Compound Interest

Percentage Accurate: 28.4% → 94.4%

Time: 21.8s

Alternatives: 14

Speedup: 16.0×

• 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: 28.4% 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: 94.4% accurate, 0.3× speedup

Math

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

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) (* n (/ (+ (* t_0 100.0) -100.0) i)) (* n 100.0)))))

C

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

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (Math.expm1((n * Math.log1p((i / n)))) * -100.0) / (-i / n);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_1 <= 0.0:
		tmp = (math.expm1((n * math.log1p((i / n)))) * -100.0) / (-i / n)
	elif t_1 <= math.inf:
		tmp = n * (((t_0 * 100.0) + -100.0) / i)
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 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(n * Float64(Float64(Float64(t_0 * 100.0) + -100.0) / i));
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

Wolfram

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

Derivation

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

Alternative 2: 92.7% accurate, 0.3× speedup

Math

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

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 (/ n i)))
     (if (<= t_1 INFINITY) (* n (/ (+ (* t_0 100.0) -100.0) i)) (* n 100.0)))))

C

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

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = Math.expm1((n * Math.log1p((i / n)))) * (100.0 * (n / i));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_1 <= 0.0:
		tmp = math.expm1((n * math.log1p((i / n)))) * (100.0 * (n / i))
	elif t_1 <= math.inf:
		tmp = n * (((t_0 * 100.0) + -100.0) / i)
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(expm1(Float64(n * log1p(Float64(i / n)))) * Float64(100.0 * Float64(n / i)));
	elseif (t_1 <= Inf)
		tmp = Float64(n * Float64(Float64(Float64(t_0 * 100.0) + -100.0) / i));
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

Wolfram

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

Derivation

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

Alternative 3: 93.7% accurate, 0.3× speedup

Math

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

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)
     (* n (* 100.0 (/ (expm1 (* n (log1p (/ i n)))) i)))
     (if (<= t_1 INFINITY) (* n (/ (+ (* t_0 100.0) -100.0) i)) (* n 100.0)))))

C

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

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = n * (100.0 * (Math.expm1((n * Math.log1p((i / n)))) / i));
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_1 <= 0.0:
		tmp = n * (100.0 * (math.expm1((n * math.log1p((i / n)))) / i))
	elif t_1 <= math.inf:
		tmp = n * (((t_0 * 100.0) + -100.0) / i)
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(n * Float64(100.0 * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / i)));
	elseif (t_1 <= Inf)
		tmp = Float64(n * Float64(Float64(Float64(t_0 * 100.0) + -100.0) / i));
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

Wolfram

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

Derivation

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

Alternative 4: 93.7% accurate, 0.3× speedup

Math

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

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)
     (* (* n 100.0) (/ (expm1 (* n (log1p (/ i n)))) i))
     (if (<= t_1 INFINITY) (* n (/ (+ (* t_0 100.0) -100.0) i)) (* n 100.0)))))

C

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

Java

public static double code(double i, double n) {
	double t_0 = Math.pow((1.0 + (i / n)), n);
	double t_1 = (t_0 + -1.0) / (i / n);
	double tmp;
	if (t_1 <= 0.0) {
		tmp = (n * 100.0) * (Math.expm1((n * Math.log1p((i / n)))) / i);
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = n * (((t_0 * 100.0) + -100.0) / i);
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = math.pow((1.0 + (i / n)), n)
	t_1 = (t_0 + -1.0) / (i / n)
	tmp = 0
	if t_1 <= 0.0:
		tmp = (n * 100.0) * (math.expm1((n * math.log1p((i / n)))) / i)
	elif t_1 <= math.inf:
		tmp = n * (((t_0 * 100.0) + -100.0) / i)
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(1.0 + Float64(i / n)) ^ n
	t_1 = Float64(Float64(t_0 + -1.0) / Float64(i / n))
	tmp = 0.0
	if (t_1 <= 0.0)
		tmp = Float64(Float64(n * 100.0) * Float64(expm1(Float64(n * log1p(Float64(i / n)))) / i));
	elseif (t_1 <= Inf)
		tmp = Float64(n * Float64(Float64(Float64(t_0 * 100.0) + -100.0) / i));
	else
		tmp = Float64(n * 100.0);
	end
	return tmp
end

Wolfram

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

Derivation

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

Alternative 5: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \mathbf{if}\;i \leq -3.5 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{-177}:\\ \;\;\;\;\frac{n \cdot \left(i \cdot 100\right)}{i}\\ \mathbf{elif}\;i \leq 0.0037:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \left(1 + i \cdot -0.5\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+168} \lor \neg \left(i \leq 3.8 \cdot 10^{+237}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ (expm1 i) (/ i n)))))
   (if (<= i -3.5e-45)
     t_0
     (if (<= i -1.5e-177)
       (/ (* n (* i 100.0)) i)
       (if (<= i 0.0037)
         (* (* n 100.0) (+ 1.0 (* i -0.5)))
         (if (or (<= i 1.35e+168) (not (<= i 3.8e+237))) t_0 0.0))))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (expm1(i) / (i / n));
	double tmp;
	if (i <= -3.5e-45) {
		tmp = t_0;
	} else if (i <= -1.5e-177) {
		tmp = (n * (i * 100.0)) / i;
	} else if (i <= 0.0037) {
		tmp = (n * 100.0) * (1.0 + (i * -0.5));
	} else if ((i <= 1.35e+168) || !(i <= 3.8e+237)) {
		tmp = t_0;
	} else {
		tmp = 0.0;
	}
	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 <= -3.5e-45) {
		tmp = t_0;
	} else if (i <= -1.5e-177) {
		tmp = (n * (i * 100.0)) / i;
	} else if (i <= 0.0037) {
		tmp = (n * 100.0) * (1.0 + (i * -0.5));
	} else if ((i <= 1.35e+168) || !(i <= 3.8e+237)) {
		tmp = t_0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (math.expm1(i) / (i / n))
	tmp = 0
	if i <= -3.5e-45:
		tmp = t_0
	elif i <= -1.5e-177:
		tmp = (n * (i * 100.0)) / i
	elif i <= 0.0037:
		tmp = (n * 100.0) * (1.0 + (i * -0.5))
	elif (i <= 1.35e+168) or not (i <= 3.8e+237):
		tmp = t_0
	else:
		tmp = 0.0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(expm1(i) / Float64(i / n)))
	tmp = 0.0
	if (i <= -3.5e-45)
		tmp = t_0;
	elseif (i <= -1.5e-177)
		tmp = Float64(Float64(n * Float64(i * 100.0)) / i);
	elseif (i <= 0.0037)
		tmp = Float64(Float64(n * 100.0) * Float64(1.0 + Float64(i * -0.5)));
	elseif ((i <= 1.35e+168) || !(i <= 3.8e+237))
		tmp = t_0;
	else
		tmp = 0.0;
	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, -3.5e-45], t$95$0, If[LessEqual[i, -1.5e-177], N[(N[(n * N[(i * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[i, 0.0037], N[(N[(n * 100.0), $MachinePrecision] * N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 1.35e+168], N[Not[LessEqual[i, 3.8e+237]], $MachinePrecision]], t$95$0, 0.0]]]]]

Derivation

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

Alternative 6: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(100 \cdot \frac{n}{i}\right) \cdot \mathsf{expm1}\left(i\right)\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{n \cdot \left(i \cdot 100\right)}{i}\\ \mathbf{elif}\;i \leq 0.0037:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \left(1 + i \cdot -0.5\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;i \leq 7.2 \cdot 10^{+236}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \frac{\mathsf{expm1}\left(i\right)}{\frac{i}{n}}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* (* 100.0 (/ n i)) (expm1 i))))
   (if (<= i -7.5e-44)
     t_0
     (if (<= i -4.2e-175)
       (/ (* n (* i 100.0)) i)
       (if (<= i 0.0037)
         (* (* n 100.0) (+ 1.0 (* i -0.5)))
         (if (<= i 1.3e+168)
           t_0
           (if (<= i 7.2e+236) 0.0 (* 100.0 (/ (expm1 i) (/ i n))))))))))

C

double code(double i, double n) {
	double t_0 = (100.0 * (n / i)) * expm1(i);
	double tmp;
	if (i <= -7.5e-44) {
		tmp = t_0;
	} else if (i <= -4.2e-175) {
		tmp = (n * (i * 100.0)) / i;
	} else if (i <= 0.0037) {
		tmp = (n * 100.0) * (1.0 + (i * -0.5));
	} else if (i <= 1.3e+168) {
		tmp = t_0;
	} else if (i <= 7.2e+236) {
		tmp = 0.0;
	} else {
		tmp = 100.0 * (expm1(i) / (i / n));
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = (100.0 * (n / i)) * Math.expm1(i);
	double tmp;
	if (i <= -7.5e-44) {
		tmp = t_0;
	} else if (i <= -4.2e-175) {
		tmp = (n * (i * 100.0)) / i;
	} else if (i <= 0.0037) {
		tmp = (n * 100.0) * (1.0 + (i * -0.5));
	} else if (i <= 1.3e+168) {
		tmp = t_0;
	} else if (i <= 7.2e+236) {
		tmp = 0.0;
	} else {
		tmp = 100.0 * (Math.expm1(i) / (i / n));
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = (100.0 * (n / i)) * math.expm1(i)
	tmp = 0
	if i <= -7.5e-44:
		tmp = t_0
	elif i <= -4.2e-175:
		tmp = (n * (i * 100.0)) / i
	elif i <= 0.0037:
		tmp = (n * 100.0) * (1.0 + (i * -0.5))
	elif i <= 1.3e+168:
		tmp = t_0
	elif i <= 7.2e+236:
		tmp = 0.0
	else:
		tmp = 100.0 * (math.expm1(i) / (i / n))
	return tmp

Julia

function code(i, n)
	t_0 = Float64(Float64(100.0 * Float64(n / i)) * expm1(i))
	tmp = 0.0
	if (i <= -7.5e-44)
		tmp = t_0;
	elseif (i <= -4.2e-175)
		tmp = Float64(Float64(n * Float64(i * 100.0)) / i);
	elseif (i <= 0.0037)
		tmp = Float64(Float64(n * 100.0) * Float64(1.0 + Float64(i * -0.5)));
	elseif (i <= 1.3e+168)
		tmp = t_0;
	elseif (i <= 7.2e+236)
		tmp = 0.0;
	else
		tmp = Float64(100.0 * Float64(expm1(i) / Float64(i / n)));
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(N[(100.0 * N[(n / i), $MachinePrecision]), $MachinePrecision] * N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.5e-44], t$95$0, If[LessEqual[i, -4.2e-175], N[(N[(n * N[(i * 100.0), $MachinePrecision]), $MachinePrecision] / i), $MachinePrecision], If[LessEqual[i, 0.0037], N[(N[(n * 100.0), $MachinePrecision] * N[(1.0 + N[(i * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+168], t$95$0, If[LessEqual[i, 7.2e+236], 0.0, N[(100.0 * N[(N[(Exp[i] - 1), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 7: 79.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -5.2 \cdot 10^{-129}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq -4.7 \cdot 10^{-231}:\\ \;\;\;\;100 \cdot \frac{n \cdot \log \left(\frac{i}{n}\right)}{\frac{i}{n}}\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -5.2e-129)
   (* 100.0 (/ n (/ i (expm1 i))))
   (if (<= n -4.7e-231)
     (* 100.0 (/ (* n (log (/ i n))) (/ i n)))
     (if (<= n 6.6e-259)
       0.0
       (if (<= n 1.35e-89)
         (* 100.0 (/ i (/ i n)))
         (* (* n 100.0) (/ (expm1 i) i)))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -5.2e-129) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (n <= -4.7e-231) {
		tmp = 100.0 * ((n * log((i / n))) / (i / n));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = (n * 100.0) * (expm1(i) / i);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -5.2e-129) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (n <= -4.7e-231) {
		tmp = 100.0 * ((n * Math.log((i / n))) / (i / n));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = (n * 100.0) * (Math.expm1(i) / i);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -5.2e-129:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif n <= -4.7e-231:
		tmp = 100.0 * ((n * math.log((i / n))) / (i / n))
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 1.35e-89:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = (n * 100.0) * (math.expm1(i) / i)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -5.2e-129)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (n <= -4.7e-231)
		tmp = Float64(100.0 * Float64(Float64(n * log(Float64(i / n))) / Float64(i / n)));
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.35e-89)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(Float64(n * 100.0) * Float64(expm1(i) / i));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[n, -5.2e-129], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, -4.7e-231], N[(100.0 * N[(N[(n * N[Log[N[(i / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 1.35e-89], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] * N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 81.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{if}\;n \leq -1.12 \cdot 10^{-209}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* 100.0 (/ n (/ i (expm1 i))))))
   (if (<= n -1.12e-209)
     t_0
     (if (<= n 6.6e-259)
       0.0
       (if (<= n 1.35e-89) (* 100.0 (/ i (/ i n))) t_0)))))

C

double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / expm1(i)));
	double tmp;
	if (n <= -1.12e-209) {
		tmp = t_0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double t_0 = 100.0 * (n / (i / Math.expm1(i)));
	double tmp;
	if (n <= -1.12e-209) {
		tmp = t_0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = 100.0 * (n / (i / math.expm1(i)))
	tmp = 0
	if n <= -1.12e-209:
		tmp = t_0
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 1.35e-89:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = t_0
	return tmp

Julia

function code(i, n)
	t_0 = Float64(100.0 * Float64(n / Float64(i / expm1(i))))
	tmp = 0.0
	if (n <= -1.12e-209)
		tmp = t_0;
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.35e-89)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[i_, n_] := Block[{t$95$0 = N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[n, -1.12e-209], t$95$0, If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 1.35e-89], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 9: 80.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -8.4 \cdot 10^{-213}:\\ \;\;\;\;100 \cdot \frac{n}{\frac{i}{\mathsf{expm1}\left(i\right)}}\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;\left(n \cdot 100\right) \cdot \frac{\mathsf{expm1}\left(i\right)}{i}\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -8.4e-213)
   (* 100.0 (/ n (/ i (expm1 i))))
   (if (<= n 6.6e-259)
     0.0
     (if (<= n 1.35e-89)
       (* 100.0 (/ i (/ i n)))
       (* (* n 100.0) (/ (expm1 i) i))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -8.4e-213) {
		tmp = 100.0 * (n / (i / expm1(i)));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = (n * 100.0) * (expm1(i) / i);
	}
	return tmp;
}

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -8.4e-213) {
		tmp = 100.0 * (n / (i / Math.expm1(i)));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = (n * 100.0) * (Math.expm1(i) / i);
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -8.4e-213:
		tmp = 100.0 * (n / (i / math.expm1(i)))
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 1.35e-89:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = (n * 100.0) * (math.expm1(i) / i)
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -8.4e-213)
		tmp = Float64(100.0 * Float64(n / Float64(i / expm1(i))));
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.35e-89)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(Float64(n * 100.0) * Float64(expm1(i) / i));
	end
	return tmp
end

Wolfram

code[i_, n_] := If[LessEqual[n, -8.4e-213], N[(100.0 * N[(n / N[(i / N[(Exp[i] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 1.35e-89], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(n * 100.0), $MachinePrecision] * N[(N[(Exp[i] - 1), $MachinePrecision] / i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 10: 62.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.35 \cdot 10^{-152}:\\ \;\;\;\;n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 1.35 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;100 \cdot \left(n + \left(i \cdot n\right) \cdot \left(0.5 - \frac{0.5}{n}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -1.35e-152)
   (* n (+ 100.0 (* i 50.0)))
   (if (<= n 6.6e-259)
     0.0
     (if (<= n 1.35e-89)
       (* 100.0 (/ i (/ i n)))
       (* 100.0 (+ n (* (* i n) (- 0.5 (/ 0.5 n)))))))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -1.35e-152) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * (n + ((i * n) * (0.5 - (0.5 / 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 <= (-1.35d-152)) then
        tmp = n * (100.0d0 + (i * 50.0d0))
    else if (n <= 6.6d-259) then
        tmp = 0.0d0
    else if (n <= 1.35d-89) then
        tmp = 100.0d0 * (i / (i / n))
    else
        tmp = 100.0d0 * (n + ((i * n) * (0.5d0 - (0.5d0 / n))))
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (n <= -1.35e-152) {
		tmp = n * (100.0 + (i * 50.0));
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.35e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = 100.0 * (n + ((i * n) * (0.5 - (0.5 / n))));
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -1.35e-152:
		tmp = n * (100.0 + (i * 50.0))
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 1.35e-89:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = 100.0 * (n + ((i * n) * (0.5 - (0.5 / n))))
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -1.35e-152)
		tmp = Float64(n * Float64(100.0 + Float64(i * 50.0)));
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.35e-89)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	else
		tmp = Float64(100.0 * Float64(n + Float64(Float64(i * n) * Float64(0.5 - Float64(0.5 / n)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (n <= -1.35e-152)
		tmp = n * (100.0 + (i * 50.0));
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.35e-89)
		tmp = 100.0 * (i / (i / n));
	else
		tmp = 100.0 * (n + ((i * n) * (0.5 - (0.5 / n))));
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -1.35e-152], N[(n * N[(100.0 + N[(i * 50.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 1.35e-89], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(100.0 * N[(n + N[(N[(i * n), $MachinePrecision] * N[(0.5 - N[(0.5 / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 11: 56.5% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -1.85 \cdot 10^{-154}:\\ \;\;\;\;n \cdot 100\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 3.2 \cdot 10^{-121}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;n \cdot 100\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= n -1.85e-154)
   (* n 100.0)
   (if (<= n 6.6e-259)
     0.0
     (if (<= n 3.2e-121) (* 100.0 (/ i (/ i n))) (* n 100.0)))))

C

double code(double i, double n) {
	double tmp;
	if (n <= -1.85e-154) {
		tmp = n * 100.0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 3.2e-121) {
		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 (n <= (-1.85d-154)) then
        tmp = n * 100.0d0
    else if (n <= 6.6d-259) then
        tmp = 0.0d0
    else if (n <= 3.2d-121) 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 (n <= -1.85e-154) {
		tmp = n * 100.0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 3.2e-121) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = n * 100.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if n <= -1.85e-154:
		tmp = n * 100.0
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 3.2e-121:
		tmp = 100.0 * (i / (i / n))
	else:
		tmp = n * 100.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (n <= -1.85e-154)
		tmp = Float64(n * 100.0);
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 3.2e-121)
		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 (n <= -1.85e-154)
		tmp = n * 100.0;
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 3.2e-121)
		tmp = 100.0 * (i / (i / n));
	else
		tmp = n * 100.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[n, -1.85e-154], N[(n * 100.0), $MachinePrecision], If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 3.2e-121], 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 12: 62.3% accurate, 8.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := n \cdot \left(100 + i \cdot 50\right)\\ \mathbf{if}\;n \leq -1 \cdot 10^{-150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;n \leq 6.6 \cdot 10^{-259}:\\ \;\;\;\;0\\ \mathbf{elif}\;n \leq 1.2 \cdot 10^{-89}:\\ \;\;\;\;100 \cdot \frac{i}{\frac{i}{n}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (let* ((t_0 (* n (+ 100.0 (* i 50.0)))))
   (if (<= n -1e-150)
     t_0
     (if (<= n 6.6e-259)
       0.0
       (if (<= n 1.2e-89) (* 100.0 (/ i (/ i n))) t_0)))))

C

double code(double i, double n) {
	double t_0 = n * (100.0 + (i * 50.0));
	double tmp;
	if (n <= -1e-150) {
		tmp = t_0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.2e-89) {
		tmp = 100.0 * (i / (i / n));
	} 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 <= (-1d-150)) then
        tmp = t_0
    else if (n <= 6.6d-259) then
        tmp = 0.0d0
    else if (n <= 1.2d-89) then
        tmp = 100.0d0 * (i / (i / n))
    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 <= -1e-150) {
		tmp = t_0;
	} else if (n <= 6.6e-259) {
		tmp = 0.0;
	} else if (n <= 1.2e-89) {
		tmp = 100.0 * (i / (i / n));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(i, n):
	t_0 = n * (100.0 + (i * 50.0))
	tmp = 0
	if n <= -1e-150:
		tmp = t_0
	elif n <= 6.6e-259:
		tmp = 0.0
	elif n <= 1.2e-89:
		tmp = 100.0 * (i / (i / n))
	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 <= -1e-150)
		tmp = t_0;
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.2e-89)
		tmp = Float64(100.0 * Float64(i / Float64(i / n)));
	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 <= -1e-150)
		tmp = t_0;
	elseif (n <= 6.6e-259)
		tmp = 0.0;
	elseif (n <= 1.2e-89)
		tmp = 100.0 * (i / (i / n));
	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, -1e-150], t$95$0, If[LessEqual[n, 6.6e-259], 0.0, If[LessEqual[n, 1.2e-89], N[(100.0 * N[(i / N[(i / n), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

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

Alternative 13: 59.0% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.1 \cdot 10^{+16}:\\ \;\;\;\;0\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{+15}:\\ \;\;\;\;n \cdot 100\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (i n)
 :precision binary64
 (if (<= i -2.1e+16) 0.0 (if (<= i 3.3e+15) (* n 100.0) 0.0)))

C

double code(double i, double n) {
	double tmp;
	if (i <= -2.1e+16) {
		tmp = 0.0;
	} else if (i <= 3.3e+15) {
		tmp = n * 100.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    real(8) :: tmp
    if (i <= (-2.1d+16)) then
        tmp = 0.0d0
    else if (i <= 3.3d+15) then
        tmp = n * 100.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double i, double n) {
	double tmp;
	if (i <= -2.1e+16) {
		tmp = 0.0;
	} else if (i <= 3.3e+15) {
		tmp = n * 100.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(i, n):
	tmp = 0
	if i <= -2.1e+16:
		tmp = 0.0
	elif i <= 3.3e+15:
		tmp = n * 100.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(i, n)
	tmp = 0.0
	if (i <= -2.1e+16)
		tmp = 0.0;
	elseif (i <= 3.3e+15)
		tmp = Float64(n * 100.0);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(i, n)
	tmp = 0.0;
	if (i <= -2.1e+16)
		tmp = 0.0;
	elseif (i <= 3.3e+15)
		tmp = n * 100.0;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[i_, n_] := If[LessEqual[i, -2.1e+16], 0.0, If[LessEqual[i, 3.3e+15], N[(n * 100.0), $MachinePrecision], 0.0]]

Derivation

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

Alternative 14: 18.3% accurate, 114.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (i n) :precision binary64 0.0)

C

double code(double i, double n) {
	return 0.0;
}

Fortran

real(8) function code(i, n)
    real(8), intent (in) :: i
    real(8), intent (in) :: n
    code = 0.0d0
end function

Java

public static double code(double i, double n) {
	return 0.0;
}

Python

def code(i, n):
	return 0.0

Julia

function code(i, n)
	return 0.0
end

MATLAB

function tmp = code(i, n)
	tmp = 0.0;
end

Wolfram

code[i_, n_] := 0.0

Derivation

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

Developer target: 34.4% 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 2024003 
(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))))