Asymptote C

Percentage Accurate: 54.0% → 99.6%

Time: 12.9s

Alternatives: 16

Speedup: 1.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Python

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}

Python

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ t_2 := t_0 - t_1\\ t_3 := {t_0}^{2}\\ \mathbf{if}\;t_2 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{{x}^{3}} - \left(\frac{3}{x} + \left(\frac{1}{{x}^{2}} + \frac{1}{{x}^{4}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 - \frac{t_1}{\frac{x + -1}{x + 1}}}{\frac{\frac{{t_0}^{4} - {t_1}^{4}}{t_2}}{t_3 + {t_1}^{2}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0)))
        (t_1 (/ (+ x 1.0) (+ x -1.0)))
        (t_2 (- t_0 t_1))
        (t_3 (pow t_0 2.0)))
   (if (<= t_2 5e-12)
     (-
      (/ -3.0 (pow x 3.0))
      (+ (/ 3.0 x) (+ (/ 1.0 (pow x 2.0)) (/ 1.0 (pow x 4.0)))))
     (/
      (- t_3 (/ t_1 (/ (+ x -1.0) (+ x 1.0))))
      (/ (/ (- (pow t_0 4.0) (pow t_1 4.0)) t_2) (+ t_3 (pow t_1 2.0)))))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double t_2 = t_0 - t_1;
	double t_3 = pow(t_0, 2.0);
	double tmp;
	if (t_2 <= 5e-12) {
		tmp = (-3.0 / pow(x, 3.0)) - ((3.0 / x) + ((1.0 / pow(x, 2.0)) + (1.0 / pow(x, 4.0))));
	} else {
		tmp = (t_3 - (t_1 / ((x + -1.0) / (x + 1.0)))) / (((pow(t_0, 4.0) - pow(t_1, 4.0)) / t_2) / (t_3 + pow(t_1, 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    t_2 = t_0 - t_1
    t_3 = t_0 ** 2.0d0
    if (t_2 <= 5d-12) then
        tmp = ((-3.0d0) / (x ** 3.0d0)) - ((3.0d0 / x) + ((1.0d0 / (x ** 2.0d0)) + (1.0d0 / (x ** 4.0d0))))
    else
        tmp = (t_3 - (t_1 / ((x + (-1.0d0)) / (x + 1.0d0)))) / ((((t_0 ** 4.0d0) - (t_1 ** 4.0d0)) / t_2) / (t_3 + (t_1 ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double t_2 = t_0 - t_1;
	double t_3 = Math.pow(t_0, 2.0);
	double tmp;
	if (t_2 <= 5e-12) {
		tmp = (-3.0 / Math.pow(x, 3.0)) - ((3.0 / x) + ((1.0 / Math.pow(x, 2.0)) + (1.0 / Math.pow(x, 4.0))));
	} else {
		tmp = (t_3 - (t_1 / ((x + -1.0) / (x + 1.0)))) / (((Math.pow(t_0, 4.0) - Math.pow(t_1, 4.0)) / t_2) / (t_3 + Math.pow(t_1, 2.0)));
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	t_2 = t_0 - t_1
	t_3 = math.pow(t_0, 2.0)
	tmp = 0
	if t_2 <= 5e-12:
		tmp = (-3.0 / math.pow(x, 3.0)) - ((3.0 / x) + ((1.0 / math.pow(x, 2.0)) + (1.0 / math.pow(x, 4.0))))
	else:
		tmp = (t_3 - (t_1 / ((x + -1.0) / (x + 1.0)))) / (((math.pow(t_0, 4.0) - math.pow(t_1, 4.0)) / t_2) / (t_3 + math.pow(t_1, 2.0)))
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	t_2 = Float64(t_0 - t_1)
	t_3 = t_0 ^ 2.0
	tmp = 0.0
	if (t_2 <= 5e-12)
		tmp = Float64(Float64(-3.0 / (x ^ 3.0)) - Float64(Float64(3.0 / x) + Float64(Float64(1.0 / (x ^ 2.0)) + Float64(1.0 / (x ^ 4.0)))));
	else
		tmp = Float64(Float64(t_3 - Float64(t_1 / Float64(Float64(x + -1.0) / Float64(x + 1.0)))) / Float64(Float64(Float64((t_0 ^ 4.0) - (t_1 ^ 4.0)) / t_2) / Float64(t_3 + (t_1 ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	t_2 = t_0 - t_1;
	t_3 = t_0 ^ 2.0;
	tmp = 0.0;
	if (t_2 <= 5e-12)
		tmp = (-3.0 / (x ^ 3.0)) - ((3.0 / x) + ((1.0 / (x ^ 2.0)) + (1.0 / (x ^ 4.0))));
	else
		tmp = (t_3 - (t_1 / ((x + -1.0) / (x + 1.0)))) / ((((t_0 ^ 4.0) - (t_1 ^ 4.0)) / t_2) / (t_3 + (t_1 ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 - t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[Power[t$95$0, 2.0], $MachinePrecision]}, If[LessEqual[t$95$2, 5e-12], N[(N[(-3.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - N[(N[(3.0 / x), $MachinePrecision] + N[(N[(1.0 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 - N[(t$95$1 / N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(N[Power[t$95$0, 4.0], $MachinePrecision] - N[Power[t$95$1, 4.0], $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] / N[(t$95$3 + N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 99.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 0.001:\\ \;\;\;\;\frac{-3}{{x}^{3}} - \left(\frac{3}{x} + \left(\frac{1}{{x}^{2}} + \frac{1}{{x}^{4}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x + 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 0.001)
   (-
    (/ -3.0 (pow x 3.0))
    (+ (/ 3.0 x) (+ (/ 1.0 (pow x 2.0)) (/ 1.0 (pow x 4.0)))))
   (+ 1.0 (* x (+ x 3.0)))))

C

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.001) {
		tmp = (-3.0 / pow(x, 3.0)) - ((3.0 / x) + ((1.0 / pow(x, 2.0)) + (1.0 / pow(x, 4.0))));
	} else {
		tmp = 1.0 + (x * (x + 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 0.001d0) then
        tmp = ((-3.0d0) / (x ** 3.0d0)) - ((3.0d0 / x) + ((1.0d0 / (x ** 2.0d0)) + (1.0d0 / (x ** 4.0d0))))
    else
        tmp = 1.0d0 + (x * (x + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.001) {
		tmp = (-3.0 / Math.pow(x, 3.0)) - ((3.0 / x) + ((1.0 / Math.pow(x, 2.0)) + (1.0 / Math.pow(x, 4.0))));
	} else {
		tmp = 1.0 + (x * (x + 3.0));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.001:
		tmp = (-3.0 / math.pow(x, 3.0)) - ((3.0 / x) + ((1.0 / math.pow(x, 2.0)) + (1.0 / math.pow(x, 4.0))))
	else:
		tmp = 1.0 + (x * (x + 3.0))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 0.001)
		tmp = Float64(Float64(-3.0 / (x ^ 3.0)) - Float64(Float64(3.0 / x) + Float64(Float64(1.0 / (x ^ 2.0)) + Float64(1.0 / (x ^ 4.0)))));
	else
		tmp = Float64(1.0 + Float64(x * Float64(x + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 0.001)
		tmp = (-3.0 / (x ^ 3.0)) - ((3.0 / x) + ((1.0 / (x ^ 2.0)) + (1.0 / (x ^ 4.0))));
	else
		tmp = 1.0 + (x * (x + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.001], N[(N[(-3.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] - N[(N[(3.0 / x), $MachinePrecision] + N[(N[(1.0 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Power[x, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * N[(x + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 - t_1 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{{x}^{3}} + \left(\frac{-3}{x} - {x}^{-2}\right)\\ \mathbf{else}:\\ \;\;\;\;\left({t_0}^{2} - {t_1}^{2}\right) \cdot \frac{1}{t_0 + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))) (t_1 (/ (+ x 1.0) (+ x -1.0))))
   (if (<= (- t_0 t_1) 5e-12)
     (+ (/ -3.0 (pow x 3.0)) (- (/ -3.0 x) (pow x -2.0)))
     (* (- (pow t_0 2.0) (pow t_1 2.0)) (/ 1.0 (+ t_0 t_1))))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / pow(x, 3.0)) + ((-3.0 / x) - pow(x, -2.0));
	} else {
		tmp = (pow(t_0, 2.0) - pow(t_1, 2.0)) * (1.0 / (t_0 + t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    if ((t_0 - t_1) <= 5d-12) then
        tmp = ((-3.0d0) / (x ** 3.0d0)) + (((-3.0d0) / x) - (x ** (-2.0d0)))
    else
        tmp = ((t_0 ** 2.0d0) - (t_1 ** 2.0d0)) * (1.0d0 / (t_0 + t_1))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / Math.pow(x, 3.0)) + ((-3.0 / x) - Math.pow(x, -2.0));
	} else {
		tmp = (Math.pow(t_0, 2.0) - Math.pow(t_1, 2.0)) * (1.0 / (t_0 + t_1));
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	tmp = 0
	if (t_0 - t_1) <= 5e-12:
		tmp = (-3.0 / math.pow(x, 3.0)) + ((-3.0 / x) - math.pow(x, -2.0))
	else:
		tmp = (math.pow(t_0, 2.0) - math.pow(t_1, 2.0)) * (1.0 / (t_0 + t_1))
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	tmp = 0.0
	if (Float64(t_0 - t_1) <= 5e-12)
		tmp = Float64(Float64(-3.0 / (x ^ 3.0)) + Float64(Float64(-3.0 / x) - (x ^ -2.0)));
	else
		tmp = Float64(Float64((t_0 ^ 2.0) - (t_1 ^ 2.0)) * Float64(1.0 / Float64(t_0 + t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	tmp = 0.0;
	if ((t_0 - t_1) <= 5e-12)
		tmp = (-3.0 / (x ^ 3.0)) + ((-3.0 / x) - (x ^ -2.0));
	else
		tmp = ((t_0 ^ 2.0) - (t_1 ^ 2.0)) * (1.0 / (t_0 + t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - t$95$1), $MachinePrecision], 5e-12], N[(N[(-3.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-3.0 / x), $MachinePrecision] - N[Power[x, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] - N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 - t_1 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{{x}^{3}} + \left(\frac{-3}{x} - {x}^{-2}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_0}{\frac{x + 1}{x}} - \frac{t_1}{\frac{x + -1}{x + 1}}}{t_0 + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))) (t_1 (/ (+ x 1.0) (+ x -1.0))))
   (if (<= (- t_0 t_1) 5e-12)
     (+ (/ -3.0 (pow x 3.0)) (- (/ -3.0 x) (pow x -2.0)))
     (/
      (- (/ t_0 (/ (+ x 1.0) x)) (/ t_1 (/ (+ x -1.0) (+ x 1.0))))
      (+ t_0 t_1)))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / pow(x, 3.0)) + ((-3.0 / x) - pow(x, -2.0));
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    if ((t_0 - t_1) <= 5d-12) then
        tmp = ((-3.0d0) / (x ** 3.0d0)) + (((-3.0d0) / x) - (x ** (-2.0d0)))
    else
        tmp = ((t_0 / ((x + 1.0d0) / x)) - (t_1 / ((x + (-1.0d0)) / (x + 1.0d0)))) / (t_0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / Math.pow(x, 3.0)) + ((-3.0 / x) - Math.pow(x, -2.0));
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	tmp = 0
	if (t_0 - t_1) <= 5e-12:
		tmp = (-3.0 / math.pow(x, 3.0)) + ((-3.0 / x) - math.pow(x, -2.0))
	else:
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1)
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	tmp = 0.0
	if (Float64(t_0 - t_1) <= 5e-12)
		tmp = Float64(Float64(-3.0 / (x ^ 3.0)) + Float64(Float64(-3.0 / x) - (x ^ -2.0)));
	else
		tmp = Float64(Float64(Float64(t_0 / Float64(Float64(x + 1.0) / x)) - Float64(t_1 / Float64(Float64(x + -1.0) / Float64(x + 1.0)))) / Float64(t_0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	tmp = 0.0;
	if ((t_0 - t_1) <= 5e-12)
		tmp = (-3.0 / (x ^ 3.0)) + ((-3.0 / x) - (x ^ -2.0));
	else
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - t$95$1), $MachinePrecision], 5e-12], N[(N[(-3.0 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-3.0 / x), $MachinePrecision] - N[Power[x, -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 / N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 - t_1 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{2}{x} - \left(3 + \frac{2}{{x}^{2}}\right)}{x + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_0}{\frac{x + 1}{x}} - \frac{t_1}{\frac{x + -1}{x + 1}}}{t_0 + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))) (t_1 (/ (+ x 1.0) (+ x -1.0))))
   (if (<= (- t_0 t_1) 5e-12)
     (/ (- (/ 2.0 x) (+ 3.0 (/ 2.0 (pow x 2.0)))) (+ x -1.0))
     (/
      (- (/ t_0 (/ (+ x 1.0) x)) (/ t_1 (/ (+ x -1.0) (+ x 1.0))))
      (+ t_0 t_1)))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = ((2.0 / x) - (3.0 + (2.0 / pow(x, 2.0)))) / (x + -1.0);
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    if ((t_0 - t_1) <= 5d-12) then
        tmp = ((2.0d0 / x) - (3.0d0 + (2.0d0 / (x ** 2.0d0)))) / (x + (-1.0d0))
    else
        tmp = ((t_0 / ((x + 1.0d0) / x)) - (t_1 / ((x + (-1.0d0)) / (x + 1.0d0)))) / (t_0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = ((2.0 / x) - (3.0 + (2.0 / Math.pow(x, 2.0)))) / (x + -1.0);
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	tmp = 0
	if (t_0 - t_1) <= 5e-12:
		tmp = ((2.0 / x) - (3.0 + (2.0 / math.pow(x, 2.0)))) / (x + -1.0)
	else:
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1)
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	tmp = 0.0
	if (Float64(t_0 - t_1) <= 5e-12)
		tmp = Float64(Float64(Float64(2.0 / x) - Float64(3.0 + Float64(2.0 / (x ^ 2.0)))) / Float64(x + -1.0));
	else
		tmp = Float64(Float64(Float64(t_0 / Float64(Float64(x + 1.0) / x)) - Float64(t_1 / Float64(Float64(x + -1.0) / Float64(x + 1.0)))) / Float64(t_0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	tmp = 0.0;
	if ((t_0 - t_1) <= 5e-12)
		tmp = ((2.0 / x) - (3.0 + (2.0 / (x ^ 2.0)))) / (x + -1.0);
	else
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - t$95$1), $MachinePrecision], 5e-12], N[(N[(N[(2.0 / x), $MachinePrecision] - N[(3.0 + N[(2.0 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 / N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 6: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 - t_1 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x} - {x}^{-2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_0}{\frac{x + 1}{x}} - \frac{t_1}{\frac{x + -1}{x + 1}}}{t_0 + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))) (t_1 (/ (+ x 1.0) (+ x -1.0))))
   (if (<= (- t_0 t_1) 5e-12)
     (- (/ -3.0 x) (pow x -2.0))
     (/
      (- (/ t_0 (/ (+ x 1.0) x)) (/ t_1 (/ (+ x -1.0) (+ x 1.0))))
      (+ t_0 t_1)))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / x) - pow(x, -2.0);
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    if ((t_0 - t_1) <= 5d-12) then
        tmp = ((-3.0d0) / x) - (x ** (-2.0d0))
    else
        tmp = ((t_0 / ((x + 1.0d0) / x)) - (t_1 / ((x + (-1.0d0)) / (x + 1.0d0)))) / (t_0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = (-3.0 / x) - Math.pow(x, -2.0);
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	tmp = 0
	if (t_0 - t_1) <= 5e-12:
		tmp = (-3.0 / x) - math.pow(x, -2.0)
	else:
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1)
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	tmp = 0.0
	if (Float64(t_0 - t_1) <= 5e-12)
		tmp = Float64(Float64(-3.0 / x) - (x ^ -2.0));
	else
		tmp = Float64(Float64(Float64(t_0 / Float64(Float64(x + 1.0) / x)) - Float64(t_1 / Float64(Float64(x + -1.0) / Float64(x + 1.0)))) / Float64(t_0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	tmp = 0.0;
	if ((t_0 - t_1) <= 5e-12)
		tmp = (-3.0 / x) - (x ^ -2.0);
	else
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - t$95$1), $MachinePrecision], 5e-12], N[(N[(-3.0 / x), $MachinePrecision] - N[Power[x, -2.0], $MachinePrecision]), $MachinePrecision], N[(N[(N[(t$95$0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 / N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 99.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t_1 := \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 - t_1 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t_0}{\frac{x + 1}{x}} - \frac{t_1}{\frac{x + -1}{x + 1}}}{t_0 + t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))) (t_1 (/ (+ x 1.0) (+ x -1.0))))
   (if (<= (- t_0 t_1) 5e-12)
     (/ -3.0 x)
     (/
      (- (/ t_0 (/ (+ x 1.0) x)) (/ t_1 (/ (+ x -1.0) (+ x 1.0))))
      (+ t_0 t_1)))))

C

double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    t_1 = (x + 1.0d0) / (x + (-1.0d0))
    if ((t_0 - t_1) <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = ((t_0 / ((x + 1.0d0) / x)) - (t_1 / ((x + (-1.0d0)) / (x + 1.0d0)))) / (t_0 + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (x + 1.0);
	double t_1 = (x + 1.0) / (x + -1.0);
	double tmp;
	if ((t_0 - t_1) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (x + 1.0)
	t_1 = (x + 1.0) / (x + -1.0)
	tmp = 0
	if (t_0 - t_1) <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1)
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(x + 1.0))
	t_1 = Float64(Float64(x + 1.0) / Float64(x + -1.0))
	tmp = 0.0
	if (Float64(t_0 - t_1) <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(Float64(Float64(t_0 / Float64(Float64(x + 1.0) / x)) - Float64(t_1 / Float64(Float64(x + -1.0) / Float64(x + 1.0)))) / Float64(t_0 + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (x + 1.0);
	t_1 = (x + 1.0) / (x + -1.0);
	tmp = 0.0;
	if ((t_0 - t_1) <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = ((t_0 / ((x + 1.0) / x)) - (t_1 / ((x + -1.0) / (x + 1.0)))) / (t_0 + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 - t$95$1), $MachinePrecision], 5e-12], N[(-3.0 / x), $MachinePrecision], N[(N[(N[(t$95$0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 / N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$0 + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 8: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + -1\right) + \left(x + 1\right) \cdot \frac{-1 - x}{x}}{\left(x + -1\right) \cdot \frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 5e-12)
   (/ -3.0 x)
   (/
    (+ (+ x -1.0) (* (+ x 1.0) (/ (- -1.0 x) x)))
    (* (+ x -1.0) (/ (+ x 1.0) x)))))

C

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x + -1.0) + ((x + 1.0) * ((-1.0 - x) / x))) / ((x + -1.0) * ((x + 1.0) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = ((x + (-1.0d0)) + ((x + 1.0d0) * (((-1.0d0) - x) / x))) / ((x + (-1.0d0)) * ((x + 1.0d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x + -1.0) + ((x + 1.0) * ((-1.0 - x) / x))) / ((x + -1.0) * ((x + 1.0) / x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = ((x + -1.0) + ((x + 1.0) * ((-1.0 - x) / x))) / ((x + -1.0) * ((x + 1.0) / x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(Float64(Float64(x + -1.0) + Float64(Float64(x + 1.0) * Float64(Float64(-1.0 - x) / x))) / Float64(Float64(x + -1.0) * Float64(Float64(x + 1.0) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = ((x + -1.0) + ((x + 1.0) * ((-1.0 - x) / x))) / ((x + -1.0) * ((x + 1.0) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e-12], N[(-3.0 / x), $MachinePrecision], N[(N[(N[(x + -1.0), $MachinePrecision] + N[(N[(x + 1.0), $MachinePrecision] * N[(N[(-1.0 - x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x + -1.0), $MachinePrecision] * N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 9: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 - x\right) + \left(x + 1\right) \cdot \left(x + 1\right)}{\left(x + 1\right) \cdot \left(1 - x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 5e-12)
   (/ -3.0 x)
   (/ (+ (* x (- 1.0 x)) (* (+ x 1.0) (+ x 1.0))) (* (+ x 1.0) (- 1.0 x)))))

C

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x * (1.0 - x)) + ((x + 1.0) * (x + 1.0))) / ((x + 1.0) * (1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = ((x * (1.0d0 - x)) + ((x + 1.0d0) * (x + 1.0d0))) / ((x + 1.0d0) * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x * (1.0 - x)) + ((x + 1.0) * (x + 1.0))) / ((x + 1.0) * (1.0 - x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = ((x * (1.0 - x)) + ((x + 1.0) * (x + 1.0))) / ((x + 1.0) * (1.0 - x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - x)) + Float64(Float64(x + 1.0) * Float64(x + 1.0))) / Float64(Float64(x + 1.0) * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = ((x * (1.0 - x)) + ((x + 1.0) * (x + 1.0))) / ((x + 1.0) * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e-12], N[(-3.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] + N[(N[(x + 1.0), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + -1}{x + 1} + \frac{-1 - x}{x}}{\frac{x + -1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 5e-12)
   (/ -3.0 x)
   (/ (+ (/ (+ x -1.0) (+ x 1.0)) (/ (- -1.0 x) x)) (/ (+ x -1.0) x))))

C

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = (((x + -1.0) / (x + 1.0)) + ((-1.0 - x) / x)) / ((x + -1.0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = (((x + (-1.0d0)) / (x + 1.0d0)) + (((-1.0d0) - x) / x)) / ((x + (-1.0d0)) / x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = (((x + -1.0) / (x + 1.0)) + ((-1.0 - x) / x)) / ((x + -1.0) / x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = (((x + -1.0) / (x + 1.0)) + ((-1.0 - x) / x)) / ((x + -1.0) / x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(Float64(Float64(Float64(x + -1.0) / Float64(x + 1.0)) + Float64(Float64(-1.0 - x) / x)) / Float64(Float64(x + -1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = (((x + -1.0) / (x + 1.0)) + ((-1.0 - x) / x)) / ((x + -1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e-12], N[(-3.0 / x), $MachinePrecision], N[(N[(N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 - x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / N[(N[(x + -1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 11: 99.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + 1} - \frac{x + 1}{x + -1} \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{x + -1}{x + 1} + \left(-1 - x\right)}{x + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0))) 5e-12)
   (/ -3.0 x)
   (/ (+ (* x (/ (+ x -1.0) (+ x 1.0))) (- -1.0 x)) (+ x -1.0))))

C

double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x * ((x + -1.0) / (x + 1.0))) + (-1.0 - x)) / (x + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))) <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = ((x * ((x + (-1.0d0)) / (x + 1.0d0))) + ((-1.0d0) - x)) / (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = ((x * ((x + -1.0) / (x + 1.0))) + (-1.0 - x)) / (x + -1.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = ((x * ((x + -1.0) / (x + 1.0))) + (-1.0 - x)) / (x + -1.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0))) <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(Float64(x + -1.0) / Float64(x + 1.0))) + Float64(-1.0 - x)) / Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))) <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = ((x * ((x + -1.0) / (x + 1.0))) + (-1.0 - x)) / (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e-12], N[(-3.0 / x), $MachinePrecision], N[(N[(N[(x * N[(N[(x + -1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1} - \frac{x + 1}{x + -1}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (+ x -1.0)))))
   (if (<= t_0 5e-12) (/ -3.0 x) t_0)))

C

double code(double x) {
	double t_0 = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	double tmp;
	if (t_0 <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / (x + 1.0d0)) - ((x + 1.0d0) / (x + (-1.0d0)))
    if (t_0 <= 5d-12) then
        tmp = (-3.0d0) / x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	double tmp;
	if (t_0 <= 5e-12) {
		tmp = -3.0 / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x):
	t_0 = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0))
	tmp = 0
	if t_0 <= 5e-12:
		tmp = -3.0 / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x)
	t_0 = Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x + -1.0)))
	tmp = 0.0
	if (t_0 <= 5e-12)
		tmp = Float64(-3.0 / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = (x / (x + 1.0)) - ((x + 1.0) / (x + -1.0));
	tmp = 0.0;
	if (t_0 <= 5e-12)
		tmp = -3.0 / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e-12], N[(-3.0 / x), $MachinePrecision], t$95$0]]

Derivation

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

Alternative 13: 98.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot \left(x + 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (/ -3.0 x) (+ 1.0 (* x (+ x 3.0)))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0 + (x * (x + 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (-3.0d0) / x
    else
        tmp = 1.0d0 + (x * (x + 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0 + (x * (x + 3.0));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = -3.0 / x
	else:
		tmp = 1.0 + (x * (x + 3.0))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(1.0 + Float64(x * Float64(x + 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = -3.0 / x;
	else
		tmp = 1.0 + (x * (x + 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(-3.0 / x), $MachinePrecision], N[(1.0 + N[(x * N[(x + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 98.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (/ -3.0 x) (+ 1.0 (* x 3.0))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (-3.0d0) / x
    else
        tmp = 1.0d0 + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0 + (x * 3.0);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = -3.0 / x
	else:
		tmp = 1.0 + (x * 3.0)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(-3.0 / x);
	else
		tmp = Float64(1.0 + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = -3.0 / x;
	else
		tmp = 1.0 + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(-3.0 / x), $MachinePrecision], N[(1.0 + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 15: 98.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{-3}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (/ -3.0 x) 1.0))

C

double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (-3.0d0) / x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = -3.0 / x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = -3.0 / x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(-3.0 / x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = -3.0 / x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(-3.0 / x), $MachinePrecision], 1.0]

Derivation

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

Alternative 16: 50.6% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

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

Java

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

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

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

Reproduce

herbie shell --seed 2023348 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))