VandenBroeck and Keller, Equation (23)

Percentage Accurate: 76.5% → 99.5%

Time: 21.1s

Alternatives: 30

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: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 2.35 \cdot 10^{+36}:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.5e+66)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 2.35e+36)
       (- (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5)) t_0)
       (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -1.5e+66) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 2.35e+36) {
		tmp = ((F / sin(B)) * pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - t_0;
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = x / tan(b)
    if (f <= (-1.5d+66)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 2.35d+36) then
        tmp = ((f / sin(b)) * ((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0))) - t_0
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(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 <= -1.5e+66) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 2.35e+36) {
		tmp = ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -1.5e+66:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 2.35e+36:
		tmp = ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1.5e+66)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 2.35e+36)
		tmp = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5)) - t_0);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x / tan(B);
	tmp = 0.0;
	if (F <= -1.5e+66)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 2.35e+36)
		tmp = ((F / sin(B)) * ((((F * F) + 2.0) + (x * 2.0)) ^ -0.5)) - t_0;
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(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, -1.5e+66], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 2.35e+36], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{1}{\tan B}\\ \mathbf{if}\;F \leq -1.75:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 1.42:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ 1.0 (tan B)))))
   (if (<= F -1.75)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 1.42)
       (- (* (/ F (sin B)) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) t_0)
       (- (/ 1.0 (sin B)) t_0)))))

C

double code(double F, double B, double x) {
	double t_0 = x * (1.0 / tan(B));
	double tmp;
	if (F <= -1.75) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 1.42) {
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - t_0;
	} else {
		tmp = (1.0 / sin(B)) - t_0;
	}
	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 <= (-1.75d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 1.42d0) then
        tmp = ((f / sin(b)) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - t_0
    else
        tmp = (1.0d0 / sin(b)) - t_0
    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 <= -1.75) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 1.42) {
		tmp = ((F / Math.sin(B)) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (1.0 / math.tan(B))
	tmp = 0
	if F <= -1.75:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 1.42:
		tmp = ((F / math.sin(B)) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(1.0 / tan(B)))
	tmp = 0.0
	if (F <= -1.75)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 1.42)
		tmp = Float64(Float64(Float64(F / sin(B)) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - t_0);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (1.0 / tan(B));
	tmp = 0.0;
	if (F <= -1.75)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 1.42)
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - t_0;
	else
		tmp = (1.0 / sin(B)) - t_0;
	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, -1.75], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.42], 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] - t$95$0), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 3: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{1}{\tan B}\\ \mathbf{if}\;F \leq -1.35:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 1.42:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5}}{\sin B} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ 1.0 (tan B)))))
   (if (<= F -1.35)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 1.42)
       (- (/ (* F (sqrt 0.5)) (sin B)) t_0)
       (- (/ 1.0 (sin B)) t_0)))))

C

double code(double F, double B, double x) {
	double t_0 = x * (1.0 / tan(B));
	double tmp;
	if (F <= -1.35) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 1.42) {
		tmp = ((F * sqrt(0.5)) / sin(B)) - t_0;
	} else {
		tmp = (1.0 / sin(B)) - t_0;
	}
	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 <= (-1.35d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 1.42d0) then
        tmp = ((f * sqrt(0.5d0)) / sin(b)) - t_0
    else
        tmp = (1.0d0 / sin(b)) - t_0
    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 <= -1.35) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 1.42) {
		tmp = ((F * Math.sqrt(0.5)) / Math.sin(B)) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (1.0 / math.tan(B))
	tmp = 0
	if F <= -1.35:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 1.42:
		tmp = ((F * math.sqrt(0.5)) / math.sin(B)) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(1.0 / tan(B)))
	tmp = 0.0
	if (F <= -1.35)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 1.42)
		tmp = Float64(Float64(Float64(F * sqrt(0.5)) / sin(B)) - t_0);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (1.0 / tan(B));
	tmp = 0.0;
	if (F <= -1.35)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 1.42)
		tmp = ((F * sqrt(0.5)) / sin(B)) - t_0;
	else
		tmp = (1.0 / sin(B)) - t_0;
	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, -1.35], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.42], N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 4: 91.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -8.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{F}{\sin B} \cdot t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 270000:\\ \;\;\;\;t_0 \cdot \frac{F}{B} - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5)) (t_1 (/ x (tan B))))
   (if (<= F -1.5e+66)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F -8.5e-86)
       (- (* (/ F (sin B)) t_0) (/ x B))
       (if (<= F 270000.0)
         (- (* t_0 (/ F B)) t_1)
         (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))))))

C

double code(double F, double B, double x) {
	double t_0 = pow((((F * F) + 2.0) + (x * 2.0)), -0.5);
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -1.5e+66) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= -8.5e-86) {
		tmp = ((F / sin(B)) * t_0) - (x / B);
	} else if (F <= 270000.0) {
		tmp = (t_0 * (F / B)) - t_1;
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)
    t_1 = x / tan(b)
    if (f <= (-1.5d+66)) then
        tmp = ((-1.0d0) / sin(b)) - t_1
    else if (f <= (-8.5d-86)) then
        tmp = ((f / sin(b)) * t_0) - (x / b)
    else if (f <= 270000.0d0) then
        tmp = (t_0 * (f / b)) - t_1
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(b)))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5);
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -1.5e+66) {
		tmp = (-1.0 / Math.sin(B)) - t_1;
	} else if (F <= -8.5e-86) {
		tmp = ((F / Math.sin(B)) * t_0) - (x / B);
	} else if (F <= 270000.0) {
		tmp = (t_0 * (F / B)) - t_1;
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -1.5e+66:
		tmp = (-1.0 / math.sin(B)) - t_1
	elif F <= -8.5e-86:
		tmp = ((F / math.sin(B)) * t_0) - (x / B)
	elif F <= 270000.0:
		tmp = (t_0 * (F / B)) - t_1
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1.5e+66)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= -8.5e-86)
		tmp = Float64(Float64(Float64(F / sin(B)) * t_0) - Float64(x / B));
	elseif (F <= 270000.0)
		tmp = Float64(Float64(t_0 * Float64(F / B)) - t_1);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (((F * F) + 2.0) + (x * 2.0)) ^ -0.5;
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -1.5e+66)
		tmp = (-1.0 / sin(B)) - t_1;
	elseif (F <= -8.5e-86)
		tmp = ((F / sin(B)) * t_0) - (x / B);
	elseif (F <= 270000.0)
		tmp = (t_0 * (F / B)) - t_1;
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.5e+66], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -8.5e-86], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 270000.0], N[(N[(t$95$0 * N[(F / B), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 5: 92.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 + x \cdot 2\\ \mathbf{if}\;F \leq -0.07:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -5.6 \cdot 10^{-85}:\\ \;\;\;\;\frac{F}{\sin B \cdot \sqrt{t_0}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 0.83:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \sqrt{\frac{1}{t_0}} \cdot \frac{F}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (+ 2.0 (* x 2.0))))
   (if (<= F -0.07)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -5.6e-85)
       (- (/ F (* (sin B) (sqrt t_0))) (/ x B))
       (if (<= F 0.83)
         (+ (* x (/ -1.0 (tan B))) (* (sqrt (/ 1.0 t_0)) (/ F B)))
         (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))))))

C

double code(double F, double B, double x) {
	double t_0 = 2.0 + (x * 2.0);
	double tmp;
	if (F <= -0.07) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -5.6e-85) {
		tmp = (F / (sin(B) * sqrt(t_0))) - (x / B);
	} else if (F <= 0.83) {
		tmp = (x * (-1.0 / tan(B))) + (sqrt((1.0 / t_0)) * (F / B));
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 + (x * 2.0d0)
    if (f <= (-0.07d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-5.6d-85)) then
        tmp = (f / (sin(b) * sqrt(t_0))) - (x / b)
    else if (f <= 0.83d0) then
        tmp = (x * ((-1.0d0) / tan(b))) + (sqrt((1.0d0 / t_0)) * (f / b))
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(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 <= -0.07) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -5.6e-85) {
		tmp = (F / (Math.sin(B) * Math.sqrt(t_0))) - (x / B);
	} else if (F <= 0.83) {
		tmp = (x * (-1.0 / Math.tan(B))) + (Math.sqrt((1.0 / t_0)) * (F / B));
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 2.0 + (x * 2.0)
	tmp = 0
	if F <= -0.07:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -5.6e-85:
		tmp = (F / (math.sin(B) * math.sqrt(t_0))) - (x / B)
	elif F <= 0.83:
		tmp = (x * (-1.0 / math.tan(B))) + (math.sqrt((1.0 / t_0)) * (F / B))
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(2.0 + Float64(x * 2.0))
	tmp = 0.0
	if (F <= -0.07)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -5.6e-85)
		tmp = Float64(Float64(F / Float64(sin(B) * sqrt(t_0))) - Float64(x / B));
	elseif (F <= 0.83)
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(sqrt(Float64(1.0 / t_0)) * Float64(F / B)));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(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 <= -0.07)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -5.6e-85)
		tmp = (F / (sin(B) * sqrt(t_0))) - (x / B);
	elseif (F <= 0.83)
		tmp = (x * (-1.0 / tan(B))) + (sqrt((1.0 / t_0)) * (F / B));
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(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, -0.07], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -5.6e-85], N[(N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.83], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 / t$95$0), $MachinePrecision]], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 6: 91.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -3.85 \cdot 10^{-87}:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 0.455:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \sqrt{\frac{1}{2 + x \cdot 2}} \cdot \frac{F}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.5e+66)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F -3.85e-87)
     (- (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5)) (/ x B))
     (if (<= F 0.455)
       (+ (* x (/ -1.0 (tan B))) (* (sqrt (/ 1.0 (+ 2.0 (* x 2.0)))) (/ F B)))
       (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.5e+66) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -3.85e-87) {
		tmp = ((F / sin(B)) * pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	} else if (F <= 0.455) {
		tmp = (x * (-1.0 / tan(B))) + (sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B));
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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 (f <= (-1.5d+66)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-3.85d-87)) then
        tmp = ((f / sin(b)) * ((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0))) - (x / b)
    else if (f <= 0.455d0) then
        tmp = (x * ((-1.0d0) / tan(b))) + (sqrt((1.0d0 / (2.0d0 + (x * 2.0d0)))) * (f / b))
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(b)))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.5e+66) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -3.85e-87) {
		tmp = ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	} else if (F <= 0.455) {
		tmp = (x * (-1.0 / Math.tan(B))) + (Math.sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B));
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.5e+66:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -3.85e-87:
		tmp = ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B)
	elif F <= 0.455:
		tmp = (x * (-1.0 / math.tan(B))) + (math.sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B))
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.5e+66)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -3.85e-87)
		tmp = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5)) - Float64(x / B));
	elseif (F <= 0.455)
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0)))) * Float64(F / B)));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.5e+66)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -3.85e-87)
		tmp = ((F / sin(B)) * ((((F * F) + 2.0) + (x * 2.0)) ^ -0.5)) - (x / B);
	elseif (F <= 0.455)
		tmp = (x * (-1.0 / tan(B))) + (sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B));
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.5e+66], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -3.85e-87], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.455], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 92.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{2 + x \cdot 2}\\ \mathbf{if}\;F \leq -0.0054:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -2 \cdot 10^{-85}:\\ \;\;\;\;\frac{F}{\sin B \cdot t_0} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 0.47:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{F}{B \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (sqrt (+ 2.0 (* x 2.0)))))
   (if (<= F -0.0054)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -2e-85)
       (- (/ F (* (sin B) t_0)) (/ x B))
       (if (<= F 0.47)
         (+ (* x (/ -1.0 (tan B))) (/ F (* B t_0)))
         (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B)))))))))

C

double code(double F, double B, double x) {
	double t_0 = sqrt((2.0 + (x * 2.0)));
	double tmp;
	if (F <= -0.0054) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -2e-85) {
		tmp = (F / (sin(B) * t_0)) - (x / B);
	} else if (F <= 0.47) {
		tmp = (x * (-1.0 / tan(B))) + (F / (B * t_0));
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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) :: t_0
    real(8) :: tmp
    t_0 = sqrt((2.0d0 + (x * 2.0d0)))
    if (f <= (-0.0054d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-2d-85)) then
        tmp = (f / (sin(b) * t_0)) - (x / b)
    else if (f <= 0.47d0) then
        tmp = (x * ((-1.0d0) / tan(b))) + (f / (b * t_0))
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(b)))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = Math.sqrt((2.0 + (x * 2.0)));
	double tmp;
	if (F <= -0.0054) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -2e-85) {
		tmp = (F / (Math.sin(B) * t_0)) - (x / B);
	} else if (F <= 0.47) {
		tmp = (x * (-1.0 / Math.tan(B))) + (F / (B * t_0));
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = math.sqrt((2.0 + (x * 2.0)))
	tmp = 0
	if F <= -0.0054:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -2e-85:
		tmp = (F / (math.sin(B) * t_0)) - (x / B)
	elif F <= 0.47:
		tmp = (x * (-1.0 / math.tan(B))) + (F / (B * t_0))
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	t_0 = sqrt(Float64(2.0 + Float64(x * 2.0)))
	tmp = 0.0
	if (F <= -0.0054)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -2e-85)
		tmp = Float64(Float64(F / Float64(sin(B) * t_0)) - Float64(x / B));
	elseif (F <= 0.47)
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(F / Float64(B * t_0)));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = sqrt((2.0 + (x * 2.0)));
	tmp = 0.0;
	if (F <= -0.0054)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -2e-85)
		tmp = (F / (sin(B) * t_0)) - (x / B);
	elseif (F <= 0.47)
		tmp = (x * (-1.0 / tan(B))) + (F / (B * t_0));
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[F, -0.0054], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -2e-85], N[(N[(F / N[(N[Sin[B], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.47], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(F / N[(B * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

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

Alternative 8: 92.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{1}{\tan B}\\ \mathbf{if}\;F \leq -0.23:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -5.8 \cdot 10^{-87}:\\ \;\;\;\;\frac{F}{\sin B \cdot \sqrt{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 0.45:\\ \;\;\;\;\frac{F}{\frac{B}{\sqrt{0.5}}} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ 1.0 (tan B)))))
   (if (<= F -0.23)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -5.8e-87)
       (- (/ F (* (sin B) (sqrt (+ 2.0 (* x 2.0))))) (/ x B))
       (if (<= F 0.45)
         (- (/ F (/ B (sqrt 0.5))) t_0)
         (- (/ 1.0 (sin B)) t_0))))))

C

double code(double F, double B, double x) {
	double t_0 = x * (1.0 / tan(B));
	double tmp;
	if (F <= -0.23) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -5.8e-87) {
		tmp = (F / (sin(B) * sqrt((2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 0.45) {
		tmp = (F / (B / sqrt(0.5))) - t_0;
	} else {
		tmp = (1.0 / sin(B)) - t_0;
	}
	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 <= (-0.23d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-5.8d-87)) then
        tmp = (f / (sin(b) * sqrt((2.0d0 + (x * 2.0d0))))) - (x / b)
    else if (f <= 0.45d0) then
        tmp = (f / (b / sqrt(0.5d0))) - t_0
    else
        tmp = (1.0d0 / sin(b)) - t_0
    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 <= -0.23) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -5.8e-87) {
		tmp = (F / (Math.sin(B) * Math.sqrt((2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 0.45) {
		tmp = (F / (B / Math.sqrt(0.5))) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (1.0 / math.tan(B))
	tmp = 0
	if F <= -0.23:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -5.8e-87:
		tmp = (F / (math.sin(B) * math.sqrt((2.0 + (x * 2.0))))) - (x / B)
	elif F <= 0.45:
		tmp = (F / (B / math.sqrt(0.5))) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(1.0 / tan(B)))
	tmp = 0.0
	if (F <= -0.23)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -5.8e-87)
		tmp = Float64(Float64(F / Float64(sin(B) * sqrt(Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	elseif (F <= 0.45)
		tmp = Float64(Float64(F / Float64(B / sqrt(0.5))) - t_0);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (1.0 / tan(B));
	tmp = 0.0;
	if (F <= -0.23)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -5.8e-87)
		tmp = (F / (sin(B) * sqrt((2.0 + (x * 2.0))))) - (x / B);
	elseif (F <= 0.45)
		tmp = (F / (B / sqrt(0.5))) - t_0;
	else
		tmp = (1.0 / sin(B)) - t_0;
	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, -0.23], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -5.8e-87], N[(N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.45], N[(N[(F / N[(B / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]

Derivation

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

Alternative 9: 85.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -2.65 \cdot 10^{-24}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 2.4 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{\sin B} \cdot \left(-\cos B\right)\\ \mathbf{elif}\;F \leq 270000:\\ \;\;\;\;{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - x \cdot \frac{1}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -2.65e-24)
   (- (/ -1.0 (sin B)) (/ x (tan B)))
   (if (<= F 2.4e-125)
     (* (/ x (sin B)) (- (cos B)))
     (if (<= F 270000.0)
       (- (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B)) (/ x B))
       (- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.65e-24) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 2.4e-125) {
		tmp = (x / sin(B)) * -cos(B);
	} else if (F <= 270000.0) {
		tmp = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	} else {
		tmp = (1.0 / sin(B)) - (x * (1.0 / 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 (f <= (-2.65d-24)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 2.4d-125) then
        tmp = (x / sin(b)) * -cos(b)
    else if (f <= 270000.0d0) then
        tmp = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) - (x / b)
    else
        tmp = (1.0d0 / sin(b)) - (x * (1.0d0 / tan(b)))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.65e-24) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 2.4e-125) {
		tmp = (x / Math.sin(B)) * -Math.cos(B);
	} else if (F <= 270000.0) {
		tmp = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	} else {
		tmp = (1.0 / Math.sin(B)) - (x * (1.0 / Math.tan(B)));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -2.65e-24:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 2.4e-125:
		tmp = (x / math.sin(B)) * -math.cos(B)
	elif F <= 270000.0:
		tmp = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B)
	else:
		tmp = (1.0 / math.sin(B)) - (x * (1.0 / math.tan(B)))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -2.65e-24)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 2.4e-125)
		tmp = Float64(Float64(x / sin(B)) * Float64(-cos(B)));
	elseif (F <= 270000.0)
		tmp = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x * Float64(1.0 / tan(B))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -2.65e-24)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 2.4e-125)
		tmp = (x / sin(B)) * -cos(B);
	elseif (F <= 270000.0)
		tmp = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) - (x / B);
	else
		tmp = (1.0 / sin(B)) - (x * (1.0 / tan(B)));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -2.65e-24], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2.4e-125], N[(N[(x / N[Sin[B], $MachinePrecision]), $MachinePrecision] * (-N[Cos[B], $MachinePrecision])), $MachinePrecision], If[LessEqual[F, 270000.0], N[(N[(N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 10: 92.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{1}{\tan B}\\ \mathbf{if}\;F \leq -0.00029:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 0.125:\\ \;\;\;\;\frac{F}{\frac{B}{\sqrt{0.5}}} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* x (/ 1.0 (tan B)))))
   (if (<= F -0.00029)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 0.125)
       (- (/ F (/ B (sqrt 0.5))) t_0)
       (- (/ 1.0 (sin B)) t_0)))))

C

double code(double F, double B, double x) {
	double t_0 = x * (1.0 / tan(B));
	double tmp;
	if (F <= -0.00029) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 0.125) {
		tmp = (F / (B / sqrt(0.5))) - t_0;
	} else {
		tmp = (1.0 / sin(B)) - t_0;
	}
	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 <= (-0.00029d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 0.125d0) then
        tmp = (f / (b / sqrt(0.5d0))) - t_0
    else
        tmp = (1.0d0 / sin(b)) - t_0
    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 <= -0.00029) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 0.125) {
		tmp = (F / (B / Math.sqrt(0.5))) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x * (1.0 / math.tan(B))
	tmp = 0
	if F <= -0.00029:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 0.125:
		tmp = (F / (B / math.sqrt(0.5))) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x * Float64(1.0 / tan(B)))
	tmp = 0.0
	if (F <= -0.00029)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 0.125)
		tmp = Float64(Float64(F / Float64(B / sqrt(0.5))) - t_0);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x * (1.0 / tan(B));
	tmp = 0.0;
	if (F <= -0.00029)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 0.125)
		tmp = (F / (B / sqrt(0.5))) - t_0;
	else
		tmp = (1.0 / sin(B)) - t_0;
	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, -0.00029], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.125], N[(N[(F / N[(B / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 11: 72.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.55 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 9.5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{\sin B} \cdot \left(-\cos B\right)\\ \mathbf{elif}\;F \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} + x \cdot \left(\frac{-1}{B} - B \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.55e-23)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 9.5e-126)
     (* (/ x (sin B)) (- (cos B)))
     (if (<= F 2.3e+21)
       (+
        (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B))
        (* x (- (/ -1.0 B) (* B -0.3333333333333333))))
       (- (/ 1.0 B) (/ x (tan B)))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 9.5e-126) {
		tmp = (x / sin(B)) * -cos(B);
	} else if (F <= 2.3e+21) {
		tmp = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	} else {
		tmp = (1.0 / B) - (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 (f <= (-1.55d-23)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 9.5d-126) then
        tmp = (x / sin(b)) * -cos(b)
    else if (f <= 2.3d+21) then
        tmp = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) + (x * (((-1.0d0) / b) - (b * (-0.3333333333333333d0))))
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 9.5e-126) {
		tmp = (x / Math.sin(B)) * -Math.cos(B);
	} else if (F <= 2.3e+21) {
		tmp = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.55e-23:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 9.5e-126:
		tmp = (x / math.sin(B)) * -math.cos(B)
	elif F <= 2.3e+21:
		tmp = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)))
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.55e-23)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 9.5e-126)
		tmp = Float64(Float64(x / sin(B)) * Float64(-cos(B)));
	elseif (F <= 2.3e+21)
		tmp = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) + Float64(x * Float64(Float64(-1.0 / B) - Float64(B * -0.3333333333333333))));
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.55e-23)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 9.5e-126)
		tmp = (x / sin(B)) * -cos(B);
	elseif (F <= 2.3e+21)
		tmp = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.55e-23], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 9.5e-126], N[(N[(x / N[Sin[B], $MachinePrecision]), $MachinePrecision] * (-N[Cos[B], $MachinePrecision])), $MachinePrecision], If[LessEqual[F, 2.3e+21], N[(N[(N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-1.0 / B), $MachinePrecision] - N[(B * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 12: 78.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 2.1 \cdot 10^{-125}:\\ \;\;\;\;\frac{x}{\sin B} \cdot \left(-\cos B\right)\\ \mathbf{elif}\;F \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} + x \cdot \left(\frac{-1}{B} - B \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.2e-26)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 2.1e-125)
       (* (/ x (sin B)) (- (cos B)))
       (if (<= F 2.3e+21)
         (+
          (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B))
          (* x (- (/ -1.0 B) (* B -0.3333333333333333))))
         (- (/ 1.0 B) t_0))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -1.2e-26) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 2.1e-125) {
		tmp = (x / sin(B)) * -cos(B);
	} else if (F <= 2.3e+21) {
		tmp = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	} else {
		tmp = (1.0 / B) - t_0;
	}
	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 <= (-1.2d-26)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 2.1d-125) then
        tmp = (x / sin(b)) * -cos(b)
    else if (f <= 2.3d+21) then
        tmp = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) + (x * (((-1.0d0) / b) - (b * (-0.3333333333333333d0))))
    else
        tmp = (1.0d0 / b) - t_0
    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 <= -1.2e-26) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 2.1e-125) {
		tmp = (x / Math.sin(B)) * -Math.cos(B);
	} else if (F <= 2.3e+21) {
		tmp = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	} else {
		tmp = (1.0 / B) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -1.2e-26:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 2.1e-125:
		tmp = (x / math.sin(B)) * -math.cos(B)
	elif F <= 2.3e+21:
		tmp = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)))
	else:
		tmp = (1.0 / B) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1.2e-26)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 2.1e-125)
		tmp = Float64(Float64(x / sin(B)) * Float64(-cos(B)));
	elseif (F <= 2.3e+21)
		tmp = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) + Float64(x * Float64(Float64(-1.0 / B) - Float64(B * -0.3333333333333333))));
	else
		tmp = Float64(Float64(1.0 / B) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x / tan(B);
	tmp = 0.0;
	if (F <= -1.2e-26)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 2.1e-125)
		tmp = (x / sin(B)) * -cos(B);
	elseif (F <= 2.3e+21)
		tmp = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	else
		tmp = (1.0 / B) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.2e-26], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 2.1e-125], N[(N[(x / N[Sin[B], $MachinePrecision]), $MachinePrecision] * (-N[Cos[B], $MachinePrecision])), $MachinePrecision], If[LessEqual[F, 2.3e+21], N[(N[(N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-1.0 / B), $MachinePrecision] - N[(B * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]

Derivation

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

Alternative 13: 64.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} + x \cdot \left(\frac{-1}{B} - B \cdot -0.3333333333333333\right)\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -420000000000:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -1.25 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-285}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_1\\ \mathbf{elif}\;F \leq 2.3 \cdot 10^{+21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0
         (+
          (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B))
          (* x (- (/ -1.0 B) (* B -0.3333333333333333)))))
        (t_1 (/ x (tan B))))
   (if (<= F -420000000000.0)
     (- (/ -1.0 (sin B)) (/ x B))
     (if (<= F -1.25e-165)
       t_0
       (if (<= F 6.6e-285)
         (- (* (/ F B) (/ 1.0 F)) t_1)
         (if (<= F 2.3e+21) t_0 (- (/ 1.0 B) t_1)))))))

C

double code(double F, double B, double x) {
	double t_0 = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -420000000000.0) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -1.25e-165) {
		tmp = t_0;
	} else if (F <= 6.6e-285) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 2.3e+21) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - t_1;
	}
	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 = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) + (x * (((-1.0d0) / b) - (b * (-0.3333333333333333d0))))
    t_1 = x / tan(b)
    if (f <= (-420000000000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-1.25d-165)) then
        tmp = t_0
    else if (f <= 6.6d-285) then
        tmp = ((f / b) * (1.0d0 / f)) - t_1
    else if (f <= 2.3d+21) then
        tmp = t_0
    else
        tmp = (1.0d0 / b) - t_1
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -420000000000.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -1.25e-165) {
		tmp = t_0;
	} else if (F <= 6.6e-285) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 2.3e+21) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - t_1;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)))
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -420000000000.0:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -1.25e-165:
		tmp = t_0
	elif F <= 6.6e-285:
		tmp = ((F / B) * (1.0 / F)) - t_1
	elif F <= 2.3e+21:
		tmp = t_0
	else:
		tmp = (1.0 / B) - t_1
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) + Float64(x * Float64(Float64(-1.0 / B) - Float64(B * -0.3333333333333333))))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -420000000000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -1.25e-165)
		tmp = t_0;
	elseif (F <= 6.6e-285)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_1);
	elseif (F <= 2.3e+21)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / B) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -420000000000.0)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -1.25e-165)
		tmp = t_0;
	elseif (F <= 6.6e-285)
		tmp = ((F / B) * (1.0 / F)) - t_1;
	elseif (F <= 2.3e+21)
		tmp = t_0;
	else
		tmp = (1.0 / B) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-1.0 / B), $MachinePrecision] - N[(B * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -420000000000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -1.25e-165], t$95$0, If[LessEqual[F, 6.6e-285], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, 2.3e+21], t$95$0, N[(N[(1.0 / B), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 14: 64.1% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{F}{B \cdot \sqrt{2 + x \cdot 2}} + x \cdot \left(\frac{-1}{B} - B \cdot -0.3333333333333333\right)\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.00024:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -2.7 \cdot 10^{-165}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 2.1 \cdot 10^{-287}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_1\\ \mathbf{elif}\;F \leq 8 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0
         (+
          (/ F (* B (sqrt (+ 2.0 (* x 2.0)))))
          (* x (- (/ -1.0 B) (* B -0.3333333333333333)))))
        (t_1 (/ x (tan B))))
   (if (<= F -0.00024)
     (- (/ -1.0 (sin B)) (/ x B))
     (if (<= F -2.7e-165)
       t_0
       (if (<= F 2.1e-287)
         (- (* (/ F B) (/ 1.0 F)) t_1)
         (if (<= F 8e-21) t_0 (- (/ 1.0 B) t_1)))))))

C

double code(double F, double B, double x) {
	double t_0 = (F / (B * sqrt((2.0 + (x * 2.0))))) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -0.00024) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -2.7e-165) {
		tmp = t_0;
	} else if (F <= 2.1e-287) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 8e-21) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - t_1;
	}
	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 = (f / (b * sqrt((2.0d0 + (x * 2.0d0))))) + (x * (((-1.0d0) / b) - (b * (-0.3333333333333333d0))))
    t_1 = x / tan(b)
    if (f <= (-0.00024d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-2.7d-165)) then
        tmp = t_0
    else if (f <= 2.1d-287) then
        tmp = ((f / b) * (1.0d0 / f)) - t_1
    else if (f <= 8d-21) then
        tmp = t_0
    else
        tmp = (1.0d0 / b) - t_1
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (F / (B * Math.sqrt((2.0 + (x * 2.0))))) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -0.00024) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -2.7e-165) {
		tmp = t_0;
	} else if (F <= 2.1e-287) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 8e-21) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - t_1;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (F / (B * math.sqrt((2.0 + (x * 2.0))))) + (x * ((-1.0 / B) - (B * -0.3333333333333333)))
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -0.00024:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -2.7e-165:
		tmp = t_0
	elif F <= 2.1e-287:
		tmp = ((F / B) * (1.0 / F)) - t_1
	elif F <= 8e-21:
		tmp = t_0
	else:
		tmp = (1.0 / B) - t_1
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(F / Float64(B * sqrt(Float64(2.0 + Float64(x * 2.0))))) + Float64(x * Float64(Float64(-1.0 / B) - Float64(B * -0.3333333333333333))))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -0.00024)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -2.7e-165)
		tmp = t_0;
	elseif (F <= 2.1e-287)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_1);
	elseif (F <= 8e-21)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / B) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (F / (B * sqrt((2.0 + (x * 2.0))))) + (x * ((-1.0 / B) - (B * -0.3333333333333333)));
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -0.00024)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -2.7e-165)
		tmp = t_0;
	elseif (F <= 2.1e-287)
		tmp = ((F / B) * (1.0 / F)) - t_1;
	elseif (F <= 8e-21)
		tmp = t_0;
	else
		tmp = (1.0 / B) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(F / N[(B * N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(-1.0 / B), $MachinePrecision] - N[(B * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -0.00024], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -2.7e-165], t$95$0, If[LessEqual[F, 2.1e-287], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, 8e-21], t$95$0, N[(N[(1.0 / B), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 15: 64.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - \frac{x}{B}\\ \mathbf{if}\;F \leq -420000000000:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -1.02 \cdot 10^{-213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 2.1 \cdot 10^{-278}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{-1}{F} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 1500000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (- (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B)) (/ x B))))
   (if (<= F -420000000000.0)
     (- (/ -1.0 (sin B)) (/ x B))
     (if (<= F -1.02e-213)
       t_0
       (if (<= F 2.1e-278)
         (- (* (/ F B) (/ -1.0 F)) (* x (/ 1.0 (tan B))))
         (if (<= F 1500000.0) t_0 (- (/ 1.0 B) (/ x (tan B)))))))))

C

double code(double F, double B, double x) {
	double t_0 = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	double tmp;
	if (F <= -420000000000.0) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -1.02e-213) {
		tmp = t_0;
	} else if (F <= 2.1e-278) {
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / tan(B)));
	} else if (F <= 1500000.0) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - (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) :: t_0
    real(8) :: tmp
    t_0 = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) - (x / b)
    if (f <= (-420000000000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-1.02d-213)) then
        tmp = t_0
    else if (f <= 2.1d-278) then
        tmp = ((f / b) * ((-1.0d0) / f)) - (x * (1.0d0 / tan(b)))
    else if (f <= 1500000.0d0) then
        tmp = t_0
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	double tmp;
	if (F <= -420000000000.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -1.02e-213) {
		tmp = t_0;
	} else if (F <= 2.1e-278) {
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / Math.tan(B)));
	} else if (F <= 1500000.0) {
		tmp = t_0;
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B)
	tmp = 0
	if F <= -420000000000.0:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -1.02e-213:
		tmp = t_0
	elif F <= 2.1e-278:
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / math.tan(B)))
	elif F <= 1500000.0:
		tmp = t_0
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) - Float64(x / B))
	tmp = 0.0
	if (F <= -420000000000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -1.02e-213)
		tmp = t_0;
	elseif (F <= 2.1e-278)
		tmp = Float64(Float64(Float64(F / B) * Float64(-1.0 / F)) - Float64(x * Float64(1.0 / tan(B))));
	elseif (F <= 1500000.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) - (x / B);
	tmp = 0.0;
	if (F <= -420000000000.0)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -1.02e-213)
		tmp = t_0;
	elseif (F <= 2.1e-278)
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / tan(B)));
	elseif (F <= 1500000.0)
		tmp = t_0;
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(N[Power[N[(N[(N[(F * F), $MachinePrecision] + 2.0), $MachinePrecision] + N[(x * 2.0), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -420000000000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -1.02e-213], t$95$0, If[LessEqual[F, 2.1e-278], N[(N[(N[(F / B), $MachinePrecision] * N[(-1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1500000.0], t$95$0, N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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1. Add Preprocessing

Alternative 16: 64.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -0.00029:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 10^{-9}:\\ \;\;\;\;\sqrt{\frac{1}{2 + x \cdot 2}} \cdot \frac{F}{B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -0.00029)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 1e-9)
     (- (* (sqrt (/ 1.0 (+ 2.0 (* x 2.0)))) (/ F B)) (/ x B))
     (- (/ 1.0 B) (/ x (tan B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.00029) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 1e-9) {
		tmp = (sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B)) - (x / B);
	} else {
		tmp = (1.0 / B) - (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 (f <= (-0.00029d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 1d-9) then
        tmp = (sqrt((1.0d0 / (2.0d0 + (x * 2.0d0)))) * (f / b)) - (x / b)
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.00029) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 1e-9) {
		tmp = (Math.sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B)) - (x / B);
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -0.00029:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 1e-9:
		tmp = (math.sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B)) - (x / B)
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -0.00029)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 1e-9)
		tmp = Float64(Float64(sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0)))) * Float64(F / B)) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -0.00029)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 1e-9)
		tmp = (sqrt((1.0 / (2.0 + (x * 2.0)))) * (F / B)) - (x / B);
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -0.00029], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1e-9], N[(N[(N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(F / B), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 17: 62.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.55 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8.8 \cdot 10^{-280}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{-1}{F} - x \cdot \frac{1}{\tan B}\\ \mathbf{elif}\;F \leq 5.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.55e-23)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 8.8e-280)
     (- (* (/ F B) (/ -1.0 F)) (* x (/ 1.0 (tan B))))
     (if (<= F 5.5e-223) (/ (- x) B) (- (/ 1.0 B) (/ x (tan B)))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 8.8e-280) {
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / tan(B)));
	} else if (F <= 5.5e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - (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 (f <= (-1.55d-23)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 8.8d-280) then
        tmp = ((f / b) * ((-1.0d0) / f)) - (x * (1.0d0 / tan(b)))
    else if (f <= 5.5d-223) then
        tmp = -x / b
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 8.8e-280) {
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / Math.tan(B)));
	} else if (F <= 5.5e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.55e-23:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 8.8e-280:
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / math.tan(B)))
	elif F <= 5.5e-223:
		tmp = -x / B
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.55e-23)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 8.8e-280)
		tmp = Float64(Float64(Float64(F / B) * Float64(-1.0 / F)) - Float64(x * Float64(1.0 / tan(B))));
	elseif (F <= 5.5e-223)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.55e-23)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 8.8e-280)
		tmp = ((F / B) * (-1.0 / F)) - (x * (1.0 / tan(B)));
	elseif (F <= 5.5e-223)
		tmp = -x / B;
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.55e-23], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.8e-280], N[(N[(N[(F / B), $MachinePrecision] * N[(-1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x * N[(1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 5.5e-223], N[((-x) / B), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 18: 64.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -0.00029:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{F}{B \cdot \sqrt{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -0.00029)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 2.2e-9)
     (- (/ F (* B (sqrt (+ 2.0 (* x 2.0))))) (/ x B))
     (- (/ 1.0 B) (/ x (tan B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.00029) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 2.2e-9) {
		tmp = (F / (B * sqrt((2.0 + (x * 2.0))))) - (x / B);
	} else {
		tmp = (1.0 / B) - (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 (f <= (-0.00029d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 2.2d-9) then
        tmp = (f / (b * sqrt((2.0d0 + (x * 2.0d0))))) - (x / b)
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.00029) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 2.2e-9) {
		tmp = (F / (B * Math.sqrt((2.0 + (x * 2.0))))) - (x / B);
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -0.00029:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 2.2e-9:
		tmp = (F / (B * math.sqrt((2.0 + (x * 2.0))))) - (x / B)
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -0.00029)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 2.2e-9)
		tmp = Float64(Float64(F / Float64(B * sqrt(Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -0.00029)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 2.2e-9)
		tmp = (F / (B * sqrt((2.0 + (x * 2.0))))) - (x / B);
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -0.00029], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2.2e-9], N[(N[(F / N[(B * N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 19: 62.0% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 2 \cdot 10^{-287}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_0\\ \mathbf{elif}\;F \leq 4.5 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -2.8e-24)
     (- (/ -1.0 (sin B)) (/ x B))
     (if (<= F 2e-287)
       (- (* (/ F B) (/ 1.0 F)) t_0)
       (if (<= F 4.5e-223) (/ (- x) B) (- (/ 1.0 B) t_0))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -2.8e-24) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 2e-287) {
		tmp = ((F / B) * (1.0 / F)) - t_0;
	} else if (F <= 4.5e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - t_0;
	}
	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 <= (-2.8d-24)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 2d-287) then
        tmp = ((f / b) * (1.0d0 / f)) - t_0
    else if (f <= 4.5d-223) then
        tmp = -x / b
    else
        tmp = (1.0d0 / b) - t_0
    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 <= -2.8e-24) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 2e-287) {
		tmp = ((F / B) * (1.0 / F)) - t_0;
	} else if (F <= 4.5e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -2.8e-24:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 2e-287:
		tmp = ((F / B) * (1.0 / F)) - t_0
	elif F <= 4.5e-223:
		tmp = -x / B
	else:
		tmp = (1.0 / B) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -2.8e-24)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 2e-287)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_0);
	elseif (F <= 4.5e-223)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 / B) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x / tan(B);
	tmp = 0.0;
	if (F <= -2.8e-24)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 2e-287)
		tmp = ((F / B) * (1.0 / F)) - t_0;
	elseif (F <= 4.5e-223)
		tmp = -x / B;
	else
		tmp = (1.0 / B) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -2.8e-24], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2e-287], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 4.5e-223], N[((-x) / B), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]

Derivation

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

Alternative 20: 61.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.65 \cdot 10^{-26}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 7.5 \cdot 10^{-287} \lor \neg \left(F \leq 9.5 \cdot 10^{-223}\right):\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.65e-26)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (or (<= F 7.5e-287) (not (<= F 9.5e-223)))
     (- (/ 1.0 B) (/ x (tan B)))
     (/ (- x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.65e-26) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if ((F <= 7.5e-287) || !(F <= 9.5e-223)) {
		tmp = (1.0 / B) - (x / tan(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 <= (-1.65d-26)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if ((f <= 7.5d-287) .or. (.not. (f <= 9.5d-223))) then
        tmp = (1.0d0 / b) - (x / tan(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 <= -1.65e-26) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if ((F <= 7.5e-287) || !(F <= 9.5e-223)) {
		tmp = (1.0 / B) - (x / Math.tan(B));
	} else {
		tmp = -x / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.65e-26:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif (F <= 7.5e-287) or not (F <= 9.5e-223):
		tmp = (1.0 / B) - (x / math.tan(B))
	else:
		tmp = -x / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.65e-26)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif ((F <= 7.5e-287) || !(F <= 9.5e-223))
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	else
		tmp = Float64(Float64(-x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.65e-26)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif ((F <= 7.5e-287) || ~((F <= 9.5e-223)))
		tmp = (1.0 / B) - (x / tan(B));
	else
		tmp = -x / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.65e-26], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 7.5e-287], N[Not[LessEqual[F, 9.5e-223]], $MachinePrecision]], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[((-x) / B), $MachinePrecision]]]

Derivation

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

Alternative 21: 61.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.55 \cdot 10^{-23}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 3.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{1}{B} + \frac{-1}{\frac{\tan B}{x}}\\ \mathbf{elif}\;F \leq 3.4 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{\tan B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.55e-23)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 3.2e-287)
     (+ (/ 1.0 B) (/ -1.0 (/ (tan B) x)))
     (if (<= F 3.4e-223) (/ (- x) B) (- (/ 1.0 B) (/ x (tan B)))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 3.2e-287) {
		tmp = (1.0 / B) + (-1.0 / (tan(B) / x));
	} else if (F <= 3.4e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - (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 (f <= (-1.55d-23)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 3.2d-287) then
        tmp = (1.0d0 / b) + ((-1.0d0) / (tan(b) / x))
    else if (f <= 3.4d-223) then
        tmp = -x / b
    else
        tmp = (1.0d0 / b) - (x / tan(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.55e-23) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 3.2e-287) {
		tmp = (1.0 / B) + (-1.0 / (Math.tan(B) / x));
	} else if (F <= 3.4e-223) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - (x / Math.tan(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.55e-23:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 3.2e-287:
		tmp = (1.0 / B) + (-1.0 / (math.tan(B) / x))
	elif F <= 3.4e-223:
		tmp = -x / B
	else:
		tmp = (1.0 / B) - (x / math.tan(B))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.55e-23)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 3.2e-287)
		tmp = Float64(Float64(1.0 / B) + Float64(-1.0 / Float64(tan(B) / x)));
	elseif (F <= 3.4e-223)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / tan(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.55e-23)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 3.2e-287)
		tmp = (1.0 / B) + (-1.0 / (tan(B) / x));
	elseif (F <= 3.4e-223)
		tmp = -x / B;
	else
		tmp = (1.0 / B) - (x / tan(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.55e-23], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.2e-287], N[(N[(1.0 / B), $MachinePrecision] + N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 3.4e-223], N[((-x) / B), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 22: 51.4% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3.1 \cdot 10^{-97}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 2 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{B} + 0.3333333333333333 \cdot \left(B \cdot x\right)\right) - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3.1e-97)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 2e-71)
     (/ (- x) B)
     (- (+ (/ 1.0 B) (* 0.3333333333333333 (* B x))) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.1e-97) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 2e-71) {
		tmp = -x / B;
	} else {
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (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 <= (-3.1d-97)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 2d-71) then
        tmp = -x / b
    else
        tmp = ((1.0d0 / b) + (0.3333333333333333d0 * (b * x))) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.1e-97) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 2e-71) {
		tmp = -x / B;
	} else {
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3.1e-97:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 2e-71:
		tmp = -x / B
	else:
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3.1e-97)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 2e-71)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(Float64(1.0 / B) + Float64(0.3333333333333333 * Float64(B * x))) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3.1e-97)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 2e-71)
		tmp = -x / B;
	else
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3.1e-97], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2e-71], N[((-x) / B), $MachinePrecision], N[(N[(N[(1.0 / B), $MachinePrecision] + N[(0.3333333333333333 * N[(B * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 23: 44.4% accurate, 18.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -5.9 \cdot 10^{-96}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 3 \cdot 10^{-72}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{B} + 0.3333333333333333 \cdot \left(B \cdot x\right)\right) - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -5.9e-96)
   (/ (- -1.0 x) B)
   (if (<= F 3e-72)
     (/ (- x) B)
     (- (+ (/ 1.0 B) (* 0.3333333333333333 (* B x))) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.9e-96) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 3e-72) {
		tmp = -x / B;
	} else {
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (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 <= (-5.9d-96)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 3d-72) then
        tmp = -x / b
    else
        tmp = ((1.0d0 / b) + (0.3333333333333333d0 * (b * x))) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.9e-96) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 3e-72) {
		tmp = -x / B;
	} else {
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -5.9e-96:
		tmp = (-1.0 - x) / B
	elif F <= 3e-72:
		tmp = -x / B
	else:
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -5.9e-96)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 3e-72)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(Float64(1.0 / B) + Float64(0.3333333333333333 * Float64(B * x))) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -5.9e-96)
		tmp = (-1.0 - x) / B;
	elseif (F <= 3e-72)
		tmp = -x / B;
	else
		tmp = ((1.0 / B) + (0.3333333333333333 * (B * x))) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -5.9e-96], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 3e-72], N[((-x) / B), $MachinePrecision], N[(N[(N[(1.0 / B), $MachinePrecision] + N[(0.3333333333333333 * N[(B * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 24: 44.4% accurate, 21.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -5.4 \cdot 10^{-96}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(B \cdot 0.3333333333333333\right) + \frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -5.4e-96)
   (/ (- -1.0 x) B)
   (if (<= F 1.8e-74)
     (/ (- x) B)
     (+ (* x (* B 0.3333333333333333)) (/ (- 1.0 x) B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.4e-96) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.8e-74) {
		tmp = -x / B;
	} else {
		tmp = (x * (B * 0.3333333333333333)) + ((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 <= (-5.4d-96)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 1.8d-74) then
        tmp = -x / b
    else
        tmp = (x * (b * 0.3333333333333333d0)) + ((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 <= -5.4e-96) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.8e-74) {
		tmp = -x / B;
	} else {
		tmp = (x * (B * 0.3333333333333333)) + ((1.0 - x) / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -5.4e-96:
		tmp = (-1.0 - x) / B
	elif F <= 1.8e-74:
		tmp = -x / B
	else:
		tmp = (x * (B * 0.3333333333333333)) + ((1.0 - x) / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -5.4e-96)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 1.8e-74)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(x * Float64(B * 0.3333333333333333)) + Float64(Float64(1.0 - x) / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -5.4e-96)
		tmp = (-1.0 - x) / B;
	elseif (F <= 1.8e-74)
		tmp = -x / B;
	else
		tmp = (x * (B * 0.3333333333333333)) + ((1.0 - x) / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -5.4e-96], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 1.8e-74], N[((-x) / B), $MachinePrecision], N[(N[(x * N[(B * 0.3333333333333333), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 25: 44.3% accurate, 29.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -5.3 \cdot 10^{-95}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 4.4 \cdot 10^{-72}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -5.3e-95)
   (/ (- -1.0 x) B)
   (if (<= F 4.4e-72) (/ (- x) B) (- (/ 1.0 B) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.3e-95) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 4.4e-72) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / 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 <= (-5.3d-95)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 4.4d-72) then
        tmp = -x / b
    else
        tmp = (1.0d0 / b) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.3e-95) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 4.4e-72) {
		tmp = -x / B;
	} else {
		tmp = (1.0 / B) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -5.3e-95:
		tmp = (-1.0 - x) / B
	elif F <= 4.4e-72:
		tmp = -x / B
	else:
		tmp = (1.0 / B) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -5.3e-95)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 4.4e-72)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 / B) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -5.3e-95)
		tmp = (-1.0 - x) / B;
	elseif (F <= 4.4e-72)
		tmp = -x / B;
	else
		tmp = (1.0 / B) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -5.3e-95], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 4.4e-72], N[((-x) / B), $MachinePrecision], N[(N[(1.0 / B), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 26: 38.1% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{elif}\;F \leq 6.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.36e-42)
   (/ -1.0 B)
   (if (<= F 6.2e-71) (/ (- x) B) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.36e-42) {
		tmp = -1.0 / B;
	} else if (F <= 6.2e-71) {
		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 <= (-1.36d-42)) then
        tmp = (-1.0d0) / b
    else if (f <= 6.2d-71) 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 <= -1.36e-42) {
		tmp = -1.0 / B;
	} else if (F <= 6.2e-71) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.36e-42:
		tmp = -1.0 / B
	elif F <= 6.2e-71:
		tmp = -x / B
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.36e-42)
		tmp = Float64(-1.0 / B);
	elseif (F <= 6.2e-71)
		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 <= -1.36e-42)
		tmp = -1.0 / B;
	elseif (F <= 6.2e-71)
		tmp = -x / B;
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.36e-42], N[(-1.0 / B), $MachinePrecision], If[LessEqual[F, 6.2e-71], N[((-x) / B), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 27: 44.3% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -2.4 \cdot 10^{-95}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -2.4e-95)
   (/ (- -1.0 x) B)
   (if (<= F 1.7e-71) (/ (- x) B) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.4e-95) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.7e-71) {
		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 <= (-2.4d-95)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 1.7d-71) 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 <= -2.4e-95) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.7e-71) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -2.4e-95:
		tmp = (-1.0 - x) / B
	elif F <= 1.7e-71:
		tmp = -x / B
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -2.4e-95)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 1.7e-71)
		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 <= -2.4e-95)
		tmp = (-1.0 - x) / B;
	elseif (F <= 1.7e-71)
		tmp = -x / B;
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -2.4e-95], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 1.7e-71], N[((-x) / B), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 28: 31.1% accurate, 39.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -7.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{elif}\;F \leq 2.15 \cdot 10^{+43}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -7.4e-43) (/ -1.0 B) (if (<= F 2.15e+43) (/ (- x) B) (/ 1.0 B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.4e-43) {
		tmp = -1.0 / B;
	} else if (F <= 2.15e+43) {
		tmp = -x / B;
	} else {
		tmp = 1.0 / 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 <= (-7.4d-43)) then
        tmp = (-1.0d0) / b
    else if (f <= 2.15d+43) then
        tmp = -x / b
    else
        tmp = 1.0d0 / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.4e-43) {
		tmp = -1.0 / B;
	} else if (F <= 2.15e+43) {
		tmp = -x / B;
	} else {
		tmp = 1.0 / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -7.4e-43:
		tmp = -1.0 / B
	elif F <= 2.15e+43:
		tmp = -x / B
	else:
		tmp = 1.0 / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -7.4e-43)
		tmp = Float64(-1.0 / B);
	elseif (F <= 2.15e+43)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(1.0 / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -7.4e-43)
		tmp = -1.0 / B;
	elseif (F <= 2.15e+43)
		tmp = -x / B;
	else
		tmp = 1.0 / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -7.4e-43], N[(-1.0 / B), $MachinePrecision], If[LessEqual[F, 2.15e+43], N[((-x) / B), $MachinePrecision], N[(1.0 / B), $MachinePrecision]]]

Derivation

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

Alternative 29: 17.7% accurate, 64.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq 1.55 \cdot 10^{-127}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x) :precision binary64 (if (<= F 1.55e-127) (/ -1.0 B) (/ 1.0 B)))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= 1.55e-127) {
		tmp = -1.0 / B;
	} else {
		tmp = 1.0 / 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 <= 1.55d-127) then
        tmp = (-1.0d0) / b
    else
        tmp = 1.0d0 / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= 1.55e-127) {
		tmp = -1.0 / B;
	} else {
		tmp = 1.0 / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= 1.55e-127:
		tmp = -1.0 / B
	else:
		tmp = 1.0 / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= 1.55e-127)
		tmp = Float64(-1.0 / B);
	else
		tmp = Float64(1.0 / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= 1.55e-127)
		tmp = -1.0 / B;
	else
		tmp = 1.0 / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, 1.55e-127], N[(-1.0 / B), $MachinePrecision], N[(1.0 / B), $MachinePrecision]]

Derivation

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

Alternative 30: 10.3% 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

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

Reproduce

herbie shell --seed 2023350 
(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))))))