2nthrt (problem 3.4.6)

Percentage Accurate: 53.2% → 84.9%

Time: 23.9s

Alternatives: 18

Speedup: 1.9×

• could not determine a ground truth

  1. x = -2
  2. n = 4.94066e-324

Specification

Math

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

FPCore

(FPCore (x n)
 :precision binary64
 (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))

C

double code(double x, double n) {
	return pow((x + 1.0), (1.0 / n)) - pow(x, (1.0 / n));
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    code = ((x + 1.0d0) ** (1.0d0 / n)) - (x ** (1.0d0 / n))
end function

Java

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

Python

def code(x, n):
	return math.pow((x + 1.0), (1.0 / n)) - math.pow(x, (1.0 / n))

Julia

function code(x, n)
	return Float64((Float64(x + 1.0) ^ Float64(1.0 / n)) - (x ^ Float64(1.0 / n)))
end

MATLAB

function tmp = code(x, n)
	tmp = ((x + 1.0) ^ (1.0 / n)) - (x ^ (1.0 / n));
end

Wolfram

code[x_, n_] := N[(N[Power[N[(x + 1.0), $MachinePrecision], N[(1.0 / n), $MachinePrecision]], $MachinePrecision] - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 53.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x n)
 :precision binary64
 (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))

C

double code(double x, double n) {
	return pow((x + 1.0), (1.0 / n)) - pow(x, (1.0 / n));
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    code = ((x + 1.0d0) ** (1.0d0 / n)) - (x ** (1.0d0 / n))
end function

Java

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

Python

def code(x, n):
	return math.pow((x + 1.0), (1.0 / n)) - math.pow(x, (1.0 / n))

Julia

function code(x, n)
	return Float64((Float64(x + 1.0) ^ Float64(1.0 / n)) - (x ^ Float64(1.0 / n)))
end

MATLAB

function tmp = code(x, n)
	tmp = ((x + 1.0) ^ (1.0 / n)) - (x ^ (1.0 / n));
end

Wolfram

code[x_, n_] := N[(N[Power[N[(x + 1.0), $MachinePrecision], N[(1.0 / n), $MachinePrecision]], $MachinePrecision] - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{e^{\frac{\log x}{n}}}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;e^{\frac{\mathsf{log1p}\left(x\right)}{n}} - {x}^{\left(\frac{1}{n}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ (exp (/ (log x) n)) (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_0
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 2e-20)
           t_0
           (- (exp (/ (log1p x) n)) (pow x (/ 1.0 n)))))))))

C

double code(double x, double n) {
	double t_0 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = exp((log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 2e-20) {
		tmp = t_0;
	} else {
		tmp = exp((log1p(x) / n)) - pow(x, (1.0 / n));
	}
	return tmp;
}

Java

public static double code(double x, double n) {
	double t_0 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = Math.exp((Math.log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 2e-20) {
		tmp = t_0;
	} else {
		tmp = Math.exp((Math.log1p(x) / n)) - Math.pow(x, (1.0 / n));
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = math.exp((math.log(x) / n)) / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_0
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 2e-20:
		tmp = t_0
	else:
		tmp = math.exp((math.log1p(x) / n)) - math.pow(x, (1.0 / n))
	return tmp

Julia

function code(x, n)
	t_0 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(exp(Float64(log(x) / n)) / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 2e-20)
		tmp = t_0;
	else
		tmp = Float64(exp(Float64(log1p(x) / n)) - (x ^ Float64(1.0 / n)));
	end
	return tmp
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(N[Exp[N[(N[Log[x], $MachinePrecision] / n), $MachinePrecision]], $MachinePrecision] / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e-20], t$95$0, N[(N[Exp[N[(N[Log[1 + x], $MachinePrecision] / n), $MachinePrecision]], $MachinePrecision] - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {x}^{\left(\frac{1}{n}\right)}\\ t_1 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t_0}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\left(1 + \frac{x}{n}\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\left(n \cdot x\right)}^{-2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (pow x (/ 1.0 n))) (t_1 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ t_0 (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_1
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_1
           (if (<= (/ 1.0 n) 2e+174)
             (- (+ 1.0 (/ x n)) t_0)
             (sqrt (pow (* n x) -2.0)))))))))

C

double code(double x, double n) {
	double t_0 = pow(x, (1.0 / n));
	double t_1 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - t_0;
	} else {
		tmp = sqrt(pow((n * x), -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x ** (1.0d0 / n)
    t_1 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = t_0 / (n * x)
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_1
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_1
    else if ((1.0d0 / n) <= 2d+174) then
        tmp = (1.0d0 + (x / n)) - t_0
    else
        tmp = sqrt(((n * x) ** (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = Math.pow(x, (1.0 / n));
	double t_1 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - t_0;
	} else {
		tmp = Math.sqrt(Math.pow((n * x), -2.0));
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = math.pow(x, (1.0 / n))
	t_1 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = t_0 / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_1
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_1
	elif (1.0 / n) <= 2e+174:
		tmp = (1.0 + (x / n)) - t_0
	else:
		tmp = math.sqrt(math.pow((n * x), -2.0))
	return tmp

Julia

function code(x, n)
	t_0 = x ^ Float64(1.0 / n)
	t_1 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(t_0 / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= 2e+174)
		tmp = Float64(Float64(1.0 + Float64(x / n)) - t_0);
	else
		tmp = sqrt((Float64(n * x) ^ -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = x ^ (1.0 / n);
	t_1 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = t_0 / (n * x);
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif ((1.0 / n) <= 2e+174)
		tmp = (1.0 + (x / n)) - t_0;
	else
		tmp = sqrt(((n * x) ^ -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(t$95$0 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+174], N[(N[(1.0 + N[(x / n), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[Sqrt[N[Power[N[(n * x), $MachinePrecision], -2.0], $MachinePrecision]], $MachinePrecision]]]]]]]]

Derivation

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

Alternative 3: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{e^{\frac{\log x}{n}}}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\left(1 + \frac{x}{n}\right) - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\left(n \cdot x\right)}^{-2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ (exp (/ (log x) n)) (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_0
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_0
           (if (<= (/ 1.0 n) 2e+174)
             (- (+ 1.0 (/ x n)) (pow x (/ 1.0 n)))
             (sqrt (pow (* n x) -2.0)))))))))

C

double code(double x, double n) {
	double t_0 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = exp((log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - pow(x, (1.0 / n));
	} else {
		tmp = sqrt(pow((n * x), -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = exp((log(x) / n)) / (n * x)
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_0
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_0
    else if ((1.0d0 / n) <= 2d+174) then
        tmp = (1.0d0 + (x / n)) - (x ** (1.0d0 / n))
    else
        tmp = sqrt(((n * x) ** (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = Math.exp((Math.log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - Math.pow(x, (1.0 / n));
	} else {
		tmp = Math.sqrt(Math.pow((n * x), -2.0));
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = math.exp((math.log(x) / n)) / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_0
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_0
	elif (1.0 / n) <= 2e+174:
		tmp = (1.0 + (x / n)) - math.pow(x, (1.0 / n))
	else:
		tmp = math.sqrt(math.pow((n * x), -2.0))
	return tmp

Julia

function code(x, n)
	t_0 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(exp(Float64(log(x) / n)) / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= 2e+174)
		tmp = Float64(Float64(1.0 + Float64(x / n)) - (x ^ Float64(1.0 / n)));
	else
		tmp = sqrt((Float64(n * x) ^ -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = exp((log(x) / n)) / (n * x);
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_0;
	elseif ((1.0 / n) <= 2e+174)
		tmp = (1.0 + (x / n)) - (x ^ (1.0 / n));
	else
		tmp = sqrt(((n * x) ^ -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(N[Exp[N[(N[Log[x], $MachinePrecision] / n), $MachinePrecision]], $MachinePrecision] / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+174], N[(N[(1.0 + N[(x / n), $MachinePrecision]), $MachinePrecision] - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sqrt[N[Power[N[(n * x), $MachinePrecision], -2.0], $MachinePrecision]], $MachinePrecision]]]]]]]

Derivation

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

Alternative 4: 85.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{e^{\frac{\log x}{n}}}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;e^{\frac{x}{n}} - {x}^{\left(\frac{1}{n}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ (exp (/ (log x) n)) (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_0
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11) t_0 (- (exp (/ x n)) (pow x (/ 1.0 n)))))))))

C

double code(double x, double n) {
	double t_0 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = exp((log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else {
		tmp = exp((x / n)) - pow(x, (1.0 / n));
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = exp((log(x) / n)) / (n * x)
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_0
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_0
    else
        tmp = exp((x / n)) - (x ** (1.0d0 / n))
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = Math.exp((Math.log(x) / n)) / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else {
		tmp = Math.exp((x / n)) - Math.pow(x, (1.0 / n));
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = math.exp((math.log(x) / n)) / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_0
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_0
	else:
		tmp = math.exp((x / n)) - math.pow(x, (1.0 / n))
	return tmp

Julia

function code(x, n)
	t_0 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(exp(Float64(log(x) / n)) / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_0;
	else
		tmp = Float64(exp(Float64(x / n)) - (x ^ Float64(1.0 / n)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = exp((log(x) / n)) / (n * x);
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_0;
	else
		tmp = exp((x / n)) - (x ^ (1.0 / n));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(N[Exp[N[(N[Log[x], $MachinePrecision] / n), $MachinePrecision]], $MachinePrecision] / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$0, N[(N[Exp[N[(x / n), $MachinePrecision]], $MachinePrecision] - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 79.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {x}^{\left(\frac{1}{n}\right)}\\ t_1 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t_0}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq 10^{+265}:\\ \;\;\;\;\left(1 + \frac{x}{n}\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (pow x (/ 1.0 n))) (t_1 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ t_0 (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_1
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_1
           (if (<= (/ 1.0 n) 1e+265)
             (- (+ 1.0 (/ x n)) t_0)
             (/ 1.0 (* n x)))))))))

C

double code(double x, double n) {
	double t_0 = pow(x, (1.0 / n));
	double t_1 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 1e+265) {
		tmp = (1.0 + (x / n)) - t_0;
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x ** (1.0d0 / n)
    t_1 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = t_0 / (n * x)
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_1
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_1
    else if ((1.0d0 / n) <= 1d+265) then
        tmp = (1.0d0 + (x / n)) - t_0
    else
        tmp = 1.0d0 / (n * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = Math.pow(x, (1.0 / n));
	double t_1 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 1e+265) {
		tmp = (1.0 + (x / n)) - t_0;
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = math.pow(x, (1.0 / n))
	t_1 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = t_0 / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_1
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_1
	elif (1.0 / n) <= 1e+265:
		tmp = (1.0 + (x / n)) - t_0
	else:
		tmp = 1.0 / (n * x)
	return tmp

Julia

function code(x, n)
	t_0 = x ^ Float64(1.0 / n)
	t_1 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(t_0 / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= 1e+265)
		tmp = Float64(Float64(1.0 + Float64(x / n)) - t_0);
	else
		tmp = Float64(1.0 / Float64(n * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = x ^ (1.0 / n);
	t_1 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = t_0 / (n * x);
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif ((1.0 / n) <= 1e+265)
		tmp = (1.0 + (x / n)) - t_0;
	else
		tmp = 1.0 / (n * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(t$95$0 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], 1e+265], N[(N[(1.0 + N[(x / n), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 6: 81.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{1 + x}\\ t_1 := {x}^{\left(\frac{1}{n}\right)}\\ t_2 := \frac{-\log t_0}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t_1}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\left(1 + \frac{x}{n}\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\mathsf{log1p}\left(t_0 + -1\right)}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ x (+ 1.0 x)))
        (t_1 (pow x (/ 1.0 n)))
        (t_2 (/ (- (log t_0)) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ t_1 (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_2
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_2
           (if (<= (/ 1.0 n) 2e+174)
             (- (+ 1.0 (/ x n)) t_1)
             (/ (- (log1p (+ t_0 -1.0))) n))))))))

C

double code(double x, double n) {
	double t_0 = x / (1.0 + x);
	double t_1 = pow(x, (1.0 / n));
	double t_2 = -log(t_0) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_1 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_2;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_2;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - t_1;
	} else {
		tmp = -log1p((t_0 + -1.0)) / n;
	}
	return tmp;
}

Java

public static double code(double x, double n) {
	double t_0 = x / (1.0 + x);
	double t_1 = Math.pow(x, (1.0 / n));
	double t_2 = -Math.log(t_0) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_1 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_2;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_2;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = (1.0 + (x / n)) - t_1;
	} else {
		tmp = -Math.log1p((t_0 + -1.0)) / n;
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = x / (1.0 + x)
	t_1 = math.pow(x, (1.0 / n))
	t_2 = -math.log(t_0) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = t_1 / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_2
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_2
	elif (1.0 / n) <= 2e+174:
		tmp = (1.0 + (x / n)) - t_1
	else:
		tmp = -math.log1p((t_0 + -1.0)) / n
	return tmp

Julia

function code(x, n)
	t_0 = Float64(x / Float64(1.0 + x))
	t_1 = x ^ Float64(1.0 / n)
	t_2 = Float64(Float64(-log(t_0)) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(t_1 / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_2;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_2;
	elseif (Float64(1.0 / n) <= 2e+174)
		tmp = Float64(Float64(1.0 + Float64(x / n)) - t_1);
	else
		tmp = Float64(Float64(-log1p(Float64(t_0 + -1.0))) / n);
	end
	return tmp
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[((-N[Log[t$95$0], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(t$95$1 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$2, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$2, If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+174], N[(N[(1.0 + N[(x / n), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[((-N[Log[1 + N[(t$95$0 + -1.0), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 7: 80.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{{x}^{\left(\frac{1}{n} + -1\right)}}{n}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+193}:\\ \;\;\;\;1 - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ (pow x (+ (/ 1.0 n) -1.0)) n)
     (if (<= (/ 1.0 n) -4e-64)
       t_0
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_0
           (if (<= (/ 1.0 n) 2e+193)
             (- 1.0 (pow x (/ 1.0 n)))
             (/ 1.0 (* n x)))))))))

C

double code(double x, double n) {
	double t_0 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = pow(x, ((1.0 / n) + -1.0)) / n;
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else if ((1.0 / n) <= 2e+193) {
		tmp = 1.0 - pow(x, (1.0 / n));
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = (x ** ((1.0d0 / n) + (-1.0d0))) / n
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_0
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_0
    else if ((1.0d0 / n) <= 2d+193) then
        tmp = 1.0d0 - (x ** (1.0d0 / n))
    else
        tmp = 1.0d0 / (n * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = Math.pow(x, ((1.0 / n) + -1.0)) / n;
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_0;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_0;
	} else if ((1.0 / n) <= 2e+193) {
		tmp = 1.0 - Math.pow(x, (1.0 / n));
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = math.pow(x, ((1.0 / n) + -1.0)) / n
	elif (1.0 / n) <= -4e-64:
		tmp = t_0
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_0
	elif (1.0 / n) <= 2e+193:
		tmp = 1.0 - math.pow(x, (1.0 / n))
	else:
		tmp = 1.0 / (n * x)
	return tmp

Julia

function code(x, n)
	t_0 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64((x ^ Float64(Float64(1.0 / n) + -1.0)) / n);
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_0;
	elseif (Float64(1.0 / n) <= 2e+193)
		tmp = Float64(1.0 - (x ^ Float64(1.0 / n)));
	else
		tmp = Float64(1.0 / Float64(n * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = (x ^ ((1.0 / n) + -1.0)) / n;
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_0;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_0;
	elseif ((1.0 / n) <= 2e+193)
		tmp = 1.0 - (x ^ (1.0 / n));
	else
		tmp = 1.0 / (n * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(N[Power[x, N[(N[(1.0 / n), $MachinePrecision] + -1.0), $MachinePrecision]], $MachinePrecision] / n), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$0, If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+193], N[(1.0 - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 8: 80.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {x}^{\left(\frac{1}{n}\right)}\\ t_1 := \frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{if}\;\frac{1}{n} \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\frac{t_0}{n \cdot x}\\ \mathbf{elif}\;\frac{1}{n} \leq -4 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq -2 \cdot 10^{-116}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{elif}\;\frac{1}{n} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+193}:\\ \;\;\;\;1 - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (pow x (/ 1.0 n))) (t_1 (/ (- (log (/ x (+ 1.0 x)))) n)))
   (if (<= (/ 1.0 n) -2e-11)
     (/ t_0 (* n x))
     (if (<= (/ 1.0 n) -4e-64)
       t_1
       (if (<= (/ 1.0 n) -2e-116)
         (/ 1.0 (* n (+ x 0.5)))
         (if (<= (/ 1.0 n) 5e-11)
           t_1
           (if (<= (/ 1.0 n) 2e+193) (- 1.0 t_0) (/ 1.0 (* n x)))))))))

C

double code(double x, double n) {
	double t_0 = pow(x, (1.0 / n));
	double t_1 = -log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 2e+193) {
		tmp = 1.0 - t_0;
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x ** (1.0d0 / n)
    t_1 = -log((x / (1.0d0 + x))) / n
    if ((1.0d0 / n) <= (-2d-11)) then
        tmp = t_0 / (n * x)
    else if ((1.0d0 / n) <= (-4d-64)) then
        tmp = t_1
    else if ((1.0d0 / n) <= (-2d-116)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else if ((1.0d0 / n) <= 5d-11) then
        tmp = t_1
    else if ((1.0d0 / n) <= 2d+193) then
        tmp = 1.0d0 - t_0
    else
        tmp = 1.0d0 / (n * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = Math.pow(x, (1.0 / n));
	double t_1 = -Math.log((x / (1.0 + x))) / n;
	double tmp;
	if ((1.0 / n) <= -2e-11) {
		tmp = t_0 / (n * x);
	} else if ((1.0 / n) <= -4e-64) {
		tmp = t_1;
	} else if ((1.0 / n) <= -2e-116) {
		tmp = 1.0 / (n * (x + 0.5));
	} else if ((1.0 / n) <= 5e-11) {
		tmp = t_1;
	} else if ((1.0 / n) <= 2e+193) {
		tmp = 1.0 - t_0;
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = math.pow(x, (1.0 / n))
	t_1 = -math.log((x / (1.0 + x))) / n
	tmp = 0
	if (1.0 / n) <= -2e-11:
		tmp = t_0 / (n * x)
	elif (1.0 / n) <= -4e-64:
		tmp = t_1
	elif (1.0 / n) <= -2e-116:
		tmp = 1.0 / (n * (x + 0.5))
	elif (1.0 / n) <= 5e-11:
		tmp = t_1
	elif (1.0 / n) <= 2e+193:
		tmp = 1.0 - t_0
	else:
		tmp = 1.0 / (n * x)
	return tmp

Julia

function code(x, n)
	t_0 = x ^ Float64(1.0 / n)
	t_1 = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -2e-11)
		tmp = Float64(t_0 / Float64(n * x));
	elseif (Float64(1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= -2e-116)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	elseif (Float64(1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif (Float64(1.0 / n) <= 2e+193)
		tmp = Float64(1.0 - t_0);
	else
		tmp = Float64(1.0 / Float64(n * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = x ^ (1.0 / n);
	t_1 = -log((x / (1.0 + x))) / n;
	tmp = 0.0;
	if ((1.0 / n) <= -2e-11)
		tmp = t_0 / (n * x);
	elseif ((1.0 / n) <= -4e-64)
		tmp = t_1;
	elseif ((1.0 / n) <= -2e-116)
		tmp = 1.0 / (n * (x + 0.5));
	elseif ((1.0 / n) <= 5e-11)
		tmp = t_1;
	elseif ((1.0 / n) <= 2e+193)
		tmp = 1.0 - t_0;
	else
		tmp = 1.0 / (n * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-11], N[(t$95$0 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], -4e-64], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], -2e-116], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 5e-11], t$95$1, If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+193], N[(1.0 - t$95$0), $MachinePrecision], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 9: 59.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{-280}:\\ \;\;\;\;\frac{-\log x}{n}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-176}:\\ \;\;\;\;1 - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{elif}\;x \leq 120000000:\\ \;\;\;\;\frac{-\log \left(\frac{x}{1 + x}\right)}{n}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+65}:\\ \;\;\;\;\frac{1}{n} \cdot \frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= x 7.6e-280)
   (/ (- (log x)) n)
   (if (<= x 4.2e-176)
     (- 1.0 (pow x (/ 1.0 n)))
     (if (<= x 120000000.0)
       (/ (- (log (/ x (+ 1.0 x)))) n)
       (if (<= x 1.55e+65) (* (/ 1.0 n) (/ 1.0 x)) (/ 0.0 n))))))

C

double code(double x, double n) {
	double tmp;
	if (x <= 7.6e-280) {
		tmp = -log(x) / n;
	} else if (x <= 4.2e-176) {
		tmp = 1.0 - pow(x, (1.0 / n));
	} else if (x <= 120000000.0) {
		tmp = -log((x / (1.0 + x))) / n;
	} else if (x <= 1.55e+65) {
		tmp = (1.0 / n) * (1.0 / x);
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (x <= 7.6d-280) then
        tmp = -log(x) / n
    else if (x <= 4.2d-176) then
        tmp = 1.0d0 - (x ** (1.0d0 / n))
    else if (x <= 120000000.0d0) then
        tmp = -log((x / (1.0d0 + x))) / n
    else if (x <= 1.55d+65) then
        tmp = (1.0d0 / n) * (1.0d0 / x)
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (x <= 7.6e-280) {
		tmp = -Math.log(x) / n;
	} else if (x <= 4.2e-176) {
		tmp = 1.0 - Math.pow(x, (1.0 / n));
	} else if (x <= 120000000.0) {
		tmp = -Math.log((x / (1.0 + x))) / n;
	} else if (x <= 1.55e+65) {
		tmp = (1.0 / n) * (1.0 / x);
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if x <= 7.6e-280:
		tmp = -math.log(x) / n
	elif x <= 4.2e-176:
		tmp = 1.0 - math.pow(x, (1.0 / n))
	elif x <= 120000000.0:
		tmp = -math.log((x / (1.0 + x))) / n
	elif x <= 1.55e+65:
		tmp = (1.0 / n) * (1.0 / x)
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (x <= 7.6e-280)
		tmp = Float64(Float64(-log(x)) / n);
	elseif (x <= 4.2e-176)
		tmp = Float64(1.0 - (x ^ Float64(1.0 / n)));
	elseif (x <= 120000000.0)
		tmp = Float64(Float64(-log(Float64(x / Float64(1.0 + x)))) / n);
	elseif (x <= 1.55e+65)
		tmp = Float64(Float64(1.0 / n) * Float64(1.0 / x));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (x <= 7.6e-280)
		tmp = -log(x) / n;
	elseif (x <= 4.2e-176)
		tmp = 1.0 - (x ^ (1.0 / n));
	elseif (x <= 120000000.0)
		tmp = -log((x / (1.0 + x))) / n;
	elseif (x <= 1.55e+65)
		tmp = (1.0 / n) * (1.0 / x);
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[x, 7.6e-280], N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 4.2e-176], N[(1.0 - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 120000000.0], N[((-N[Log[N[(x / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 1.55e+65], N[(N[(1.0 / n), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]

Derivation

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

Alternative 10: 58.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 8.5 \cdot 10^{-280}:\\ \;\;\;\;\frac{-\log x}{n}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-175}:\\ \;\;\;\;1 - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;\frac{1}{\frac{n}{x - \log x}}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right) - \frac{n \cdot 0.08333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= x 8.5e-280)
   (/ (- (log x)) n)
   (if (<= x 1.05e-175)
     (- 1.0 (pow x (/ 1.0 n)))
     (if (<= x 0.5)
       (/ 1.0 (/ n (- x (log x))))
       (if (<= x 5.8e+64)
         (/ 1.0 (- (* n (+ x 0.5)) (/ (* n 0.08333333333333333) x)))
         (/ 0.0 n))))))

C

double code(double x, double n) {
	double tmp;
	if (x <= 8.5e-280) {
		tmp = -log(x) / n;
	} else if (x <= 1.05e-175) {
		tmp = 1.0 - pow(x, (1.0 / n));
	} else if (x <= 0.5) {
		tmp = 1.0 / (n / (x - log(x)));
	} else if (x <= 5.8e+64) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (x <= 8.5d-280) then
        tmp = -log(x) / n
    else if (x <= 1.05d-175) then
        tmp = 1.0d0 - (x ** (1.0d0 / n))
    else if (x <= 0.5d0) then
        tmp = 1.0d0 / (n / (x - log(x)))
    else if (x <= 5.8d+64) then
        tmp = 1.0d0 / ((n * (x + 0.5d0)) - ((n * 0.08333333333333333d0) / x))
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (x <= 8.5e-280) {
		tmp = -Math.log(x) / n;
	} else if (x <= 1.05e-175) {
		tmp = 1.0 - Math.pow(x, (1.0 / n));
	} else if (x <= 0.5) {
		tmp = 1.0 / (n / (x - Math.log(x)));
	} else if (x <= 5.8e+64) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if x <= 8.5e-280:
		tmp = -math.log(x) / n
	elif x <= 1.05e-175:
		tmp = 1.0 - math.pow(x, (1.0 / n))
	elif x <= 0.5:
		tmp = 1.0 / (n / (x - math.log(x)))
	elif x <= 5.8e+64:
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x))
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (x <= 8.5e-280)
		tmp = Float64(Float64(-log(x)) / n);
	elseif (x <= 1.05e-175)
		tmp = Float64(1.0 - (x ^ Float64(1.0 / n)));
	elseif (x <= 0.5)
		tmp = Float64(1.0 / Float64(n / Float64(x - log(x))));
	elseif (x <= 5.8e+64)
		tmp = Float64(1.0 / Float64(Float64(n * Float64(x + 0.5)) - Float64(Float64(n * 0.08333333333333333) / x)));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (x <= 8.5e-280)
		tmp = -log(x) / n;
	elseif (x <= 1.05e-175)
		tmp = 1.0 - (x ^ (1.0 / n));
	elseif (x <= 0.5)
		tmp = 1.0 / (n / (x - log(x)));
	elseif (x <= 5.8e+64)
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[x, 8.5e-280], N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 1.05e-175], N[(1.0 - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.5], N[(1.0 / N[(n / N[(x - N[Log[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+64], N[(1.0 / N[(N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(n * 0.08333333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]

Derivation

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

Alternative 11: 59.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.75 \cdot 10^{-276}:\\ \;\;\;\;\frac{-\log x}{n}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-177}:\\ \;\;\;\;1 - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{elif}\;x \leq 6400:\\ \;\;\;\;\frac{\log \left(\frac{1 + x}{x}\right)}{n}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right) - \frac{n \cdot 0.08333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= x 1.75e-276)
   (/ (- (log x)) n)
   (if (<= x 6.8e-177)
     (- 1.0 (pow x (/ 1.0 n)))
     (if (<= x 6400.0)
       (/ (log (/ (+ 1.0 x) x)) n)
       (if (<= x 3.4e+60)
         (/ 1.0 (- (* n (+ x 0.5)) (/ (* n 0.08333333333333333) x)))
         (/ 0.0 n))))))

C

double code(double x, double n) {
	double tmp;
	if (x <= 1.75e-276) {
		tmp = -log(x) / n;
	} else if (x <= 6.8e-177) {
		tmp = 1.0 - pow(x, (1.0 / n));
	} else if (x <= 6400.0) {
		tmp = log(((1.0 + x) / x)) / n;
	} else if (x <= 3.4e+60) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (x <= 1.75d-276) then
        tmp = -log(x) / n
    else if (x <= 6.8d-177) then
        tmp = 1.0d0 - (x ** (1.0d0 / n))
    else if (x <= 6400.0d0) then
        tmp = log(((1.0d0 + x) / x)) / n
    else if (x <= 3.4d+60) then
        tmp = 1.0d0 / ((n * (x + 0.5d0)) - ((n * 0.08333333333333333d0) / x))
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (x <= 1.75e-276) {
		tmp = -Math.log(x) / n;
	} else if (x <= 6.8e-177) {
		tmp = 1.0 - Math.pow(x, (1.0 / n));
	} else if (x <= 6400.0) {
		tmp = Math.log(((1.0 + x) / x)) / n;
	} else if (x <= 3.4e+60) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if x <= 1.75e-276:
		tmp = -math.log(x) / n
	elif x <= 6.8e-177:
		tmp = 1.0 - math.pow(x, (1.0 / n))
	elif x <= 6400.0:
		tmp = math.log(((1.0 + x) / x)) / n
	elif x <= 3.4e+60:
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x))
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (x <= 1.75e-276)
		tmp = Float64(Float64(-log(x)) / n);
	elseif (x <= 6.8e-177)
		tmp = Float64(1.0 - (x ^ Float64(1.0 / n)));
	elseif (x <= 6400.0)
		tmp = Float64(log(Float64(Float64(1.0 + x) / x)) / n);
	elseif (x <= 3.4e+60)
		tmp = Float64(1.0 / Float64(Float64(n * Float64(x + 0.5)) - Float64(Float64(n * 0.08333333333333333) / x)));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (x <= 1.75e-276)
		tmp = -log(x) / n;
	elseif (x <= 6.8e-177)
		tmp = 1.0 - (x ^ (1.0 / n));
	elseif (x <= 6400.0)
		tmp = log(((1.0 + x) / x)) / n;
	elseif (x <= 3.4e+60)
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[x, 1.75e-276], N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 6.8e-177], N[(1.0 - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6400.0], N[(N[Log[N[(N[(1.0 + x), $MachinePrecision] / x), $MachinePrecision]], $MachinePrecision] / n), $MachinePrecision], If[LessEqual[x, 3.4e+60], N[(1.0 / N[(N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(n * 0.08333333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]

Derivation

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

Alternative 12: 58.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.3 \cdot 10^{-238}:\\ \;\;\;\;\frac{-\log x}{n}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-210}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;\frac{x - \log x}{n}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right) - \frac{n \cdot 0.08333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= x 1.3e-238)
   (/ (- (log x)) n)
   (if (<= x 7.5e-210)
     (/ 1.0 (* n x))
     (if (<= x 0.5)
       (/ (- x (log x)) n)
       (if (<= x 3.2e+62)
         (/ 1.0 (- (* n (+ x 0.5)) (/ (* n 0.08333333333333333) x)))
         (/ 0.0 n))))))

C

double code(double x, double n) {
	double tmp;
	if (x <= 1.3e-238) {
		tmp = -log(x) / n;
	} else if (x <= 7.5e-210) {
		tmp = 1.0 / (n * x);
	} else if (x <= 0.5) {
		tmp = (x - log(x)) / n;
	} else if (x <= 3.2e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (x <= 1.3d-238) then
        tmp = -log(x) / n
    else if (x <= 7.5d-210) then
        tmp = 1.0d0 / (n * x)
    else if (x <= 0.5d0) then
        tmp = (x - log(x)) / n
    else if (x <= 3.2d+62) then
        tmp = 1.0d0 / ((n * (x + 0.5d0)) - ((n * 0.08333333333333333d0) / x))
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (x <= 1.3e-238) {
		tmp = -Math.log(x) / n;
	} else if (x <= 7.5e-210) {
		tmp = 1.0 / (n * x);
	} else if (x <= 0.5) {
		tmp = (x - Math.log(x)) / n;
	} else if (x <= 3.2e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if x <= 1.3e-238:
		tmp = -math.log(x) / n
	elif x <= 7.5e-210:
		tmp = 1.0 / (n * x)
	elif x <= 0.5:
		tmp = (x - math.log(x)) / n
	elif x <= 3.2e+62:
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x))
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (x <= 1.3e-238)
		tmp = Float64(Float64(-log(x)) / n);
	elseif (x <= 7.5e-210)
		tmp = Float64(1.0 / Float64(n * x));
	elseif (x <= 0.5)
		tmp = Float64(Float64(x - log(x)) / n);
	elseif (x <= 3.2e+62)
		tmp = Float64(1.0 / Float64(Float64(n * Float64(x + 0.5)) - Float64(Float64(n * 0.08333333333333333) / x)));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (x <= 1.3e-238)
		tmp = -log(x) / n;
	elseif (x <= 7.5e-210)
		tmp = 1.0 / (n * x);
	elseif (x <= 0.5)
		tmp = (x - log(x)) / n;
	elseif (x <= 3.2e+62)
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[x, 1.3e-238], N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 7.5e-210], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.5], N[(N[(x - N[Log[x], $MachinePrecision]), $MachinePrecision] / n), $MachinePrecision], If[LessEqual[x, 3.2e+62], N[(1.0 / N[(N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(n * 0.08333333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]

Derivation

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

Alternative 13: 58.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.95 \cdot 10^{-280}:\\ \;\;\;\;\frac{-\log x}{n}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-176}:\\ \;\;\;\;1 - {x}^{\left(\frac{1}{n}\right)}\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;\frac{x - \log x}{n}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+62}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right) - \frac{n \cdot 0.08333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= x 1.95e-280)
   (/ (- (log x)) n)
   (if (<= x 1.1e-176)
     (- 1.0 (pow x (/ 1.0 n)))
     (if (<= x 0.5)
       (/ (- x (log x)) n)
       (if (<= x 1.05e+62)
         (/ 1.0 (- (* n (+ x 0.5)) (/ (* n 0.08333333333333333) x)))
         (/ 0.0 n))))))

C

double code(double x, double n) {
	double tmp;
	if (x <= 1.95e-280) {
		tmp = -log(x) / n;
	} else if (x <= 1.1e-176) {
		tmp = 1.0 - pow(x, (1.0 / n));
	} else if (x <= 0.5) {
		tmp = (x - log(x)) / n;
	} else if (x <= 1.05e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (x <= 1.95d-280) then
        tmp = -log(x) / n
    else if (x <= 1.1d-176) then
        tmp = 1.0d0 - (x ** (1.0d0 / n))
    else if (x <= 0.5d0) then
        tmp = (x - log(x)) / n
    else if (x <= 1.05d+62) then
        tmp = 1.0d0 / ((n * (x + 0.5d0)) - ((n * 0.08333333333333333d0) / x))
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (x <= 1.95e-280) {
		tmp = -Math.log(x) / n;
	} else if (x <= 1.1e-176) {
		tmp = 1.0 - Math.pow(x, (1.0 / n));
	} else if (x <= 0.5) {
		tmp = (x - Math.log(x)) / n;
	} else if (x <= 1.05e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if x <= 1.95e-280:
		tmp = -math.log(x) / n
	elif x <= 1.1e-176:
		tmp = 1.0 - math.pow(x, (1.0 / n))
	elif x <= 0.5:
		tmp = (x - math.log(x)) / n
	elif x <= 1.05e+62:
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x))
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (x <= 1.95e-280)
		tmp = Float64(Float64(-log(x)) / n);
	elseif (x <= 1.1e-176)
		tmp = Float64(1.0 - (x ^ Float64(1.0 / n)));
	elseif (x <= 0.5)
		tmp = Float64(Float64(x - log(x)) / n);
	elseif (x <= 1.05e+62)
		tmp = Float64(1.0 / Float64(Float64(n * Float64(x + 0.5)) - Float64(Float64(n * 0.08333333333333333) / x)));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (x <= 1.95e-280)
		tmp = -log(x) / n;
	elseif (x <= 1.1e-176)
		tmp = 1.0 - (x ^ (1.0 / n));
	elseif (x <= 0.5)
		tmp = (x - log(x)) / n;
	elseif (x <= 1.05e+62)
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[x, 1.95e-280], N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision], If[LessEqual[x, 1.1e-176], N[(1.0 - N[Power[x, N[(1.0 / n), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.5], N[(N[(x - N[Log[x], $MachinePrecision]), $MachinePrecision] / n), $MachinePrecision], If[LessEqual[x, 1.05e+62], N[(1.0 / N[(N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(n * 0.08333333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]

Derivation

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

Alternative 14: 58.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-\log x}{n}\\ \mathbf{if}\;x \leq 1.3 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-210}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \mathbf{elif}\;x \leq 0.32:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{+62}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right) - \frac{n \cdot 0.08333333333333333}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{0}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (let* ((t_0 (/ (- (log x)) n)))
   (if (<= x 1.3e-238)
     t_0
     (if (<= x 7.5e-210)
       (/ 1.0 (* n x))
       (if (<= x 0.32)
         t_0
         (if (<= x 1.95e+62)
           (/ 1.0 (- (* n (+ x 0.5)) (/ (* n 0.08333333333333333) x)))
           (/ 0.0 n)))))))

C

double code(double x, double n) {
	double t_0 = -log(x) / n;
	double tmp;
	if (x <= 1.3e-238) {
		tmp = t_0;
	} else if (x <= 7.5e-210) {
		tmp = 1.0 / (n * x);
	} else if (x <= 0.32) {
		tmp = t_0;
	} else if (x <= 1.95e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -log(x) / n
    if (x <= 1.3d-238) then
        tmp = t_0
    else if (x <= 7.5d-210) then
        tmp = 1.0d0 / (n * x)
    else if (x <= 0.32d0) then
        tmp = t_0
    else if (x <= 1.95d+62) then
        tmp = 1.0d0 / ((n * (x + 0.5d0)) - ((n * 0.08333333333333333d0) / x))
    else
        tmp = 0.0d0 / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double t_0 = -Math.log(x) / n;
	double tmp;
	if (x <= 1.3e-238) {
		tmp = t_0;
	} else if (x <= 7.5e-210) {
		tmp = 1.0 / (n * x);
	} else if (x <= 0.32) {
		tmp = t_0;
	} else if (x <= 1.95e+62) {
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	} else {
		tmp = 0.0 / n;
	}
	return tmp;
}

Python

def code(x, n):
	t_0 = -math.log(x) / n
	tmp = 0
	if x <= 1.3e-238:
		tmp = t_0
	elif x <= 7.5e-210:
		tmp = 1.0 / (n * x)
	elif x <= 0.32:
		tmp = t_0
	elif x <= 1.95e+62:
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x))
	else:
		tmp = 0.0 / n
	return tmp

Julia

function code(x, n)
	t_0 = Float64(Float64(-log(x)) / n)
	tmp = 0.0
	if (x <= 1.3e-238)
		tmp = t_0;
	elseif (x <= 7.5e-210)
		tmp = Float64(1.0 / Float64(n * x));
	elseif (x <= 0.32)
		tmp = t_0;
	elseif (x <= 1.95e+62)
		tmp = Float64(1.0 / Float64(Float64(n * Float64(x + 0.5)) - Float64(Float64(n * 0.08333333333333333) / x)));
	else
		tmp = Float64(0.0 / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	t_0 = -log(x) / n;
	tmp = 0.0;
	if (x <= 1.3e-238)
		tmp = t_0;
	elseif (x <= 7.5e-210)
		tmp = 1.0 / (n * x);
	elseif (x <= 0.32)
		tmp = t_0;
	elseif (x <= 1.95e+62)
		tmp = 1.0 / ((n * (x + 0.5)) - ((n * 0.08333333333333333) / x));
	else
		tmp = 0.0 / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := Block[{t$95$0 = N[((-N[Log[x], $MachinePrecision]) / n), $MachinePrecision]}, If[LessEqual[x, 1.3e-238], t$95$0, If[LessEqual[x, 7.5e-210], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.32], t$95$0, If[LessEqual[x, 1.95e+62], N[(1.0 / N[(N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision] - N[(N[(n * 0.08333333333333333), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.0 / n), $MachinePrecision]]]]]]

Derivation

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

Alternative 15: 50.5% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{1}{n} \leq -4:\\ \;\;\;\;\frac{0}{n}\\ \mathbf{elif}\;\frac{1}{n} \leq 2 \cdot 10^{+174}:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{n \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= (/ 1.0 n) -4.0)
   (/ 0.0 n)
   (if (<= (/ 1.0 n) 2e+174) (/ 1.0 (* n (+ x 0.5))) (/ 1.0 (* n x)))))

C

double code(double x, double n) {
	double tmp;
	if ((1.0 / n) <= -4.0) {
		tmp = 0.0 / n;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = 1.0 / (n * (x + 0.5));
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if ((1.0d0 / n) <= (-4.0d0)) then
        tmp = 0.0d0 / n
    else if ((1.0d0 / n) <= 2d+174) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else
        tmp = 1.0d0 / (n * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if ((1.0 / n) <= -4.0) {
		tmp = 0.0 / n;
	} else if ((1.0 / n) <= 2e+174) {
		tmp = 1.0 / (n * (x + 0.5));
	} else {
		tmp = 1.0 / (n * x);
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if (1.0 / n) <= -4.0:
		tmp = 0.0 / n
	elif (1.0 / n) <= 2e+174:
		tmp = 1.0 / (n * (x + 0.5))
	else:
		tmp = 1.0 / (n * x)
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (Float64(1.0 / n) <= -4.0)
		tmp = Float64(0.0 / n);
	elseif (Float64(1.0 / n) <= 2e+174)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	else
		tmp = Float64(1.0 / Float64(n * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if ((1.0 / n) <= -4.0)
		tmp = 0.0 / n;
	elseif ((1.0 / n) <= 2e+174)
		tmp = 1.0 / (n * (x + 0.5));
	else
		tmp = 1.0 / (n * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[N[(1.0 / n), $MachinePrecision], -4.0], N[(0.0 / n), $MachinePrecision], If[LessEqual[N[(1.0 / n), $MachinePrecision], 2e+174], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 16: 42.6% accurate, 23.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;n \leq -2:\\ \;\;\;\;\frac{1}{n \cdot \left(x + 0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x}}{n}\\ \end{array} \end{array} \]

FPCore

(FPCore (x n)
 :precision binary64
 (if (<= n -2.0) (/ 1.0 (* n (+ x 0.5))) (/ (/ 1.0 x) n)))

C

double code(double x, double n) {
	double tmp;
	if (n <= -2.0) {
		tmp = 1.0 / (n * (x + 0.5));
	} else {
		tmp = (1.0 / x) / n;
	}
	return tmp;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    real(8) :: tmp
    if (n <= (-2.0d0)) then
        tmp = 1.0d0 / (n * (x + 0.5d0))
    else
        tmp = (1.0d0 / x) / n
    end if
    code = tmp
end function

Java

public static double code(double x, double n) {
	double tmp;
	if (n <= -2.0) {
		tmp = 1.0 / (n * (x + 0.5));
	} else {
		tmp = (1.0 / x) / n;
	}
	return tmp;
}

Python

def code(x, n):
	tmp = 0
	if n <= -2.0:
		tmp = 1.0 / (n * (x + 0.5))
	else:
		tmp = (1.0 / x) / n
	return tmp

Julia

function code(x, n)
	tmp = 0.0
	if (n <= -2.0)
		tmp = Float64(1.0 / Float64(n * Float64(x + 0.5)));
	else
		tmp = Float64(Float64(1.0 / x) / n);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, n)
	tmp = 0.0;
	if (n <= -2.0)
		tmp = 1.0 / (n * (x + 0.5));
	else
		tmp = (1.0 / x) / n;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, n_] := If[LessEqual[n, -2.0], N[(1.0 / N[(n * N[(x + 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / x), $MachinePrecision] / n), $MachinePrecision]]

Derivation

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

Alternative 17: 40.9% accurate, 42.2× speedup

Math

\[\begin{array}{l} \\ \frac{1}{n \cdot x} \end{array} \]

FPCore

(FPCore (x n) :precision binary64 (/ 1.0 (* n x)))

C

double code(double x, double n) {
	return 1.0 / (n * x);
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    code = 1.0d0 / (n * x)
end function

Java

public static double code(double x, double n) {
	return 1.0 / (n * x);
}

Python

def code(x, n):
	return 1.0 / (n * x)

Julia

function code(x, n)
	return Float64(1.0 / Float64(n * x))
end

MATLAB

function tmp = code(x, n)
	tmp = 1.0 / (n * x);
end

Wolfram

code[x_, n_] := N[(1.0 / N[(n * x), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 18: 41.5% accurate, 42.2× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{1}{x}}{n} \end{array} \]

FPCore

(FPCore (x n) :precision binary64 (/ (/ 1.0 x) n))

C

double code(double x, double n) {
	return (1.0 / x) / n;
}

Fortran

real(8) function code(x, n)
    real(8), intent (in) :: x
    real(8), intent (in) :: n
    code = (1.0d0 / x) / n
end function

Java

public static double code(double x, double n) {
	return (1.0 / x) / n;
}

Python

def code(x, n):
	return (1.0 / x) / n

Julia

function code(x, n)
	return Float64(Float64(1.0 / x) / n)
end

MATLAB

function tmp = code(x, n)
	tmp = (1.0 / x) / n;
end

Wolfram

code[x_, n_] := N[(N[(1.0 / x), $MachinePrecision] / n), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  :precision binary64
  (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))