VandenBroeck and Keller, Equation (23)

Percentage Accurate: 76.5% → 99.6%

Time: 20.3s

Alternatives: 22

Speedup: 1.5×

Specification

Math

\[\begin{array}{l} \\ \left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (+
  (- (* x (/ 1.0 (tan B))))
  (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))

C

double code(double F, double B, double x) {
	return -(x * (1.0 / tan(B))) + ((F / sin(B)) * pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)));
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    code = -(x * (1.0d0 / tan(b))) + ((f / sin(b)) * ((((f * f) + 2.0d0) + (2.0d0 * x)) ** -(1.0d0 / 2.0d0)))
end function

Java

public static double code(double F, double B, double x) {
	return -(x * (1.0 / Math.tan(B))) + ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)));
}

Python

def code(F, B, x):
	return -(x * (1.0 / math.tan(B))) + ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)))

Julia

function code(F, B, x)
	return Float64(Float64(-Float64(x * Float64(1.0 / tan(B)))) + Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(2.0 * x)) ^ Float64(-Float64(1.0 / 2.0)))))
end

MATLAB

function tmp = code(F, B, x)
	tmp = -(x * (1.0 / tan(B))) + ((F / sin(B)) * ((((F * F) + 2.0) + (2.0 * x)) ^ -(1.0 / 2.0)));
end

Wolfram

code[F_, B_, x_] := N[((-N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], (-N[(1.0 / 2.0), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (+
  (- (* x (/ 1.0 (tan B))))
  (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))

C

double code(double F, double B, double x) {
	return -(x * (1.0 / tan(B))) + ((F / sin(B)) * pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)));
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    code = -(x * (1.0d0 / tan(b))) + ((f / sin(b)) * ((((f * f) + 2.0d0) + (2.0d0 * x)) ** -(1.0d0 / 2.0d0)))
end function

Java

public static double code(double F, double B, double x) {
	return -(x * (1.0 / Math.tan(B))) + ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)));
}

Python

def code(F, B, x):
	return -(x * (1.0 / math.tan(B))) + ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (2.0 * x)), -(1.0 / 2.0)))

Julia

function code(F, B, x)
	return Float64(Float64(-Float64(x * Float64(1.0 / tan(B)))) + Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(2.0 * x)) ^ Float64(-Float64(1.0 / 2.0)))))
end

MATLAB

function tmp = code(F, B, x)
	tmp = -(x * (1.0 / tan(B))) + ((F / sin(B)) * ((((F * F) + 2.0) + (2.0 * x)) ^ -(1.0 / 2.0)));
end

Wolfram

code[F_, B_, x_] := N[((-N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]) + N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(2.0 * x), $MachinePrecision]), $MachinePrecision], (-N[(1.0 / 2.0), $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.7 \cdot 10^{+36}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 2400000:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1 + -0.5 \cdot \frac{2 + x \cdot 2}{{F}^{2}}}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -2.7e+36)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 2400000.0)
       (- (* (/ F (sin B)) (pow (+ (+ 2.0 (* F F)) (* x 2.0)) -0.5)) t_0)
       (+
        (* x (/ -1.0 (tan B)))
        (/ (+ 1.0 (* -0.5 (/ (+ 2.0 (* x 2.0)) (pow F 2.0)))) (sin B)))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -2.7e+36) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 2400000.0) {
		tmp = ((F / sin(B)) * pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - t_0;
	} else {
		tmp = (x * (-1.0 / tan(B))) + ((1.0 + (-0.5 * ((2.0 + (x * 2.0)) / pow(F, 2.0)))) / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / tan(b)
    if (f <= (-2.7d+36)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 2400000.0d0) then
        tmp = ((f / sin(b)) * (((2.0d0 + (f * f)) + (x * 2.0d0)) ** (-0.5d0))) - t_0
    else
        tmp = (x * ((-1.0d0) / tan(b))) + ((1.0d0 + ((-0.5d0) * ((2.0d0 + (x * 2.0d0)) / (f ** 2.0d0)))) / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = x / Math.tan(B);
	double tmp;
	if (F <= -2.7e+36) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 2400000.0) {
		tmp = ((F / Math.sin(B)) * Math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - t_0;
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + ((1.0 + (-0.5 * ((2.0 + (x * 2.0)) / Math.pow(F, 2.0)))) / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -2.7e+36:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 2400000.0:
		tmp = ((F / math.sin(B)) * math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - t_0
	else:
		tmp = (x * (-1.0 / math.tan(B))) + ((1.0 + (-0.5 * ((2.0 + (x * 2.0)) / math.pow(F, 2.0)))) / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -2.7e+36)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 2400000.0)
		tmp = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(2.0 + Float64(F * F)) + Float64(x * 2.0)) ^ -0.5)) - t_0);
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(Float64(1.0 + Float64(-0.5 * Float64(Float64(2.0 + Float64(x * 2.0)) / (F ^ 2.0)))) / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x / tan(B);
	tmp = 0.0;
	if (F <= -2.7e+36)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 2400000.0)
		tmp = ((F / sin(B)) * (((2.0 + (F * F)) + (x * 2.0)) ^ -0.5)) - t_0;
	else
		tmp = (x * (-1.0 / tan(B))) + ((1.0 + (-0.5 * ((2.0 + (x * 2.0)) / (F ^ 2.0)))) / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -2.7e+36], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 2400000.0], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(2.0 + N[(F * F), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 + N[(-0.5 * N[(N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 99.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{F}{\sin B \cdot \mathsf{hypot}\left(F, \sqrt{\mathsf{fma}\left(2, x, 2\right)}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= x -1.0)
   (/ (- x) (tan B))
   (+
    (/ -1.0 (/ (tan B) x))
    (/ F (* (sin B) (hypot F (sqrt (fma 2.0 x 2.0))))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x / tan(B);
	} else {
		tmp = (-1.0 / (tan(B) / x)) + (F / (sin(B) * hypot(F, sqrt(fma(2.0, x, 2.0)))));
	}
	return tmp;
}

Julia

function code(F, B, x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(F / Float64(sin(B) * hypot(F, sqrt(fma(2.0, x, 2.0))))));
	end
	return tmp
end

Wolfram

code[F_, B_, x_] := If[LessEqual[x, -1.0], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[F ^ 2 + N[Sqrt[N[(2.0 * x + 2.0), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 3: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + x \cdot 2\\ \mathbf{if}\;F \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 8.5:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{F}{\sin B \cdot \sqrt{t_0}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1 + -0.5 \cdot \frac{t_0}{{F}^{2}}}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (+ 2.0 (* x 2.0))))
   (if (<= F -6.4e+16)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 8.5)
       (+ (/ -1.0 (/ (tan B) x)) (/ F (* (sin B) (sqrt t_0))))
       (+
        (* x (/ -1.0 (tan B)))
        (/ (+ 1.0 (* -0.5 (/ t_0 (pow F 2.0)))) (sin B)))))))

C

double code(double F, double B, double x) {
	double t_0 = 2.0 + (x * 2.0);
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 8.5) {
		tmp = (-1.0 / (tan(B) / x)) + (F / (sin(B) * sqrt(t_0)));
	} else {
		tmp = (x * (-1.0 / tan(B))) + ((1.0 + (-0.5 * (t_0 / pow(F, 2.0)))) / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 + (x * 2.0d0)
    if (f <= (-6.4d+16)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 8.5d0) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (f / (sin(b) * sqrt(t_0)))
    else
        tmp = (x * ((-1.0d0) / tan(b))) + ((1.0d0 + ((-0.5d0) * (t_0 / (f ** 2.0d0)))) / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = 2.0 + (x * 2.0);
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 8.5) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (F / (Math.sin(B) * Math.sqrt(t_0)));
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + ((1.0 + (-0.5 * (t_0 / Math.pow(F, 2.0)))) / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 2.0 + (x * 2.0)
	tmp = 0
	if F <= -6.4e+16:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 8.5:
		tmp = (-1.0 / (math.tan(B) / x)) + (F / (math.sin(B) * math.sqrt(t_0)))
	else:
		tmp = (x * (-1.0 / math.tan(B))) + ((1.0 + (-0.5 * (t_0 / math.pow(F, 2.0)))) / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(2.0 + Float64(x * 2.0))
	tmp = 0.0
	if (F <= -6.4e+16)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 8.5)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(F / Float64(sin(B) * sqrt(t_0))));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(Float64(1.0 + Float64(-0.5 * Float64(t_0 / (F ^ 2.0)))) / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 2.0 + (x * 2.0);
	tmp = 0.0;
	if (F <= -6.4e+16)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 8.5)
		tmp = (-1.0 / (tan(B) / x)) + (F / (sin(B) * sqrt(t_0)));
	else
		tmp = (x * (-1.0 / tan(B))) + ((1.0 + (-0.5 * (t_0 / (F ^ 2.0)))) / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -6.4e+16], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.5], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 + N[(-0.5 * N[(t$95$0 / N[Power[F, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-1}{\tan B}\\ \mathbf{if}\;F \leq -1.5:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 1.4:\\ \;\;\;\;t_0 + \frac{F}{\sin B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ -1.0 (tan B)))))
   (if (<= F -1.5)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 1.4)
       (+ t_0 (* (/ F (sin B)) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))))
       (+ t_0 (/ 1.0 (sin B)))))))

C

double code(double F, double B, double x) {
	double t_0 = x * (-1.0 / tan(B));
	double tmp;
	if (F <= -1.5) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 1.4) {
		tmp = t_0 + ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0)))));
	} else {
		tmp = t_0 + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * ((-1.0d0) / tan(b))
    if (f <= (-1.5d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 1.4d0) then
        tmp = t_0 + ((f / sin(b)) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0)))))
    else
        tmp = t_0 + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = x * (-1.0 / Math.tan(B));
	double tmp;
	if (F <= -1.5) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 1.4) {
		tmp = t_0 + ((F / Math.sin(B)) * Math.sqrt((1.0 / (2.0 + (x * 2.0)))));
	} else {
		tmp = t_0 + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (-1.0 / math.tan(B))
	tmp = 0
	if F <= -1.5:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 1.4:
		tmp = t_0 + ((F / math.sin(B)) * math.sqrt((1.0 / (2.0 + (x * 2.0)))))
	else:
		tmp = t_0 + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(-1.0 / tan(B)))
	tmp = 0.0
	if (F <= -1.5)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 1.4)
		tmp = Float64(t_0 + Float64(Float64(F / sin(B)) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))));
	else
		tmp = Float64(t_0 + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (-1.0 / tan(B));
	tmp = 0.0;
	if (F <= -1.5)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 1.4)
		tmp = t_0 + ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0)))));
	else
		tmp = t_0 + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.5], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.4], N[(t$95$0 + N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 1.4:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{F}{\sin B \cdot \sqrt{2 + x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -6.4e+16)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F 1.4)
     (+ (/ -1.0 (/ (tan B) x)) (/ F (* (sin B) (sqrt (+ 2.0 (* x 2.0))))))
     (+ (* x (/ -1.0 (tan B))) (/ 1.0 (sin B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 1.4) {
		tmp = (-1.0 / (tan(B) / x)) + (F / (sin(B) * sqrt((2.0 + (x * 2.0)))));
	} else {
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-6.4d+16)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 1.4d0) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (f / (sin(b) * sqrt((2.0d0 + (x * 2.0d0)))))
    else
        tmp = (x * ((-1.0d0) / tan(b))) + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 1.4) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (F / (Math.sin(B) * Math.sqrt((2.0 + (x * 2.0)))));
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -6.4e+16:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 1.4:
		tmp = (-1.0 / (math.tan(B) / x)) + (F / (math.sin(B) * math.sqrt((2.0 + (x * 2.0)))))
	else:
		tmp = (x * (-1.0 / math.tan(B))) + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -6.4e+16)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 1.4)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(F / Float64(sin(B) * sqrt(Float64(2.0 + Float64(x * 2.0))))));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -6.4e+16)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 1.4)
		tmp = (-1.0 / (tan(B) / x)) + (F / (sin(B) * sqrt((2.0 + (x * 2.0)))));
	else
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -6.4e+16], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.4], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 92.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-1}{\tan B}\\ t_1 := {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5}\\ \mathbf{if}\;F \leq -3300000000000:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -7.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{F}{\sin B} \cdot t_1 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1200:\\ \;\;\;\;t_0 + t_1 \cdot \frac{F}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ -1.0 (tan B))))
        (t_1 (pow (+ (+ 2.0 (* F F)) (* x 2.0)) -0.5)))
   (if (<= F -3300000000000.0)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -7.5e-109)
       (- (* (/ F (sin B)) t_1) (/ x B))
       (if (<= F 1200.0) (+ t_0 (* t_1 (/ F B))) (+ t_0 (/ 1.0 (sin B))))))))

C

double code(double F, double B, double x) {
	double t_0 = x * (-1.0 / tan(B));
	double t_1 = pow(((2.0 + (F * F)) + (x * 2.0)), -0.5);
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -7.5e-109) {
		tmp = ((F / sin(B)) * t_1) - (x / B);
	} else if (F <= 1200.0) {
		tmp = t_0 + (t_1 * (F / B));
	} else {
		tmp = t_0 + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-1.0d0) / tan(b))
    t_1 = ((2.0d0 + (f * f)) + (x * 2.0d0)) ** (-0.5d0)
    if (f <= (-3300000000000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-7.5d-109)) then
        tmp = ((f / sin(b)) * t_1) - (x / b)
    else if (f <= 1200.0d0) then
        tmp = t_0 + (t_1 * (f / b))
    else
        tmp = t_0 + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = x * (-1.0 / Math.tan(B));
	double t_1 = Math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5);
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -7.5e-109) {
		tmp = ((F / Math.sin(B)) * t_1) - (x / B);
	} else if (F <= 1200.0) {
		tmp = t_0 + (t_1 * (F / B));
	} else {
		tmp = t_0 + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (-1.0 / math.tan(B))
	t_1 = math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)
	tmp = 0
	if F <= -3300000000000.0:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -7.5e-109:
		tmp = ((F / math.sin(B)) * t_1) - (x / B)
	elif F <= 1200.0:
		tmp = t_0 + (t_1 * (F / B))
	else:
		tmp = t_0 + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(-1.0 / tan(B)))
	t_1 = Float64(Float64(2.0 + Float64(F * F)) + Float64(x * 2.0)) ^ -0.5
	tmp = 0.0
	if (F <= -3300000000000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -7.5e-109)
		tmp = Float64(Float64(Float64(F / sin(B)) * t_1) - Float64(x / B));
	elseif (F <= 1200.0)
		tmp = Float64(t_0 + Float64(t_1 * Float64(F / B)));
	else
		tmp = Float64(t_0 + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (-1.0 / tan(B));
	t_1 = ((2.0 + (F * F)) + (x * 2.0)) ^ -0.5;
	tmp = 0.0;
	if (F <= -3300000000000.0)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -7.5e-109)
		tmp = ((F / sin(B)) * t_1) - (x / B);
	elseif (F <= 1200.0)
		tmp = t_0 + (t_1 * (F / B));
	else
		tmp = t_0 + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Power[N[(N[(2.0 + N[(F * F), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]}, If[LessEqual[F, -3300000000000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -7.5e-109], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1200.0], N[(t$95$0 + N[(t$95$1 * N[(F / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 7: 91.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5}\\ \mathbf{if}\;F \leq -3300000000000:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -3.7 \cdot 10^{-135}:\\ \;\;\;\;\frac{F}{\sin B} \cdot t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 32:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + t_0 \cdot \frac{F}{B}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (pow (+ (+ 2.0 (* F F)) (* x 2.0)) -0.5)))
   (if (<= F -3300000000000.0)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -3.7e-135)
       (- (* (/ F (sin B)) t_0) (/ x B))
       (if (<= F 32.0)
         (+ (/ -1.0 (/ (tan B) x)) (* t_0 (/ F B)))
         (+ (* x (/ -1.0 (tan B))) (/ 1.0 (sin B))))))))

C

double code(double F, double B, double x) {
	double t_0 = pow(((2.0 + (F * F)) + (x * 2.0)), -0.5);
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -3.7e-135) {
		tmp = ((F / sin(B)) * t_0) - (x / B);
	} else if (F <= 32.0) {
		tmp = (-1.0 / (tan(B) / x)) + (t_0 * (F / B));
	} else {
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((2.0d0 + (f * f)) + (x * 2.0d0)) ** (-0.5d0)
    if (f <= (-3300000000000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-3.7d-135)) then
        tmp = ((f / sin(b)) * t_0) - (x / b)
    else if (f <= 32.0d0) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (t_0 * (f / b))
    else
        tmp = (x * ((-1.0d0) / tan(b))) + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = Math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5);
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -3.7e-135) {
		tmp = ((F / Math.sin(B)) * t_0) - (x / B);
	} else if (F <= 32.0) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (t_0 * (F / B));
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)
	tmp = 0
	if F <= -3300000000000.0:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -3.7e-135:
		tmp = ((F / math.sin(B)) * t_0) - (x / B)
	elif F <= 32.0:
		tmp = (-1.0 / (math.tan(B) / x)) + (t_0 * (F / B))
	else:
		tmp = (x * (-1.0 / math.tan(B))) + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(2.0 + Float64(F * F)) + Float64(x * 2.0)) ^ -0.5
	tmp = 0.0
	if (F <= -3300000000000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -3.7e-135)
		tmp = Float64(Float64(Float64(F / sin(B)) * t_0) - Float64(x / B));
	elseif (F <= 32.0)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(t_0 * Float64(F / B)));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = ((2.0 + (F * F)) + (x * 2.0)) ^ -0.5;
	tmp = 0.0;
	if (F <= -3300000000000.0)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -3.7e-135)
		tmp = ((F / sin(B)) * t_0) - (x / B);
	elseif (F <= 32.0)
		tmp = (-1.0 / (tan(B) / x)) + (t_0 * (F / B));
	else
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[Power[N[(N[(2.0 + N[(F * F), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]}, If[LessEqual[F, -3300000000000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -3.7e-135], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 32.0], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(F / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 87.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -4 \cdot 10^{+14}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -4.4 \cdot 10^{-189}:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(2 + F \cdot F\right) + x \cdot 2\right)}^{-0.5} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 3.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -4e+14)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F -4.4e-189)
     (- (* (/ F (sin B)) (pow (+ (+ 2.0 (* F F)) (* x 2.0)) -0.5)) (/ x B))
     (if (<= F 3.2e-20)
       (/ (- x) (tan B))
       (+ (* x (/ -1.0 (tan B))) (/ 1.0 (sin B)))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -4e+14) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -4.4e-189) {
		tmp = ((F / sin(B)) * pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - (x / B);
	} else if (F <= 3.2e-20) {
		tmp = -x / tan(B);
	} else {
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-4d+14)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-4.4d-189)) then
        tmp = ((f / sin(b)) * (((2.0d0 + (f * f)) + (x * 2.0d0)) ** (-0.5d0))) - (x / b)
    else if (f <= 3.2d-20) then
        tmp = -x / tan(b)
    else
        tmp = (x * ((-1.0d0) / tan(b))) + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -4e+14) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -4.4e-189) {
		tmp = ((F / Math.sin(B)) * Math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - (x / B);
	} else if (F <= 3.2e-20) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -4e+14:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -4.4e-189:
		tmp = ((F / math.sin(B)) * math.pow(((2.0 + (F * F)) + (x * 2.0)), -0.5)) - (x / B)
	elif F <= 3.2e-20:
		tmp = -x / math.tan(B)
	else:
		tmp = (x * (-1.0 / math.tan(B))) + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -4e+14)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -4.4e-189)
		tmp = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(2.0 + Float64(F * F)) + Float64(x * 2.0)) ^ -0.5)) - Float64(x / B));
	elseif (F <= 3.2e-20)
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -4e+14)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -4.4e-189)
		tmp = ((F / sin(B)) * (((2.0 + (F * F)) + (x * 2.0)) ^ -0.5)) - (x / B);
	elseif (F <= 3.2e-20)
		tmp = -x / tan(B);
	else
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -4e+14], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -4.4e-189], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(2.0 + N[(F * F), $MachinePrecision]), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.2e-20], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 9: 86.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3300000000000:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -3.8 \cdot 10^{-189}:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8.5 \cdot 10^{-20}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3300000000000.0)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F -3.8e-189)
     (- (* (/ F (sin B)) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B))
     (if (<= F 8.5e-20)
       (/ (- x) (tan B))
       (+ (* x (/ -1.0 (tan B))) (/ 1.0 (sin B)))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -3.8e-189) {
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 8.5e-20) {
		tmp = -x / tan(B);
	} else {
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-3300000000000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-3.8d-189)) then
        tmp = ((f / sin(b)) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    else if (f <= 8.5d-20) then
        tmp = -x / tan(b)
    else
        tmp = (x * ((-1.0d0) / tan(b))) + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3300000000000.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -3.8e-189) {
		tmp = ((F / Math.sin(B)) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 8.5e-20) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3300000000000.0:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -3.8e-189:
		tmp = ((F / math.sin(B)) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	elif F <= 8.5e-20:
		tmp = -x / math.tan(B)
	else:
		tmp = (x * (-1.0 / math.tan(B))) + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3300000000000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -3.8e-189)
		tmp = Float64(Float64(Float64(F / sin(B)) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	elseif (F <= 8.5e-20)
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3300000000000.0)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -3.8e-189)
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	elseif (F <= 8.5e-20)
		tmp = -x / tan(B);
	else
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3300000000000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -3.8e-189], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.5e-20], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 10: 84.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 7.8 \cdot 10^{-20}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3.2e-70)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F 7.8e-20)
     (/ (- x) (tan B))
     (+ (* x (/ -1.0 (tan B))) (/ 1.0 (sin B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.2e-70) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 7.8e-20) {
		tmp = -x / tan(B);
	} else {
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-3.2d-70)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 7.8d-20) then
        tmp = -x / tan(b)
    else
        tmp = (x * ((-1.0d0) / tan(b))) + (1.0d0 / sin(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.2e-70) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 7.8e-20) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (x * (-1.0 / Math.tan(B))) + (1.0 / Math.sin(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3.2e-70:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 7.8e-20:
		tmp = -x / math.tan(B)
	else:
		tmp = (x * (-1.0 / math.tan(B))) + (1.0 / math.sin(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3.2e-70)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 7.8e-20)
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(1.0 / sin(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3.2e-70)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 7.8e-20)
		tmp = -x / tan(B);
	else
		tmp = (x * (-1.0 / tan(B))) + (1.0 / sin(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3.2e-70], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 7.8e-20], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 76.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -9 \cdot 10^{-70}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-19} \lor \neg \left(F \leq 6.8 \cdot 10^{+162}\right) \land F \leq 5.3 \cdot 10^{+219}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -9e-70)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (or (<= F 8.6e-19) (and (not (<= F 6.8e+162)) (<= F 5.3e+219)))
     (/ (- x) (tan B))
     (- (/ 1.0 (sin B)) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -9e-70) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if ((F <= 8.6e-19) || (!(F <= 6.8e+162) && (F <= 5.3e+219))) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-9d-70)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if ((f <= 8.6d-19) .or. (.not. (f <= 6.8d+162)) .and. (f <= 5.3d+219)) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -9e-70) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if ((F <= 8.6e-19) || (!(F <= 6.8e+162) && (F <= 5.3e+219))) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -9e-70:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif (F <= 8.6e-19) or (not (F <= 6.8e+162) and (F <= 5.3e+219)):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -9e-70)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif ((F <= 8.6e-19) || (!(F <= 6.8e+162) && (F <= 5.3e+219)))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -9e-70)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif ((F <= 8.6e-19) || (~((F <= 6.8e+162)) && (F <= 5.3e+219)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -9e-70], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 8.6e-19], And[N[Not[LessEqual[F, 6.8e+162]], $MachinePrecision], LessEqual[F, 5.3e+219]]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 12: 70.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-19} \lor \neg \left(F \leq 5.4 \cdot 10^{+162}\right) \land F \leq 8.2 \cdot 10^{+219}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -6.4e+16)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (or (<= F 8.6e-19) (and (not (<= F 5.4e+162)) (<= F 8.2e+219)))
     (/ (- x) (tan B))
     (- (/ 1.0 (sin B)) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if ((F <= 8.6e-19) || (!(F <= 5.4e+162) && (F <= 8.2e+219))) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-6.4d+16)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if ((f <= 8.6d-19) .or. (.not. (f <= 5.4d+162)) .and. (f <= 8.2d+219)) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if ((F <= 8.6e-19) || (!(F <= 5.4e+162) && (F <= 8.2e+219))) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -6.4e+16:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif (F <= 8.6e-19) or (not (F <= 5.4e+162) and (F <= 8.2e+219)):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -6.4e+16)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif ((F <= 8.6e-19) || (!(F <= 5.4e+162) && (F <= 8.2e+219)))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -6.4e+16)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif ((F <= 8.6e-19) || (~((F <= 5.4e+162)) && (F <= 8.2e+219)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -6.4e+16], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 8.6e-19], And[N[Not[LessEqual[F, 5.4e+162]], $MachinePrecision], LessEqual[F, 8.2e+219]]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 13: 63.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{-1}{B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 7.5 \cdot 10^{-19} \lor \neg \left(F \leq 3.2 \cdot 10^{+79}\right) \land F \leq 3.7 \cdot 10^{+220}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3.2e-70)
   (- (/ -1.0 B) (/ x (tan B)))
   (if (or (<= F 7.5e-19) (and (not (<= F 3.2e+79)) (<= F 3.7e+220)))
     (/ (- x) (tan B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.2e-70) {
		tmp = (-1.0 / B) - (x / tan(B));
	} else if ((F <= 7.5e-19) || (!(F <= 3.2e+79) && (F <= 3.7e+220))) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-3.2d-70)) then
        tmp = ((-1.0d0) / b) - (x / tan(b))
    else if ((f <= 7.5d-19) .or. (.not. (f <= 3.2d+79)) .and. (f <= 3.7d+220)) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.2e-70) {
		tmp = (-1.0 / B) - (x / Math.tan(B));
	} else if ((F <= 7.5e-19) || (!(F <= 3.2e+79) && (F <= 3.7e+220))) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3.2e-70:
		tmp = (-1.0 / B) - (x / math.tan(B))
	elif (F <= 7.5e-19) or (not (F <= 3.2e+79) and (F <= 3.7e+220)):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3.2e-70)
		tmp = Float64(Float64(-1.0 / B) - Float64(x / tan(B)));
	elseif ((F <= 7.5e-19) || (!(F <= 3.2e+79) && (F <= 3.7e+220)))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3.2e-70)
		tmp = (-1.0 / B) - (x / tan(B));
	elseif ((F <= 7.5e-19) || (~((F <= 3.2e+79)) && (F <= 3.7e+220)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3.2e-70], N[(N[(-1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 7.5e-19], And[N[Not[LessEqual[F, 3.2e+79]], $MachinePrecision], LessEqual[F, 3.7e+220]]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 14: 64.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -6.4 \cdot 10^{+16}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8.6 \cdot 10^{-19} \lor \neg \left(F \leq 1.3 \cdot 10^{+80}\right) \land F \leq 3 \cdot 10^{+220}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -6.4e+16)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (or (<= F 8.6e-19) (and (not (<= F 1.3e+80)) (<= F 3e+220)))
     (/ (- x) (tan B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if ((F <= 8.6e-19) || (!(F <= 1.3e+80) && (F <= 3e+220))) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-6.4d+16)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if ((f <= 8.6d-19) .or. (.not. (f <= 1.3d+80)) .and. (f <= 3d+220)) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e+16) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if ((F <= 8.6e-19) || (!(F <= 1.3e+80) && (F <= 3e+220))) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -6.4e+16:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif (F <= 8.6e-19) or (not (F <= 1.3e+80) and (F <= 3e+220)):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -6.4e+16)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif ((F <= 8.6e-19) || (!(F <= 1.3e+80) && (F <= 3e+220)))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -6.4e+16)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif ((F <= 8.6e-19) || (~((F <= 1.3e+80)) && (F <= 3e+220)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -6.4e+16], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 8.6e-19], And[N[Not[LessEqual[F, 1.3e+80]], $MachinePrecision], LessEqual[F, 3e+220]]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 15: 42.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 9 \cdot 10^{-200}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;B \leq 6.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{elif}\;B \leq 1.4 \cdot 10^{-26}:\\ \;\;\;\;\frac{1 - x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= B 9e-200)
   (/ (- -1.0 x) B)
   (if (<= B 6.2e-67)
     (/ (- x) B)
     (if (<= B 1.4e-26) (/ (- 1.0 x) B) (/ (- x) (tan B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (B <= 9e-200) {
		tmp = (-1.0 - x) / B;
	} else if (B <= 6.2e-67) {
		tmp = -x / B;
	} else if (B <= 1.4e-26) {
		tmp = (1.0 - x) / B;
	} else {
		tmp = -x / tan(B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (b <= 9d-200) then
        tmp = ((-1.0d0) - x) / b
    else if (b <= 6.2d-67) then
        tmp = -x / b
    else if (b <= 1.4d-26) then
        tmp = (1.0d0 - x) / b
    else
        tmp = -x / tan(b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (B <= 9e-200) {
		tmp = (-1.0 - x) / B;
	} else if (B <= 6.2e-67) {
		tmp = -x / B;
	} else if (B <= 1.4e-26) {
		tmp = (1.0 - x) / B;
	} else {
		tmp = -x / Math.tan(B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if B <= 9e-200:
		tmp = (-1.0 - x) / B
	elif B <= 6.2e-67:
		tmp = -x / B
	elif B <= 1.4e-26:
		tmp = (1.0 - x) / B
	else:
		tmp = -x / math.tan(B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (B <= 9e-200)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (B <= 6.2e-67)
		tmp = Float64(Float64(-x) / B);
	elseif (B <= 1.4e-26)
		tmp = Float64(Float64(1.0 - x) / B);
	else
		tmp = Float64(Float64(-x) / tan(B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (B <= 9e-200)
		tmp = (-1.0 - x) / B;
	elseif (B <= 6.2e-67)
		tmp = -x / B;
	elseif (B <= 1.4e-26)
		tmp = (1.0 - x) / B;
	else
		tmp = -x / tan(B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[B, 9e-200], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[B, 6.2e-67], N[((-x) / B), $MachinePrecision], If[LessEqual[B, 1.4e-26], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 16: 44.5% accurate, 18.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3.3 \cdot 10^{-72}:\\ \;\;\;\;\frac{-1 - x}{B} + B \cdot \left(x \cdot 0.3333333333333333 - 0.16666666666666666\right)\\ \mathbf{elif}\;F \leq 1.05 \cdot 10^{-20}:\\ \;\;\;\;B \cdot \left(x \cdot -0.16666666666666666 - x \cdot -0.5\right) - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3.3e-72)
   (+ (/ (- -1.0 x) B) (* B (- (* x 0.3333333333333333) 0.16666666666666666)))
   (if (<= F 1.05e-20)
     (- (* B (- (* x -0.16666666666666666) (* x -0.5))) (/ x B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.3e-72) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.05e-20) {
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-3.3d-72)) then
        tmp = (((-1.0d0) - x) / b) + (b * ((x * 0.3333333333333333d0) - 0.16666666666666666d0))
    else if (f <= 1.05d-20) then
        tmp = (b * ((x * (-0.16666666666666666d0)) - (x * (-0.5d0)))) - (x / b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.3e-72) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.05e-20) {
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3.3e-72:
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666))
	elif F <= 1.05e-20:
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3.3e-72)
		tmp = Float64(Float64(Float64(-1.0 - x) / B) + Float64(B * Float64(Float64(x * 0.3333333333333333) - 0.16666666666666666)));
	elseif (F <= 1.05e-20)
		tmp = Float64(Float64(B * Float64(Float64(x * -0.16666666666666666) - Float64(x * -0.5))) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3.3e-72)
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	elseif (F <= 1.05e-20)
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3.3e-72], N[(N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision] + N[(B * N[(N[(x * 0.3333333333333333), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.05e-20], N[(N[(B * N[(N[(x * -0.16666666666666666), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 17: 44.5% accurate, 21.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -6.4 \cdot 10^{-70}:\\ \;\;\;\;\frac{-1 - x}{B} + B \cdot \left(x \cdot 0.3333333333333333 - 0.16666666666666666\right)\\ \mathbf{elif}\;F \leq 3.1 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(B \cdot 0.3333333333333333 + \frac{-1}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -6.4e-70)
   (+ (/ (- -1.0 x) B) (* B (- (* x 0.3333333333333333) 0.16666666666666666)))
   (if (<= F 3.1e-21)
     (* x (+ (* B 0.3333333333333333) (/ -1.0 B)))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e-70) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 3.1e-21) {
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-6.4d-70)) then
        tmp = (((-1.0d0) - x) / b) + (b * ((x * 0.3333333333333333d0) - 0.16666666666666666d0))
    else if (f <= 3.1d-21) then
        tmp = x * ((b * 0.3333333333333333d0) + ((-1.0d0) / b))
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.4e-70) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 3.1e-21) {
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -6.4e-70:
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666))
	elif F <= 3.1e-21:
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B))
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -6.4e-70)
		tmp = Float64(Float64(Float64(-1.0 - x) / B) + Float64(B * Float64(Float64(x * 0.3333333333333333) - 0.16666666666666666)));
	elseif (F <= 3.1e-21)
		tmp = Float64(x * Float64(Float64(B * 0.3333333333333333) + Float64(-1.0 / B)));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -6.4e-70)
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	elseif (F <= 3.1e-21)
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -6.4e-70], N[(N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision] + N[(B * N[(N[(x * 0.3333333333333333), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.1e-21], N[(x * N[(N[(B * 0.3333333333333333), $MachinePrecision] + N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 18: 44.5% accurate, 24.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -7.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 6.1 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \left(B \cdot 0.3333333333333333 + \frac{-1}{B}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -7.3e-50)
   (/ (- -1.0 x) B)
   (if (<= F 6.1e-21)
     (* x (+ (* B 0.3333333333333333) (/ -1.0 B)))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.3e-50) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 6.1e-21) {
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-7.3d-50)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 6.1d-21) then
        tmp = x * ((b * 0.3333333333333333d0) + ((-1.0d0) / b))
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.3e-50) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 6.1e-21) {
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -7.3e-50:
		tmp = (-1.0 - x) / B
	elif F <= 6.1e-21:
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B))
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -7.3e-50)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 6.1e-21)
		tmp = Float64(x * Float64(Float64(B * 0.3333333333333333) + Float64(-1.0 / B)));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -7.3e-50)
		tmp = (-1.0 - x) / B;
	elseif (F <= 6.1e-21)
		tmp = x * ((B * 0.3333333333333333) + (-1.0 / B));
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -7.3e-50], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 6.1e-21], N[(x * N[(N[(B * 0.3333333333333333), $MachinePrecision] + N[(-1.0 / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 19: 44.5% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.1 \cdot 10^{-70}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 7.5 \cdot 10^{-19}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.1e-70)
   (/ (- -1.0 x) B)
   (if (<= F 7.5e-19) (/ (- x) B) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.1e-70) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 7.5e-19) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-1.1d-70)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 7.5d-19) then
        tmp = -x / b
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.1e-70) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 7.5e-19) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.1e-70:
		tmp = (-1.0 - x) / B
	elif F <= 7.5e-19:
		tmp = -x / B
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.1e-70)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 7.5e-19)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.1e-70)
		tmp = (-1.0 - x) / B;
	elseif (F <= 7.5e-19)
		tmp = -x / B;
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.1e-70], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 7.5e-19], N[((-x) / B), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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Alternative 20: 36.9% accurate, 45.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -2.6 \cdot 10^{-73}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -2.6e-73) (/ (- -1.0 x) B) (/ (- x) B)))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.6e-73) {
		tmp = (-1.0 - x) / B;
	} else {
		tmp = -x / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-2.6d-73)) then
        tmp = ((-1.0d0) - x) / b
    else
        tmp = -x / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.6e-73) {
		tmp = (-1.0 - x) / B;
	} else {
		tmp = -x / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -2.6e-73:
		tmp = (-1.0 - x) / B
	else:
		tmp = -x / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -2.6e-73)
		tmp = Float64(Float64(-1.0 - x) / B);
	else
		tmp = Float64(Float64(-x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -2.6e-73)
		tmp = (-1.0 - x) / B;
	else
		tmp = -x / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -2.6e-73], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], N[((-x) / B), $MachinePrecision]]

Derivation

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Alternative 21: 30.4% accurate, 53.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -4.2e+49) (/ -1.0 B) (/ (- x) B)))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -4.2e+49) {
		tmp = -1.0 / B;
	} else {
		tmp = -x / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-4.2d+49)) then
        tmp = (-1.0d0) / b
    else
        tmp = -x / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -4.2e+49) {
		tmp = -1.0 / B;
	} else {
		tmp = -x / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -4.2e+49:
		tmp = -1.0 / B
	else:
		tmp = -x / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -4.2e+49)
		tmp = Float64(-1.0 / B);
	else
		tmp = Float64(Float64(-x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -4.2e+49)
		tmp = -1.0 / B;
	else
		tmp = -x / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -4.2e+49], N[(-1.0 / B), $MachinePrecision], N[((-x) / B), $MachinePrecision]]

Derivation

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Alternative 22: 11.1% accurate, 108.0× speedup

Math

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

FPCore

(FPCore (F B x) :precision binary64 (/ -1.0 B))

C

double code(double F, double B, double x) {
	return -1.0 / B;
}

Fortran

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

Java

public static double code(double F, double B, double x) {
	return -1.0 / B;
}

Python

def code(F, B, x):
	return -1.0 / B

Julia

function code(F, B, x)
	return Float64(-1.0 / B)
end

MATLAB

function tmp = code(F, B, x)
	tmp = -1.0 / B;
end

Wolfram

code[F_, B_, x_] := N[(-1.0 / B), $MachinePrecision]

Derivation

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Reproduce

herbie shell --seed 2023348 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))))