], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, 1.15e-34], t$95$2, If[LessEqual[n, 2.8e+149], N[(N[(N[(N[(n * 100.0), $MachinePrecision] * N[(n * 100.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(100.0 * N[(N[(i * n), $MachinePrecision] * N[(N[(0.5 / n), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(n * 100.0), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

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

Alternative 13: 65.1% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{if}\;n \leq -3 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -4.5 \cdot 10^{-211}:\\ \;\;\;\;\frac{1}{\frac{i}{n} \cdot -0.005 + 0.01 \cdot \frac{1}{n}}\\ \mathbf{elif}\;n \leq 6.2 \cdot 10^{-168}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0)))))
   (if (<= n -3e+191)
     t_0
     (if (<= n -4.5e-211)
       (/ 1.0 (+ (* (/ i n) -0.005) (* 0.01 (/ 1.0 n))))
       (if (<= n 6.2e-168) (/ (* n 0.0) i) t_0)))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double tmp;
	if (n <= -3e+191) {
		tmp = t_0;
	} else if (n <= -4.5e-211) {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	} else if (n <= 6.2e-168) {
		tmp = (n * 0.0) / i;
	} 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 <= (-3d+191)) then
        tmp = t_0
    else if (n <= (-4.5d-211)) then
        tmp = 1.0d0 / (((i / n) * (-0.005d0)) + (0.01d0 * (1.0d0 / n)))
    else if (n <= 6.2d-168) then
        tmp = (n * 0.0d0) / i
    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 <= -3e+191) {
		tmp = t_0;
	} else if (n <= -4.5e-211) {
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	} else if (n <= 6.2e-168) {
		tmp = (n * 0.0) / i;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	tmp = 0
	if n <= -3e+191:
		tmp = t_0
	elif n <= -4.5e-211:
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)))
	elif n <= 6.2e-168:
		tmp = (n * 0.0) / i
	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 <= -3e+191)
		tmp = t_0;
	elseif (n <= -4.5e-211)
		tmp = Float64(1.0 / Float64(Float64(Float64(i / n) * -0.005) + Float64(0.01 * Float64(1.0 / n))));
	elseif (n <= 6.2e-168)
		tmp = Float64(Float64(n * 0.0) / i);
	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 <= -3e+191)
		tmp = t_0;
	elseif (n <= -4.5e-211)
		tmp = 1.0 / (((i / n) * -0.005) + (0.01 * (1.0 / n)));
	elseif (n <= 6.2e-168)
		tmp = (n * 0.0) / i;
	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, -3e+191], t$95$0, If[LessEqual[n, -4.5e-211], N[(1.0 / N[(N[(N[(i / n), $MachinePrecision] * -0.005), $MachinePrecision] + N[(0.01 * N[(1.0 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.2e-168], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 14: 63.6% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{100 \cdot \left(i \cdot n\right)}{i}\\ \mathbf{elif}\;n \leq -6.2 \cdot 10^{-211}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 3.1 \cdot 10^{-168}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -2.9e+85)
   (/ (* 100.0 (* i n)) i)
   (if (<= n -6.2e-211)
     (* 100.0 (/ i (/ i n)))
     (if (<= n 3.1e-168) (/ (* n 0.0) i) (* n (+ 100.0 (* i 50.0)))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -2.9e+85) {
		tmp = (100.0 * (i * n)) / i;
	} else if (n <= -6.2e-211) {
		tmp = 100.0 * (i / (i / n));
	} else if (n <= 3.1e-168) {
		tmp = (n * 0.0) / i;
	} 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 <= (-2.9d+85)) then
        tmp = (100.0d0 * (i * n)) / i
    else if (n <= (-6.2d-211)) then
        tmp = 100.0d0 * (i / (i / n))
    else if (n <= 3.1d-168) then
        tmp = (n * 0.0d0) / i
    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 <= -2.9e+85) {
		tmp = (100.0 * (i * n)) / i;
	} else if (n <= -6.2e-211) {
		tmp = 100.0 * (i / (i / n));
	} else if (n <= 3.1e-168) {
		tmp = (n * 0.0) / i;
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -2.9e+85:
		tmp = (100.0 * (i * n)) / i
	elif n <= -6.2e-211:
		tmp = 100.0 * (i / (i / n))
	elif n <= 3.1e-168:
		tmp = (n * 0.0) / i
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -2.9e+85)
		tmp = Float64(Float64(100.0 * Float64(i * n)) / i);
	elseif (n <= -6.2e-211)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	elseif (n <= 3.1e-168)
		tmp = Float64(Float64(n * 0.0) / i);
	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 <= -2.9e+85)
		tmp = (100.0 * (i * n)) / i;
	elseif (n <= -6.2e-211)
		tmp = 100.0 * (i / (i / n));
	elseif (n <= 3.1e-168)
		tmp = (n * 0.0) / i;
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -2.9e+85], N[(N[(100.0 * N[(i * n), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, -6.2e-211], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 3.1e-168], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 15: 65.0% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{if}\;n \leq -3 \cdot 10^{+191}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq -3.6 \cdot 10^{-211}:\\ \;\;\;\;10000 \cdot \frac{n}{100 - i \cdot 50}\\ \mathbf{elif}\;n \leq 2 \cdot 10^{-168}:\\ \;\;\;\;\frac{n \cdot 0}{i}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0)))))
   (if (<= n -3e+191)
     t_0
     (if (<= n -3.6e-211)
       (* 10000.0 (/ n (- 100.0 (* i 50.0))))
       (if (<= n 2e-168) (/ (* n 0.0) i) t_0)))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double tmp;
	if (n <= -3e+191) {
		tmp = t_0;
	} else if (n <= -3.6e-211) {
		tmp = 10000.0 * (n / (100.0 - (i * 50.0)));
	} else if (n <= 2e-168) {
		tmp = (n * 0.0) / i;
	} 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 <= (-3d+191)) then
        tmp = t_0
    else if (n <= (-3.6d-211)) then
        tmp = 10000.0d0 * (n / (100.0d0 - (i * 50.0d0)))
    else if (n <= 2d-168) then
        tmp = (n * 0.0d0) / i
    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 <= -3e+191) {
		tmp = t_0;
	} else if (n <= -3.6e-211) {
		tmp = 10000.0 * (n / (100.0 - (i * 50.0)));
	} else if (n <= 2e-168) {
		tmp = (n * 0.0) / i;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	tmp = 0
	if n <= -3e+191:
		tmp = t_0
	elif n <= -3.6e-211:
		tmp = 10000.0 * (n / (100.0 - (i * 50.0)))
	elif n <= 2e-168:
		tmp = (n * 0.0) / i
	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 <= -3e+191)
		tmp = t_0;
	elseif (n <= -3.6e-211)
		tmp = Float64(10000.0 * Float64(n / Float64(100.0 - Float64(i * 50.0))));
	elseif (n <= 2e-168)
		tmp = Float64(Float64(n * 0.0) / i);
	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 <= -3e+191)
		tmp = t_0;
	elseif (n <= -3.6e-211)
		tmp = 10000.0 * (n / (100.0 - (i * 50.0)));
	elseif (n <= 2e-168)
		tmp = (n * 0.0) / i;
	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, -3e+191], t$95$0, If[LessEqual[n, -3.6e-211], N[(10000.0 * N[(n / N[(100.0 - N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 2e-168], N[(N[(n * 0.0), $MachinePrecision] / i), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 16: 56.5% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -4 \cdot 10^{+49} \lor \neg \left(i \leq 5 \cdot 10^{+14}\right):\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= i -4e+49) (not (<= i 5e+14)))
   (* 100.0 (/ i (/ i n)))
   (* n 100.0)))

C

double code(double i, double n) {
	double tmp;
	if ((i <= -4e+49) || !(i <= 5e+14)) {
		tmp = 100.0 * (i / (i / n));
	} 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 <= (-4d+49)) .or. (.not. (i <= 5d+14))) then
        tmp = 100.0d0 * (i / (i / n))
    else
        tmp = n * 100.0d0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if ((i <= -4e+49) || !(i <= 5e+14)) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if (i <= -4e+49) or not (i <= 5e+14):
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if ((i <= -4e+49) || !(i <= 5e+14))
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if ((i <= -4e+49) || ~((i <= 5e+14)))
		tmp = 100.0 * (i / (i / n));
	else
		tmp = n * 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[Or[LessEqual[i, -4e+49], N[Not[LessEqual[i, 5e+14]], $MachinePrecision]], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n * 100.0), $MachinePrecision]]

Derivation

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

Alternative 17: 62.2% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -5.5 \cdot 10^{+86} \lor \neg \left(n \leq 1.35 \cdot 10^{-34}\right):\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (or (<= n -5.5e+86) (not (<= n 1.35e-34)))
   (* n (+ 100.0 (* i 50.0)))
   (* 100.0 (/ i (/ i n)))))

C

double code(double i, double n) {
	double tmp;
	if ((n <= -5.5e+86) || !(n <= 1.35e-34)) {
		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 <= (-5.5d+86)) .or. (.not. (n <= 1.35d-34))) 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 <= -5.5e+86) || !(n <= 1.35e-34)) {
		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 <= -5.5e+86) or not (n <= 1.35e-34):
		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 <= -5.5e+86) || !(n <= 1.35e-34))
		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 <= -5.5e+86) || ~((n <= 1.35e-34)))
		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, -5.5e+86], N[Not[LessEqual[n, 1.35e-34]], $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 18: 62.3% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -2.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{100 \cdot \left(i \cdot n\right)}{i}\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-34}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -2.9e+85)
   (/ (* 100.0 (* i n)) i)
   (if (<= n 1.35e-34) (* 100.0 (/ i (/ i n))) (* n (+ 100.0 (* i 50.0))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -2.9e+85) {
		tmp = (100.0 * (i * n)) / i;
	} else if (n <= 1.35e-34) {
		tmp = 100.0 * (i / (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 <= (-2.9d+85)) then
        tmp = (100.0d0 * (i * n)) / i
    else if (n <= 1.35d-34) then
        tmp = 100.0d0 * (i / (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 <= -2.9e+85) {
		tmp = (100.0 * (i * n)) / i;
	} else if (n <= 1.35e-34) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = n * (100.0 + (i * 50.0));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -2.9e+85:
		tmp = (100.0 * (i * n)) / i
	elif n <= 1.35e-34:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = n * (100.0 + (i * 50.0))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -2.9e+85)
		tmp = Float64(Float64(100.0 * Float64(i * n)) / i);
	elseif (n <= 1.35e-34)
		tmp = Float64(100.0 * Float64(i / 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 <= -2.9e+85)
		tmp = (100.0 * (i * n)) / i;
	elseif (n <= 1.35e-34)
		tmp = 100.0 * (i / (i / n));
	else
		tmp = n * (100.0 + (i * 50.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -2.9e+85], N[(N[(100.0 * N[(i * n), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[n, 1.35e-34], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 19: 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 20: 49.3% 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: 34.0% 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 2023343 
(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))))