VandenBroeck and Keller, Equation (23)

Percentage Accurate: 76.0% → 99.6%

Time: 22.9s

Alternatives: 25

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: 76.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1 \cdot 10^{+45}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 200000000:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1e+45)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 200000000.0)
       (- (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5)) t_0)
       (- (/ 1.0 (sin B)) t_0)))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -1e+45) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 200000000.0) {
		tmp = ((F / sin(B)) * pow((((F * F) + 2.0) + (x * 2.0)), -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 / tan(b)
    if (f <= (-1d+45)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 200000000.0d0) then
        tmp = ((f / sin(b)) * ((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-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 / Math.tan(B);
	double tmp;
	if (F <= -1e+45) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 200000000.0) {
		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)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -1e+45:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 200000000.0:
		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)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1e+45)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 200000000.0)
		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)) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = x / tan(B);
	tmp = 0.0;
	if (F <= -1e+45)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 200000000.0)
		tmp = ((F / sin(B)) * ((((F * F) + 2.0) + (x * 2.0)) ^ -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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1e+45], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 200000000.0], 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] - t$95$0), $MachinePrecision]]]]

Derivation

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

Alternative 2: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.45:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 1.42:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.45)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 1.42)
       (- (* (/ F (sin 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 / tan(B);
	double tmp;
	if (F <= -1.45) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 1.42) {
		tmp = ((F / sin(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 / tan(b)
    if (f <= (-1.45d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 1.42d0) then
        tmp = ((f / sin(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 / Math.tan(B);
	double tmp;
	if (F <= -1.45) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 1.42) {
		tmp = ((F / Math.sin(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 / math.tan(B)
	tmp = 0
	if F <= -1.45:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 1.42:
		tmp = ((F / math.sin(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 / tan(B))
	tmp = 0.0
	if (F <= -1.45)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 1.42)
		tmp = Float64(Float64(Float64(F / sin(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 / tan(B);
	tmp = 0.0;
	if (F <= -1.45)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 1.42)
		tmp = ((F / sin(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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.45], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 1.42], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[0.5], $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: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.45:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 1.42:\\ \;\;\;\;\frac{F}{\frac{\sin B}{\sqrt{0.5}}} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.45)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 1.42)
       (- (/ F (/ (sin 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 / tan(B);
	double tmp;
	if (F <= -1.45) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 1.42) {
		tmp = (F / (sin(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 / tan(b)
    if (f <= (-1.45d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 1.42d0) then
        tmp = (f / (sin(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 / Math.tan(B);
	double tmp;
	if (F <= -1.45) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 1.42) {
		tmp = (F / (Math.sin(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 / math.tan(B)
	tmp = 0
	if F <= -1.45:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 1.42:
		tmp = (F / (math.sin(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 / tan(B))
	tmp = 0.0
	if (F <= -1.45)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 1.42)
		tmp = Float64(Float64(F / Float64(sin(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 / tan(B);
	tmp = 0.0;
	if (F <= -1.45)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 1.42)
		tmp = (F / (sin(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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.45], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 1.42], N[(N[(F / N[(N[Sin[B], $MachinePrecision] / 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 4: 89.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - \frac{x}{B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -59000:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -1.62 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 2.55 \cdot 10^{-123}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 2500000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0
         (-
          (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5))
          (/ x B)))
        (t_1 (/ x (tan B))))
   (if (<= F -59000.0)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F -1.62e-133)
       t_0
       (if (<= F 2.55e-123)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 2500000.0) t_0 (- (/ 1.0 (sin B)) t_1)))))))

C

double code(double F, double B, double x) {
	double t_0 = ((F / sin(B)) * pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -59000.0) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= -1.62e-133) {
		tmp = t_0;
	} else if (F <= 2.55e-123) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 2500000.0) {
		tmp = t_0;
	} else {
		tmp = (1.0 / sin(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 / sin(b)) * ((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0))) - (x / b)
    t_1 = x / tan(b)
    if (f <= (-59000.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_1
    else if (f <= (-1.62d-133)) then
        tmp = t_0
    else if (f <= 2.55d-123) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 2500000.0d0) then
        tmp = t_0
    else
        tmp = (1.0d0 / sin(b)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -59000.0) {
		tmp = (-1.0 / Math.sin(B)) - t_1;
	} else if (F <= -1.62e-133) {
		tmp = t_0;
	} else if (F <= 2.55e-123) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 2500000.0) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_1;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B)
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -59000.0:
		tmp = (-1.0 / math.sin(B)) - t_1
	elif F <= -1.62e-133:
		tmp = t_0
	elif F <= 2.55e-123:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 2500000.0:
		tmp = t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_1
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5)) - Float64(x / B))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -59000.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= -1.62e-133)
		tmp = t_0;
	elseif (F <= 2.55e-123)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 2500000.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = ((F / sin(B)) * ((((F * F) + 2.0) + (x * 2.0)) ^ -0.5)) - (x / B);
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -59000.0)
		tmp = (-1.0 / sin(B)) - t_1;
	elseif (F <= -1.62e-133)
		tmp = t_0;
	elseif (F <= 2.55e-123)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 2500000.0)
		tmp = t_0;
	else
		tmp = (1.0 / sin(B)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = 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]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -59000.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -1.62e-133], t$95$0, If[LessEqual[F, 2.55e-123], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2500000.0], t$95$0, N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 5: 89.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\frac{1}{2 + x \cdot 2}}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.31:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -1.55 \cdot 10^{-133}:\\ \;\;\;\;\frac{F}{\sin B} \cdot t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 4.1 \cdot 10^{-123}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 0.72:\\ \;\;\;\;\frac{t_0}{\frac{\sin B}{F}} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (t_1 (/ x (tan B))))
   (if (<= F -0.31)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F -1.55e-133)
       (- (* (/ F (sin B)) t_0) (/ x B))
       (if (<= F 4.1e-123)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 0.72)
           (- (/ t_0 (/ (sin B) F)) (/ x B))
           (- (/ 1.0 (sin B)) t_1)))))))

C

double code(double F, double B, double x) {
	double t_0 = sqrt((1.0 / (2.0 + (x * 2.0))));
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -0.31) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= -1.55e-133) {
		tmp = ((F / sin(B)) * t_0) - (x / B);
	} else if (F <= 4.1e-123) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 0.72) {
		tmp = (t_0 / (sin(B) / F)) - (x / B);
	} else {
		tmp = (1.0 / sin(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 = sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))
    t_1 = x / tan(b)
    if (f <= (-0.31d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_1
    else if (f <= (-1.55d-133)) then
        tmp = ((f / sin(b)) * t_0) - (x / b)
    else if (f <= 4.1d-123) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 0.72d0) then
        tmp = (t_0 / (sin(b) / f)) - (x / b)
    else
        tmp = (1.0d0 / sin(b)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = Math.sqrt((1.0 / (2.0 + (x * 2.0))));
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -0.31) {
		tmp = (-1.0 / Math.sin(B)) - t_1;
	} else if (F <= -1.55e-133) {
		tmp = ((F / Math.sin(B)) * t_0) - (x / B);
	} else if (F <= 4.1e-123) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 0.72) {
		tmp = (t_0 / (Math.sin(B) / F)) - (x / B);
	} else {
		tmp = (1.0 / Math.sin(B)) - t_1;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = math.sqrt((1.0 / (2.0 + (x * 2.0))))
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -0.31:
		tmp = (-1.0 / math.sin(B)) - t_1
	elif F <= -1.55e-133:
		tmp = ((F / math.sin(B)) * t_0) - (x / B)
	elif F <= 4.1e-123:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 0.72:
		tmp = (t_0 / (math.sin(B) / F)) - (x / B)
	else:
		tmp = (1.0 / math.sin(B)) - t_1
	return tmp

Julia

function code(F, B, x)
	t_0 = sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -0.31)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= -1.55e-133)
		tmp = Float64(Float64(Float64(F / sin(B)) * t_0) - Float64(x / B));
	elseif (F <= 4.1e-123)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 0.72)
		tmp = Float64(Float64(t_0 / Float64(sin(B) / F)) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = sqrt((1.0 / (2.0 + (x * 2.0))));
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -0.31)
		tmp = (-1.0 / sin(B)) - t_1;
	elseif (F <= -1.55e-133)
		tmp = ((F / sin(B)) * t_0) - (x / B);
	elseif (F <= 4.1e-123)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 0.72)
		tmp = (t_0 / (sin(B) / F)) - (x / B);
	else
		tmp = (1.0 / sin(B)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -0.31], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -1.55e-133], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * t$95$0), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 4.1e-123], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.72], N[(N[(t$95$0 / N[(N[Sin[B], $MachinePrecision] / F), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 6: 92.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1600:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 640:\\ \;\;\;\;{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1600.0)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 640.0)
       (- (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B)) t_0)
       (- (/ 1.0 (sin B)) t_0)))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -1600.0) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 640.0) {
		tmp = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / 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 / tan(b)
    if (f <= (-1600.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 640.0d0) then
        tmp = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / 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 / Math.tan(B);
	double tmp;
	if (F <= -1600.0) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 640.0) {
		tmp = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -1600.0:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 640.0:
		tmp = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1600.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 640.0)
		tmp = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / 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 / tan(B);
	tmp = 0.0;
	if (F <= -1600.0)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 640.0)
		tmp = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / 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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1600.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 640.0], 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] - 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 7: 89.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.31:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq -6.8 \cdot 10^{-130}:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 2.7 \cdot 10^{-123}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 0.064:\\ \;\;\;\;\frac{F}{\frac{\sin B}{\sqrt{0.5}}} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -0.31)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F -6.8e-130)
       (- (* (/ F (sin B)) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B))
       (if (<= F 2.7e-123)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 0.064)
           (- (/ F (/ (sin B) (sqrt 0.5))) (/ x B))
           (- (/ 1.0 (sin B)) t_0)))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -0.31) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= -6.8e-130) {
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 2.7e-123) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 0.064) {
		tmp = (F / (sin(B) / sqrt(0.5))) - (x / B);
	} 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 / tan(b)
    if (f <= (-0.31d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= (-6.8d-130)) then
        tmp = ((f / sin(b)) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    else if (f <= 2.7d-123) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 0.064d0) then
        tmp = (f / (sin(b) / sqrt(0.5d0))) - (x / b)
    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 / Math.tan(B);
	double tmp;
	if (F <= -0.31) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= -6.8e-130) {
		tmp = ((F / Math.sin(B)) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 2.7e-123) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 0.064) {
		tmp = (F / (Math.sin(B) / Math.sqrt(0.5))) - (x / B);
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -0.31:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= -6.8e-130:
		tmp = ((F / math.sin(B)) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	elif F <= 2.7e-123:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 0.064:
		tmp = (F / (math.sin(B) / math.sqrt(0.5))) - (x / B)
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -0.31)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= -6.8e-130)
		tmp = Float64(Float64(Float64(F / sin(B)) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	elseif (F <= 2.7e-123)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 0.064)
		tmp = Float64(Float64(F / Float64(sin(B) / sqrt(0.5))) - Float64(x / B));
	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 / tan(B);
	tmp = 0.0;
	if (F <= -0.31)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= -6.8e-130)
		tmp = ((F / sin(B)) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	elseif (F <= 2.7e-123)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 0.064)
		tmp = (F / (sin(B) / sqrt(0.5))) - (x / B);
	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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -0.31], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, -6.8e-130], N[(N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2.7e-123], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.064], N[(N[(F / N[(N[Sin[B], $MachinePrecision] / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]

Derivation

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

Alternative 8: 89.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{F}{\frac{\sin B}{\sqrt{0.5}}} - \frac{x}{B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.205:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -1.7 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 2.55 \cdot 10^{-123}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 0.47:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (- (/ F (/ (sin B) (sqrt 0.5))) (/ x B))) (t_1 (/ x (tan B))))
   (if (<= F -0.205)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F -1.7e-131)
       t_0
       (if (<= F 2.55e-123)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 0.47) t_0 (- (/ 1.0 (sin B)) t_1)))))))

C

double code(double F, double B, double x) {
	double t_0 = (F / (sin(B) / sqrt(0.5))) - (x / B);
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -0.205) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= -1.7e-131) {
		tmp = t_0;
	} else if (F <= 2.55e-123) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 0.47) {
		tmp = t_0;
	} else {
		tmp = (1.0 / sin(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 / (sin(b) / sqrt(0.5d0))) - (x / b)
    t_1 = x / tan(b)
    if (f <= (-0.205d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_1
    else if (f <= (-1.7d-131)) then
        tmp = t_0
    else if (f <= 2.55d-123) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 0.47d0) then
        tmp = t_0
    else
        tmp = (1.0d0 / sin(b)) - t_1
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (F / (Math.sin(B) / Math.sqrt(0.5))) - (x / B);
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -0.205) {
		tmp = (-1.0 / Math.sin(B)) - t_1;
	} else if (F <= -1.7e-131) {
		tmp = t_0;
	} else if (F <= 2.55e-123) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 0.47) {
		tmp = t_0;
	} else {
		tmp = (1.0 / Math.sin(B)) - t_1;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (F / (math.sin(B) / math.sqrt(0.5))) - (x / B)
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -0.205:
		tmp = (-1.0 / math.sin(B)) - t_1
	elif F <= -1.7e-131:
		tmp = t_0
	elif F <= 2.55e-123:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 0.47:
		tmp = t_0
	else:
		tmp = (1.0 / math.sin(B)) - t_1
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(F / Float64(sin(B) / sqrt(0.5))) - Float64(x / B))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -0.205)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= -1.7e-131)
		tmp = t_0;
	elseif (F <= 2.55e-123)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 0.47)
		tmp = t_0;
	else
		tmp = Float64(Float64(1.0 / sin(B)) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (F / (sin(B) / sqrt(0.5))) - (x / B);
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -0.205)
		tmp = (-1.0 / sin(B)) - t_1;
	elseif (F <= -1.7e-131)
		tmp = t_0;
	elseif (F <= 2.55e-123)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 0.47)
		tmp = t_0;
	else
		tmp = (1.0 / sin(B)) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(F / N[(N[Sin[B], $MachinePrecision] / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -0.205], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -1.7e-131], t$95$0, If[LessEqual[F, 2.55e-123], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.47], t$95$0, N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]]]

Derivation

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

Alternative 9: 72.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ \mathbf{if}\;F \leq -1.28 \cdot 10^{+147}:\\ \;\;\;\;\frac{-1}{B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -0.002:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -6.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5}}{\sin B}\\ \mathbf{elif}\;F \leq 10^{-117}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 8.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{0.5}\\ \mathbf{elif}\;F \leq 4.5 \cdot 10^{+211}:\\ \;\;\;\;t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.95 \cdot 10^{+288}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B))))
   (if (<= F -1.28e+147)
     (- (/ -1.0 B) (/ x (tan B)))
     (if (<= F -0.002)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -6.8e-102)
         (/ (* F (sqrt 0.5)) (sin B))
         (if (<= F 1e-117)
           (/ (- (* x (cos B))) (sin B))
           (if (<= F 8.2e-10)
             (* (/ F (sin B)) (sqrt 0.5))
             (if (<= F 4.5e+211)
               (- t_0 (/ x B))
               (if (<= F 1.95e+288)
                 (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
                 t_0)))))))))

C

double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double tmp;
	if (F <= -1.28e+147) {
		tmp = (-1.0 / B) - (x / tan(B));
	} else if (F <= -0.002) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -6.8e-102) {
		tmp = (F * sqrt(0.5)) / sin(B);
	} else if (F <= 1e-117) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / sin(B)) * sqrt(0.5);
	} else if (F <= 4.5e+211) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.95e+288) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = 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 = 1.0d0 / sin(b)
    if (f <= (-1.28d+147)) then
        tmp = ((-1.0d0) / b) - (x / tan(b))
    else if (f <= (-0.002d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-6.8d-102)) then
        tmp = (f * sqrt(0.5d0)) / sin(b)
    else if (f <= 1d-117) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 8.2d-10) then
        tmp = (f / sin(b)) * sqrt(0.5d0)
    else if (f <= 4.5d+211) then
        tmp = t_0 - (x / b)
    else if (f <= 1.95d+288) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = 1.0 / Math.sin(B);
	double tmp;
	if (F <= -1.28e+147) {
		tmp = (-1.0 / B) - (x / Math.tan(B));
	} else if (F <= -0.002) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -6.8e-102) {
		tmp = (F * Math.sqrt(0.5)) / Math.sin(B);
	} else if (F <= 1e-117) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / Math.sin(B)) * Math.sqrt(0.5);
	} else if (F <= 4.5e+211) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.95e+288) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 1.0 / math.sin(B)
	tmp = 0
	if F <= -1.28e+147:
		tmp = (-1.0 / B) - (x / math.tan(B))
	elif F <= -0.002:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -6.8e-102:
		tmp = (F * math.sqrt(0.5)) / math.sin(B)
	elif F <= 1e-117:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 8.2e-10:
		tmp = (F / math.sin(B)) * math.sqrt(0.5)
	elif F <= 4.5e+211:
		tmp = t_0 - (x / B)
	elif F <= 1.95e+288:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	tmp = 0.0
	if (F <= -1.28e+147)
		tmp = Float64(Float64(-1.0 / B) - Float64(x / tan(B)));
	elseif (F <= -0.002)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -6.8e-102)
		tmp = Float64(Float64(F * sqrt(0.5)) / sin(B));
	elseif (F <= 1e-117)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 8.2e-10)
		tmp = Float64(Float64(F / sin(B)) * sqrt(0.5));
	elseif (F <= 4.5e+211)
		tmp = Float64(t_0 - Float64(x / B));
	elseif (F <= 1.95e+288)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 1.0 / sin(B);
	tmp = 0.0;
	if (F <= -1.28e+147)
		tmp = (-1.0 / B) - (x / tan(B));
	elseif (F <= -0.002)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -6.8e-102)
		tmp = (F * sqrt(0.5)) / sin(B);
	elseif (F <= 1e-117)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 8.2e-10)
		tmp = (F / sin(B)) * sqrt(0.5);
	elseif (F <= 4.5e+211)
		tmp = t_0 - (x / B);
	elseif (F <= 1.95e+288)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.28e+147], N[(N[(-1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -0.002], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -6.8e-102], N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1e-117], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.2e-10], N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 4.5e+211], N[(t$95$0 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.95e+288], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

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

Alternative 10: 86.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.95 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq -8.8 \cdot 10^{-102}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5}}{\sin B}\\ \mathbf{elif}\;F \leq 2.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 8.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.95e-5)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F -8.8e-102)
       (/ (* F (sqrt 0.5)) (sin B))
       (if (<= F 2.8e-115)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 8.2e-10)
           (* (/ F (sin B)) (sqrt 0.5))
           (- (/ 1.0 (sin B)) t_0)))))))

C

double code(double F, double B, double x) {
	double t_0 = x / tan(B);
	double tmp;
	if (F <= -1.95e-5) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= -8.8e-102) {
		tmp = (F * sqrt(0.5)) / sin(B);
	} else if (F <= 2.8e-115) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / sin(B)) * sqrt(0.5);
	} 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 / tan(b)
    if (f <= (-1.95d-5)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= (-8.8d-102)) then
        tmp = (f * sqrt(0.5d0)) / sin(b)
    else if (f <= 2.8d-115) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 8.2d-10) then
        tmp = (f / sin(b)) * sqrt(0.5d0)
    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 / Math.tan(B);
	double tmp;
	if (F <= -1.95e-5) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= -8.8e-102) {
		tmp = (F * Math.sqrt(0.5)) / Math.sin(B);
	} else if (F <= 2.8e-115) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / Math.sin(B)) * Math.sqrt(0.5);
	} else {
		tmp = (1.0 / Math.sin(B)) - t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = x / math.tan(B)
	tmp = 0
	if F <= -1.95e-5:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= -8.8e-102:
		tmp = (F * math.sqrt(0.5)) / math.sin(B)
	elif F <= 2.8e-115:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 8.2e-10:
		tmp = (F / math.sin(B)) * math.sqrt(0.5)
	else:
		tmp = (1.0 / math.sin(B)) - t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -1.95e-5)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= -8.8e-102)
		tmp = Float64(Float64(F * sqrt(0.5)) / sin(B));
	elseif (F <= 2.8e-115)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 8.2e-10)
		tmp = Float64(Float64(F / sin(B)) * sqrt(0.5));
	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 / tan(B);
	tmp = 0.0;
	if (F <= -1.95e-5)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= -8.8e-102)
		tmp = (F * sqrt(0.5)) / sin(B);
	elseif (F <= 2.8e-115)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 8.2e-10)
		tmp = (F / sin(B)) * sqrt(0.5);
	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[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.95e-5], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, -8.8e-102], N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2.8e-115], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.2e-10], N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]]

Derivation

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

Alternative 11: 79.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ \mathbf{if}\;F \leq -2.35 \cdot 10^{-7}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq -9 \cdot 10^{-100}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5}}{\sin B}\\ \mathbf{elif}\;F \leq 1.02 \cdot 10^{-114}:\\ \;\;\;\;\frac{-x \cdot \cos B}{\sin B}\\ \mathbf{elif}\;F \leq 8.2 \cdot 10^{-10}:\\ \;\;\;\;\frac{F}{\sin B} \cdot \sqrt{0.5}\\ \mathbf{elif}\;F \leq 1.4 \cdot 10^{+214}:\\ \;\;\;\;t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.4 \cdot 10^{+288}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B))))
   (if (<= F -2.35e-7)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F -9e-100)
       (/ (* F (sqrt 0.5)) (sin B))
       (if (<= F 1.02e-114)
         (/ (- (* x (cos B))) (sin B))
         (if (<= F 8.2e-10)
           (* (/ F (sin B)) (sqrt 0.5))
           (if (<= F 1.4e+214)
             (- t_0 (/ x B))
             (if (<= F 1.4e+288)
               (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
               t_0))))))))

C

double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double tmp;
	if (F <= -2.35e-7) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= -9e-100) {
		tmp = (F * sqrt(0.5)) / sin(B);
	} else if (F <= 1.02e-114) {
		tmp = -(x * cos(B)) / sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / sin(B)) * sqrt(0.5);
	} else if (F <= 1.4e+214) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.4e+288) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = 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 = 1.0d0 / sin(b)
    if (f <= (-2.35d-7)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= (-9d-100)) then
        tmp = (f * sqrt(0.5d0)) / sin(b)
    else if (f <= 1.02d-114) then
        tmp = -(x * cos(b)) / sin(b)
    else if (f <= 8.2d-10) then
        tmp = (f / sin(b)) * sqrt(0.5d0)
    else if (f <= 1.4d+214) then
        tmp = t_0 - (x / b)
    else if (f <= 1.4d+288) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = 1.0 / Math.sin(B);
	double tmp;
	if (F <= -2.35e-7) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= -9e-100) {
		tmp = (F * Math.sqrt(0.5)) / Math.sin(B);
	} else if (F <= 1.02e-114) {
		tmp = -(x * Math.cos(B)) / Math.sin(B);
	} else if (F <= 8.2e-10) {
		tmp = (F / Math.sin(B)) * Math.sqrt(0.5);
	} else if (F <= 1.4e+214) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.4e+288) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 1.0 / math.sin(B)
	tmp = 0
	if F <= -2.35e-7:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= -9e-100:
		tmp = (F * math.sqrt(0.5)) / math.sin(B)
	elif F <= 1.02e-114:
		tmp = -(x * math.cos(B)) / math.sin(B)
	elif F <= 8.2e-10:
		tmp = (F / math.sin(B)) * math.sqrt(0.5)
	elif F <= 1.4e+214:
		tmp = t_0 - (x / B)
	elif F <= 1.4e+288:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	tmp = 0.0
	if (F <= -2.35e-7)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= -9e-100)
		tmp = Float64(Float64(F * sqrt(0.5)) / sin(B));
	elseif (F <= 1.02e-114)
		tmp = Float64(Float64(-Float64(x * cos(B))) / sin(B));
	elseif (F <= 8.2e-10)
		tmp = Float64(Float64(F / sin(B)) * sqrt(0.5));
	elseif (F <= 1.4e+214)
		tmp = Float64(t_0 - Float64(x / B));
	elseif (F <= 1.4e+288)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 1.0 / sin(B);
	tmp = 0.0;
	if (F <= -2.35e-7)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= -9e-100)
		tmp = (F * sqrt(0.5)) / sin(B);
	elseif (F <= 1.02e-114)
		tmp = -(x * cos(B)) / sin(B);
	elseif (F <= 8.2e-10)
		tmp = (F / sin(B)) * sqrt(0.5);
	elseif (F <= 1.4e+214)
		tmp = t_0 - (x / B);
	elseif (F <= 1.4e+288)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -2.35e-7], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -9e-100], N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.02e-114], N[((-N[(x * N[Cos[B], $MachinePrecision]), $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8.2e-10], N[(N[(F / N[Sin[B], $MachinePrecision]), $MachinePrecision] * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.4e+214], N[(t$95$0 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.4e+288], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 12: 65.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - \frac{x}{B}\\ t_2 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -9.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{-1}{B} - t_2\\ \mathbf{elif}\;F \leq -1550:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -1.1 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 4.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_2\\ \mathbf{elif}\;F \leq 360:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 1.95 \cdot 10^{+214}:\\ \;\;\;\;t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.35 \cdot 10^{+287}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B)))
        (t_1 (- (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B)) (/ x B)))
        (t_2 (/ x (tan B))))
   (if (<= F -9.2e+135)
     (- (/ -1.0 B) t_2)
     (if (<= F -1550.0)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -1.1e-267)
         t_1
         (if (<= F 4.2e-295)
           (- (* (/ F B) (/ 1.0 F)) t_2)
           (if (<= F 360.0)
             t_1
             (if (<= F 1.95e+214)
               (- t_0 (/ x B))
               (if (<= F 1.35e+287)
                 (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
                 t_0)))))))))

C

double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double t_1 = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	double t_2 = x / tan(B);
	double tmp;
	if (F <= -9.2e+135) {
		tmp = (-1.0 / B) - t_2;
	} else if (F <= -1550.0) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -1.1e-267) {
		tmp = t_1;
	} else if (F <= 4.2e-295) {
		tmp = ((F / B) * (1.0 / F)) - t_2;
	} else if (F <= 360.0) {
		tmp = t_1;
	} else if (F <= 1.95e+214) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.35e+287) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 / sin(b)
    t_1 = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) - (x / b)
    t_2 = x / tan(b)
    if (f <= (-9.2d+135)) then
        tmp = ((-1.0d0) / b) - t_2
    else if (f <= (-1550.0d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-1.1d-267)) then
        tmp = t_1
    else if (f <= 4.2d-295) then
        tmp = ((f / b) * (1.0d0 / f)) - t_2
    else if (f <= 360.0d0) then
        tmp = t_1
    else if (f <= 1.95d+214) then
        tmp = t_0 - (x / b)
    else if (f <= 1.35d+287) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = 1.0 / Math.sin(B);
	double t_1 = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	double t_2 = x / Math.tan(B);
	double tmp;
	if (F <= -9.2e+135) {
		tmp = (-1.0 / B) - t_2;
	} else if (F <= -1550.0) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -1.1e-267) {
		tmp = t_1;
	} else if (F <= 4.2e-295) {
		tmp = ((F / B) * (1.0 / F)) - t_2;
	} else if (F <= 360.0) {
		tmp = t_1;
	} else if (F <= 1.95e+214) {
		tmp = t_0 - (x / B);
	} else if (F <= 1.35e+287) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 1.0 / math.sin(B)
	t_1 = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B)
	t_2 = x / math.tan(B)
	tmp = 0
	if F <= -9.2e+135:
		tmp = (-1.0 / B) - t_2
	elif F <= -1550.0:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -1.1e-267:
		tmp = t_1
	elif F <= 4.2e-295:
		tmp = ((F / B) * (1.0 / F)) - t_2
	elif F <= 360.0:
		tmp = t_1
	elif F <= 1.95e+214:
		tmp = t_0 - (x / B)
	elif F <= 1.35e+287:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	t_1 = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) - Float64(x / B))
	t_2 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -9.2e+135)
		tmp = Float64(Float64(-1.0 / B) - t_2);
	elseif (F <= -1550.0)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -1.1e-267)
		tmp = t_1;
	elseif (F <= 4.2e-295)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_2);
	elseif (F <= 360.0)
		tmp = t_1;
	elseif (F <= 1.95e+214)
		tmp = Float64(t_0 - Float64(x / B));
	elseif (F <= 1.35e+287)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 1.0 / sin(B);
	t_1 = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) - (x / B);
	t_2 = x / tan(B);
	tmp = 0.0;
	if (F <= -9.2e+135)
		tmp = (-1.0 / B) - t_2;
	elseif (F <= -1550.0)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -1.1e-267)
		tmp = t_1;
	elseif (F <= 4.2e-295)
		tmp = ((F / B) * (1.0 / F)) - t_2;
	elseif (F <= 360.0)
		tmp = t_1;
	elseif (F <= 1.95e+214)
		tmp = t_0 - (x / B);
	elseif (F <= 1.35e+287)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = 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]}, Block[{t$95$2 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -9.2e+135], N[(N[(-1.0 / B), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[F, -1550.0], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -1.1e-267], t$95$1, If[LessEqual[F, 4.2e-295], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[F, 360.0], t$95$1, If[LessEqual[F, 1.95e+214], N[(t$95$0 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.35e+287], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

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

Alternative 13: 65.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -5.5 \cdot 10^{+148}:\\ \;\;\;\;\frac{-1}{B} - t_1\\ \mathbf{elif}\;F \leq -0.13:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -7.2 \cdot 10^{-261}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5} - x}{B}\\ \mathbf{elif}\;F \leq 9.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_1\\ \mathbf{elif}\;F \leq 0.135:\\ \;\;\;\;\frac{F}{B} \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 6.5 \cdot 10^{+212}:\\ \;\;\;\;t_0 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 2.6 \cdot 10^{+286}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B))) (t_1 (/ x (tan B))))
   (if (<= F -5.5e+148)
     (- (/ -1.0 B) t_1)
     (if (<= F -0.13)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -7.2e-261)
         (/ (- (* F (sqrt 0.5)) x) B)
         (if (<= F 9.2e-295)
           (- (* (/ F B) (/ 1.0 F)) t_1)
           (if (<= F 0.135)
             (- (* (/ F B) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B))
             (if (<= F 6.5e+212)
               (- t_0 (/ x B))
               (if (<= F 2.6e+286)
                 (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
                 t_0)))))))))

C

double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double t_1 = x / tan(B);
	double tmp;
	if (F <= -5.5e+148) {
		tmp = (-1.0 / B) - t_1;
	} else if (F <= -0.13) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -7.2e-261) {
		tmp = ((F * sqrt(0.5)) - x) / B;
	} else if (F <= 9.2e-295) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 0.135) {
		tmp = ((F / B) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 6.5e+212) {
		tmp = t_0 - (x / B);
	} else if (F <= 2.6e+286) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 / sin(b)
    t_1 = x / tan(b)
    if (f <= (-5.5d+148)) then
        tmp = ((-1.0d0) / b) - t_1
    else if (f <= (-0.13d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-7.2d-261)) then
        tmp = ((f * sqrt(0.5d0)) - x) / b
    else if (f <= 9.2d-295) then
        tmp = ((f / b) * (1.0d0 / f)) - t_1
    else if (f <= 0.135d0) then
        tmp = ((f / b) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    else if (f <= 6.5d+212) then
        tmp = t_0 - (x / b)
    else if (f <= 2.6d+286) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = 1.0 / Math.sin(B);
	double t_1 = x / Math.tan(B);
	double tmp;
	if (F <= -5.5e+148) {
		tmp = (-1.0 / B) - t_1;
	} else if (F <= -0.13) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -7.2e-261) {
		tmp = ((F * Math.sqrt(0.5)) - x) / B;
	} else if (F <= 9.2e-295) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 0.135) {
		tmp = ((F / B) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 6.5e+212) {
		tmp = t_0 - (x / B);
	} else if (F <= 2.6e+286) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 1.0 / math.sin(B)
	t_1 = x / math.tan(B)
	tmp = 0
	if F <= -5.5e+148:
		tmp = (-1.0 / B) - t_1
	elif F <= -0.13:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -7.2e-261:
		tmp = ((F * math.sqrt(0.5)) - x) / B
	elif F <= 9.2e-295:
		tmp = ((F / B) * (1.0 / F)) - t_1
	elif F <= 0.135:
		tmp = ((F / B) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	elif F <= 6.5e+212:
		tmp = t_0 - (x / B)
	elif F <= 2.6e+286:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_0
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	t_1 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -5.5e+148)
		tmp = Float64(Float64(-1.0 / B) - t_1);
	elseif (F <= -0.13)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -7.2e-261)
		tmp = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B);
	elseif (F <= 9.2e-295)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_1);
	elseif (F <= 0.135)
		tmp = Float64(Float64(Float64(F / B) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	elseif (F <= 6.5e+212)
		tmp = Float64(t_0 - Float64(x / B));
	elseif (F <= 2.6e+286)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 1.0 / sin(B);
	t_1 = x / tan(B);
	tmp = 0.0;
	if (F <= -5.5e+148)
		tmp = (-1.0 / B) - t_1;
	elseif (F <= -0.13)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -7.2e-261)
		tmp = ((F * sqrt(0.5)) - x) / B;
	elseif (F <= 9.2e-295)
		tmp = ((F / B) * (1.0 / F)) - t_1;
	elseif (F <= 0.135)
		tmp = ((F / B) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	elseif (F <= 6.5e+212)
		tmp = t_0 - (x / B);
	elseif (F <= 2.6e+286)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -5.5e+148], N[(N[(-1.0 / B), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -0.13], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -7.2e-261], N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 9.2e-295], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, 0.135], N[(N[(N[(F / B), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 6.5e+212], N[(t$95$0 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 2.6e+286], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

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

Alternative 14: 64.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{F \cdot \sqrt{0.5} - x}{B}\\ t_1 := \frac{-1}{B} - \frac{x}{\tan B}\\ t_2 := \frac{1}{\sin B}\\ \mathbf{if}\;F \leq -7.5 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq -0.225:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -8.2 \cdot 10^{-268}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.65 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 0.49:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.7 \cdot 10^{+212}:\\ \;\;\;\;t_2 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 8 \cdot 10^{+286}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ (- (* F (sqrt 0.5)) x) B))
        (t_1 (- (/ -1.0 B) (/ x (tan B))))
        (t_2 (/ 1.0 (sin B))))
   (if (<= F -7.5e+139)
     t_1
     (if (<= F -0.225)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -8.2e-268)
         t_0
         (if (<= F 1.65e-295)
           t_1
           (if (<= F 0.49)
             t_0
             (if (<= F 1.7e+212)
               (- t_2 (/ x B))
               (if (<= F 8e+286)
                 (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
                 t_2)))))))))

C

double code(double F, double B, double x) {
	double t_0 = ((F * sqrt(0.5)) - x) / B;
	double t_1 = (-1.0 / B) - (x / tan(B));
	double t_2 = 1.0 / sin(B);
	double tmp;
	if (F <= -7.5e+139) {
		tmp = t_1;
	} else if (F <= -0.225) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -8.2e-268) {
		tmp = t_0;
	} else if (F <= 1.65e-295) {
		tmp = t_1;
	} else if (F <= 0.49) {
		tmp = t_0;
	} else if (F <= 1.7e+212) {
		tmp = t_2 - (x / B);
	} else if (F <= 8e+286) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = ((f * sqrt(0.5d0)) - x) / b
    t_1 = ((-1.0d0) / b) - (x / tan(b))
    t_2 = 1.0d0 / sin(b)
    if (f <= (-7.5d+139)) then
        tmp = t_1
    else if (f <= (-0.225d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-8.2d-268)) then
        tmp = t_0
    else if (f <= 1.65d-295) then
        tmp = t_1
    else if (f <= 0.49d0) then
        tmp = t_0
    else if (f <= 1.7d+212) then
        tmp = t_2 - (x / b)
    else if (f <= 8d+286) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = ((F * Math.sqrt(0.5)) - x) / B;
	double t_1 = (-1.0 / B) - (x / Math.tan(B));
	double t_2 = 1.0 / Math.sin(B);
	double tmp;
	if (F <= -7.5e+139) {
		tmp = t_1;
	} else if (F <= -0.225) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -8.2e-268) {
		tmp = t_0;
	} else if (F <= 1.65e-295) {
		tmp = t_1;
	} else if (F <= 0.49) {
		tmp = t_0;
	} else if (F <= 1.7e+212) {
		tmp = t_2 - (x / B);
	} else if (F <= 8e+286) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = ((F * math.sqrt(0.5)) - x) / B
	t_1 = (-1.0 / B) - (x / math.tan(B))
	t_2 = 1.0 / math.sin(B)
	tmp = 0
	if F <= -7.5e+139:
		tmp = t_1
	elif F <= -0.225:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -8.2e-268:
		tmp = t_0
	elif F <= 1.65e-295:
		tmp = t_1
	elif F <= 0.49:
		tmp = t_0
	elif F <= 1.7e+212:
		tmp = t_2 - (x / B)
	elif F <= 8e+286:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_2
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B)
	t_1 = Float64(Float64(-1.0 / B) - Float64(x / tan(B)))
	t_2 = Float64(1.0 / sin(B))
	tmp = 0.0
	if (F <= -7.5e+139)
		tmp = t_1;
	elseif (F <= -0.225)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -8.2e-268)
		tmp = t_0;
	elseif (F <= 1.65e-295)
		tmp = t_1;
	elseif (F <= 0.49)
		tmp = t_0;
	elseif (F <= 1.7e+212)
		tmp = Float64(t_2 - Float64(x / B));
	elseif (F <= 8e+286)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = ((F * sqrt(0.5)) - x) / B;
	t_1 = (-1.0 / B) - (x / tan(B));
	t_2 = 1.0 / sin(B);
	tmp = 0.0;
	if (F <= -7.5e+139)
		tmp = t_1;
	elseif (F <= -0.225)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -8.2e-268)
		tmp = t_0;
	elseif (F <= 1.65e-295)
		tmp = t_1;
	elseif (F <= 0.49)
		tmp = t_0;
	elseif (F <= 1.7e+212)
		tmp = t_2 - (x / B);
	elseif (F <= 8e+286)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(N[(-1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -7.5e+139], t$95$1, If[LessEqual[F, -0.225], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -8.2e-268], t$95$0, If[LessEqual[F, 1.65e-295], t$95$1, If[LessEqual[F, 0.49], t$95$0, If[LessEqual[F, 1.7e+212], N[(t$95$2 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 8e+286], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

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

Alternative 15: 65.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{F \cdot \sqrt{0.5} - x}{B}\\ t_1 := \frac{x}{\tan B}\\ t_2 := \frac{1}{\sin B}\\ \mathbf{if}\;F \leq -4.3 \cdot 10^{+142}:\\ \;\;\;\;\frac{-1}{B} - t_1\\ \mathbf{elif}\;F \leq -0.3:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -2.7 \cdot 10^{-267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 2.4 \cdot 10^{-294}:\\ \;\;\;\;\frac{F}{B} \cdot \frac{1}{F} - t_1\\ \mathbf{elif}\;F \leq 0.27:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 4.3 \cdot 10^{+213}:\\ \;\;\;\;t_2 - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.3 \cdot 10^{+288}:\\ \;\;\;\;\frac{-1}{\frac{\tan B}{x}} + \frac{1}{B}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ (- (* F (sqrt 0.5)) x) B))
        (t_1 (/ x (tan B)))
        (t_2 (/ 1.0 (sin B))))
   (if (<= F -4.3e+142)
     (- (/ -1.0 B) t_1)
     (if (<= F -0.3)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -2.7e-267)
         t_0
         (if (<= F 2.4e-294)
           (- (* (/ F B) (/ 1.0 F)) t_1)
           (if (<= F 0.27)
             t_0
             (if (<= F 4.3e+213)
               (- t_2 (/ x B))
               (if (<= F 1.3e+288)
                 (+ (/ -1.0 (/ (tan B) x)) (/ 1.0 B))
                 t_2)))))))))

C

double code(double F, double B, double x) {
	double t_0 = ((F * sqrt(0.5)) - x) / B;
	double t_1 = x / tan(B);
	double t_2 = 1.0 / sin(B);
	double tmp;
	if (F <= -4.3e+142) {
		tmp = (-1.0 / B) - t_1;
	} else if (F <= -0.3) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -2.7e-267) {
		tmp = t_0;
	} else if (F <= 2.4e-294) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 0.27) {
		tmp = t_0;
	} else if (F <= 4.3e+213) {
		tmp = t_2 - (x / B);
	} else if (F <= 1.3e+288) {
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_0 = ((f * sqrt(0.5d0)) - x) / b
    t_1 = x / tan(b)
    t_2 = 1.0d0 / sin(b)
    if (f <= (-4.3d+142)) then
        tmp = ((-1.0d0) / b) - t_1
    else if (f <= (-0.3d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-2.7d-267)) then
        tmp = t_0
    else if (f <= 2.4d-294) then
        tmp = ((f / b) * (1.0d0 / f)) - t_1
    else if (f <= 0.27d0) then
        tmp = t_0
    else if (f <= 4.3d+213) then
        tmp = t_2 - (x / b)
    else if (f <= 1.3d+288) then
        tmp = ((-1.0d0) / (tan(b) / x)) + (1.0d0 / b)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = ((F * Math.sqrt(0.5)) - x) / B;
	double t_1 = x / Math.tan(B);
	double t_2 = 1.0 / Math.sin(B);
	double tmp;
	if (F <= -4.3e+142) {
		tmp = (-1.0 / B) - t_1;
	} else if (F <= -0.3) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -2.7e-267) {
		tmp = t_0;
	} else if (F <= 2.4e-294) {
		tmp = ((F / B) * (1.0 / F)) - t_1;
	} else if (F <= 0.27) {
		tmp = t_0;
	} else if (F <= 4.3e+213) {
		tmp = t_2 - (x / B);
	} else if (F <= 1.3e+288) {
		tmp = (-1.0 / (Math.tan(B) / x)) + (1.0 / B);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = ((F * math.sqrt(0.5)) - x) / B
	t_1 = x / math.tan(B)
	t_2 = 1.0 / math.sin(B)
	tmp = 0
	if F <= -4.3e+142:
		tmp = (-1.0 / B) - t_1
	elif F <= -0.3:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -2.7e-267:
		tmp = t_0
	elif F <= 2.4e-294:
		tmp = ((F / B) * (1.0 / F)) - t_1
	elif F <= 0.27:
		tmp = t_0
	elif F <= 4.3e+213:
		tmp = t_2 - (x / B)
	elif F <= 1.3e+288:
		tmp = (-1.0 / (math.tan(B) / x)) + (1.0 / B)
	else:
		tmp = t_2
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B)
	t_1 = Float64(x / tan(B))
	t_2 = Float64(1.0 / sin(B))
	tmp = 0.0
	if (F <= -4.3e+142)
		tmp = Float64(Float64(-1.0 / B) - t_1);
	elseif (F <= -0.3)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -2.7e-267)
		tmp = t_0;
	elseif (F <= 2.4e-294)
		tmp = Float64(Float64(Float64(F / B) * Float64(1.0 / F)) - t_1);
	elseif (F <= 0.27)
		tmp = t_0;
	elseif (F <= 4.3e+213)
		tmp = Float64(t_2 - Float64(x / B));
	elseif (F <= 1.3e+288)
		tmp = Float64(Float64(-1.0 / Float64(tan(B) / x)) + Float64(1.0 / B));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = ((F * sqrt(0.5)) - x) / B;
	t_1 = x / tan(B);
	t_2 = 1.0 / sin(B);
	tmp = 0.0;
	if (F <= -4.3e+142)
		tmp = (-1.0 / B) - t_1;
	elseif (F <= -0.3)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -2.7e-267)
		tmp = t_0;
	elseif (F <= 2.4e-294)
		tmp = ((F / B) * (1.0 / F)) - t_1;
	elseif (F <= 0.27)
		tmp = t_0;
	elseif (F <= 4.3e+213)
		tmp = t_2 - (x / B);
	elseif (F <= 1.3e+288)
		tmp = (-1.0 / (tan(B) / x)) + (1.0 / B);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -4.3e+142], N[(N[(-1.0 / B), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -0.3], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -2.7e-267], t$95$0, If[LessEqual[F, 2.4e-294], N[(N[(N[(F / B), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, 0.27], t$95$0, If[LessEqual[F, 4.3e+213], N[(t$95$2 - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.3e+288], N[(N[(-1.0 / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / B), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

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

Alternative 16: 65.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-1}{B} - \frac{x}{\tan B}\\ t_1 := \frac{F \cdot \sqrt{0.5} - x}{B}\\ \mathbf{if}\;F \leq -1.05 \cdot 10^{+148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq -0.39:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq -2.4 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 1.9 \cdot 10^{-295}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 0.58:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (- (/ -1.0 B) (/ x (tan B)))) (t_1 (/ (- (* F (sqrt 0.5)) x) B)))
   (if (<= F -1.05e+148)
     t_0
     (if (<= F -0.39)
       (- (/ -1.0 (sin B)) (/ x B))
       (if (<= F -2.4e-259)
         t_1
         (if (<= F 1.9e-295)
           t_0
           (if (<= F 0.58) t_1 (- (/ 1.0 (sin B)) (/ x B)))))))))

C

double code(double F, double B, double x) {
	double t_0 = (-1.0 / B) - (x / tan(B));
	double t_1 = ((F * sqrt(0.5)) - x) / B;
	double tmp;
	if (F <= -1.05e+148) {
		tmp = t_0;
	} else if (F <= -0.39) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= -2.4e-259) {
		tmp = t_1;
	} else if (F <= 1.9e-295) {
		tmp = t_0;
	} else if (F <= 0.58) {
		tmp = t_1;
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((-1.0d0) / b) - (x / tan(b))
    t_1 = ((f * sqrt(0.5d0)) - x) / b
    if (f <= (-1.05d+148)) then
        tmp = t_0
    else if (f <= (-0.39d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= (-2.4d-259)) then
        tmp = t_1
    else if (f <= 1.9d-295) then
        tmp = t_0
    else if (f <= 0.58d0) then
        tmp = t_1
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (-1.0 / B) - (x / Math.tan(B));
	double t_1 = ((F * Math.sqrt(0.5)) - x) / B;
	double tmp;
	if (F <= -1.05e+148) {
		tmp = t_0;
	} else if (F <= -0.39) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= -2.4e-259) {
		tmp = t_1;
	} else if (F <= 1.9e-295) {
		tmp = t_0;
	} else if (F <= 0.58) {
		tmp = t_1;
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (-1.0 / B) - (x / math.tan(B))
	t_1 = ((F * math.sqrt(0.5)) - x) / B
	tmp = 0
	if F <= -1.05e+148:
		tmp = t_0
	elif F <= -0.39:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= -2.4e-259:
		tmp = t_1
	elif F <= 1.9e-295:
		tmp = t_0
	elif F <= 0.58:
		tmp = t_1
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(-1.0 / B) - Float64(x / tan(B)))
	t_1 = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B)
	tmp = 0.0
	if (F <= -1.05e+148)
		tmp = t_0;
	elseif (F <= -0.39)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= -2.4e-259)
		tmp = t_1;
	elseif (F <= 1.9e-295)
		tmp = t_0;
	elseif (F <= 0.58)
		tmp = t_1;
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (-1.0 / B) - (x / tan(B));
	t_1 = ((F * sqrt(0.5)) - x) / B;
	tmp = 0.0;
	if (F <= -1.05e+148)
		tmp = t_0;
	elseif (F <= -0.39)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= -2.4e-259)
		tmp = t_1;
	elseif (F <= 1.9e-295)
		tmp = t_0;
	elseif (F <= 0.58)
		tmp = t_1;
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(-1.0 / B), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision]}, If[LessEqual[F, -1.05e+148], t$95$0, If[LessEqual[F, -0.39], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, -2.4e-259], t$95$1, If[LessEqual[F, 1.9e-295], t$95$0, If[LessEqual[F, 0.58], t$95$1, N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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

Alternative 17: 44.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -2.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{-1 - x}{B} + B \cdot \left(x \cdot 0.3333333333333333 - 0.16666666666666666\right)\\ \mathbf{elif}\;F \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{elif}\;F \leq 3.6 \cdot 10^{+75} \lor \neg \left(F \leq 1.45 \cdot 10^{+289}\right):\\ \;\;\;\;\frac{1}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;B \cdot 0.16666666666666666 + \frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -2.3e-31)
   (+ (/ (- -1.0 x) B) (* B (- (* x 0.3333333333333333) 0.16666666666666666)))
   (if (<= F 1.1e-7)
     (- (/ x B))
     (if (or (<= F 3.6e+75) (not (<= F 1.45e+289)))
       (/ 1.0 (sin B))
       (+ (* B 0.16666666666666666) (/ (- 1.0 x) B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.3e-31) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.1e-7) {
		tmp = -(x / B);
	} else if ((F <= 3.6e+75) || !(F <= 1.45e+289)) {
		tmp = 1.0 / sin(B);
	} else {
		tmp = (B * 0.16666666666666666) + ((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 <= (-2.3d-31)) then
        tmp = (((-1.0d0) - x) / b) + (b * ((x * 0.3333333333333333d0) - 0.16666666666666666d0))
    else if (f <= 1.1d-7) then
        tmp = -(x / b)
    else if ((f <= 3.6d+75) .or. (.not. (f <= 1.45d+289))) then
        tmp = 1.0d0 / sin(b)
    else
        tmp = (b * 0.16666666666666666d0) + ((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 <= -2.3e-31) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.1e-7) {
		tmp = -(x / B);
	} else if ((F <= 3.6e+75) || !(F <= 1.45e+289)) {
		tmp = 1.0 / Math.sin(B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -2.3e-31:
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666))
	elif F <= 1.1e-7:
		tmp = -(x / B)
	elif (F <= 3.6e+75) or not (F <= 1.45e+289):
		tmp = 1.0 / math.sin(B)
	else:
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -2.3e-31)
		tmp = Float64(Float64(Float64(-1.0 - x) / B) + Float64(B * Float64(Float64(x * 0.3333333333333333) - 0.16666666666666666)));
	elseif (F <= 1.1e-7)
		tmp = Float64(-Float64(x / B));
	elseif ((F <= 3.6e+75) || !(F <= 1.45e+289))
		tmp = Float64(1.0 / sin(B));
	else
		tmp = Float64(Float64(B * 0.16666666666666666) + Float64(Float64(1.0 - x) / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -2.3e-31)
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	elseif (F <= 1.1e-7)
		tmp = -(x / B);
	elseif ((F <= 3.6e+75) || ~((F <= 1.45e+289)))
		tmp = 1.0 / sin(B);
	else
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -2.3e-31], N[(N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision] + N[(B * N[(N[(x * 0.3333333333333333), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.1e-7], (-N[(x / B), $MachinePrecision]), If[Or[LessEqual[F, 3.6e+75], N[Not[LessEqual[F, 1.45e+289]], $MachinePrecision]], N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision], N[(N[(B * 0.16666666666666666), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 18: 51.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.15 \cdot 10^{-7}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{elif}\;F \leq 10^{+75} \lor \neg \left(F \leq 2.15 \cdot 10^{+285}\right):\\ \;\;\;\;\frac{1}{\sin B}\\ \mathbf{else}:\\ \;\;\;\;B \cdot 0.16666666666666666 + \frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.2e-31)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 1.15e-7)
     (- (/ x B))
     (if (or (<= F 1e+75) (not (<= F 2.15e+285)))
       (/ 1.0 (sin B))
       (+ (* B 0.16666666666666666) (/ (- 1.0 x) B))))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.2e-31) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 1.15e-7) {
		tmp = -(x / B);
	} else if ((F <= 1e+75) || !(F <= 2.15e+285)) {
		tmp = 1.0 / sin(B);
	} else {
		tmp = (B * 0.16666666666666666) + ((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 <= (-1.2d-31)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 1.15d-7) then
        tmp = -(x / b)
    else if ((f <= 1d+75) .or. (.not. (f <= 2.15d+285))) then
        tmp = 1.0d0 / sin(b)
    else
        tmp = (b * 0.16666666666666666d0) + ((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 <= -1.2e-31) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 1.15e-7) {
		tmp = -(x / B);
	} else if ((F <= 1e+75) || !(F <= 2.15e+285)) {
		tmp = 1.0 / Math.sin(B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.2e-31:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 1.15e-7:
		tmp = -(x / B)
	elif (F <= 1e+75) or not (F <= 2.15e+285):
		tmp = 1.0 / math.sin(B)
	else:
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.2e-31)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 1.15e-7)
		tmp = Float64(-Float64(x / B));
	elseif ((F <= 1e+75) || !(F <= 2.15e+285))
		tmp = Float64(1.0 / sin(B));
	else
		tmp = Float64(Float64(B * 0.16666666666666666) + Float64(Float64(1.0 - x) / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.2e-31)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 1.15e-7)
		tmp = -(x / B);
	elseif ((F <= 1e+75) || ~((F <= 2.15e+285)))
		tmp = 1.0 / sin(B);
	else
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.2e-31], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.15e-7], (-N[(x / B), $MachinePrecision]), If[Or[LessEqual[F, 1e+75], N[Not[LessEqual[F, 2.15e+285]], $MachinePrecision]], N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision], N[(N[(B * 0.16666666666666666), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 19: 57.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -5.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.75 \cdot 10^{-122}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -5.8e-32)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 1.75e-122) (- (/ x B)) (- (/ 1.0 (sin B)) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.8e-32) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 1.75e-122) {
		tmp = -(x / B);
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-5.8d-32)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 1.75d-122) then
        tmp = -(x / b)
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -5.8e-32) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 1.75e-122) {
		tmp = -(x / B);
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -5.8e-32:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 1.75e-122:
		tmp = -(x / B)
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -5.8e-32)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 1.75e-122)
		tmp = Float64(-Float64(x / B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -5.8e-32)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 1.75e-122)
		tmp = -(x / B);
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -5.8e-32], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.75e-122], (-N[(x / B), $MachinePrecision]), N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 20: 65.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -0.38:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 0.135:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5} - x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -0.38)
   (- (/ -1.0 (sin B)) (/ x B))
   (if (<= F 0.135) (/ (- (* F (sqrt 0.5)) x) B) (- (/ 1.0 (sin B)) (/ x B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.38) {
		tmp = (-1.0 / sin(B)) - (x / B);
	} else if (F <= 0.135) {
		tmp = ((F * sqrt(0.5)) - x) / B;
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-0.38d0)) then
        tmp = ((-1.0d0) / sin(b)) - (x / b)
    else if (f <= 0.135d0) then
        tmp = ((f * sqrt(0.5d0)) - x) / b
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -0.38) {
		tmp = (-1.0 / Math.sin(B)) - (x / B);
	} else if (F <= 0.135) {
		tmp = ((F * Math.sqrt(0.5)) - x) / B;
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -0.38:
		tmp = (-1.0 / math.sin(B)) - (x / B)
	elif F <= 0.135:
		tmp = ((F * math.sqrt(0.5)) - x) / B
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -0.38)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / B));
	elseif (F <= 0.135)
		tmp = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B);
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -0.38)
		tmp = (-1.0 / sin(B)) - (x / B);
	elseif (F <= 0.135)
		tmp = ((F * sqrt(0.5)) - x) / B;
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -0.38], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.135], N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 21: 43.6% accurate, 21.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -7.7 \cdot 10^{-31}:\\ \;\;\;\;\frac{-1 - x}{B} + B \cdot \left(x \cdot 0.3333333333333333 - 0.16666666666666666\right)\\ \mathbf{elif}\;F \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;B \cdot 0.16666666666666666 + \frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -7.7e-31)
   (+ (/ (- -1.0 x) B) (* B (- (* x 0.3333333333333333) 0.16666666666666666)))
   (if (<= F 1.9e-121)
     (- (/ x B))
     (+ (* B 0.16666666666666666) (/ (- 1.0 x) B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.7e-31) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-7.7d-31)) then
        tmp = (((-1.0d0) - x) / b) + (b * ((x * 0.3333333333333333d0) - 0.16666666666666666d0))
    else if (f <= 1.9d-121) then
        tmp = -(x / b)
    else
        tmp = (b * 0.16666666666666666d0) + ((1.0d0 - x) / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -7.7e-31) {
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	} else if (F <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -7.7e-31:
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666))
	elif F <= 1.9e-121:
		tmp = -(x / B)
	else:
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -7.7e-31)
		tmp = Float64(Float64(Float64(-1.0 - x) / B) + Float64(B * Float64(Float64(x * 0.3333333333333333) - 0.16666666666666666)));
	elseif (F <= 1.9e-121)
		tmp = Float64(-Float64(x / B));
	else
		tmp = Float64(Float64(B * 0.16666666666666666) + Float64(Float64(1.0 - x) / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -7.7e-31)
		tmp = ((-1.0 - x) / B) + (B * ((x * 0.3333333333333333) - 0.16666666666666666));
	elseif (F <= 1.9e-121)
		tmp = -(x / B);
	else
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -7.7e-31], N[(N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision] + N[(B * N[(N[(x * 0.3333333333333333), $MachinePrecision] - 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 1.9e-121], (-N[(x / B), $MachinePrecision]), N[(N[(B * 0.16666666666666666), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 22: 43.5% accurate, 24.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -3.15 \cdot 10^{-34}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;B \cdot 0.16666666666666666 + \frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -3.15e-34)
   (/ (- -1.0 x) B)
   (if (<= F 1.9e-121)
     (- (/ x B))
     (+ (* B 0.16666666666666666) (/ (- 1.0 x) B)))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.15e-34) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-3.15d-34)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 1.9d-121) then
        tmp = -(x / b)
    else
        tmp = (b * 0.16666666666666666d0) + ((1.0d0 - x) / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -3.15e-34) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -3.15e-34:
		tmp = (-1.0 - x) / B
	elif F <= 1.9e-121:
		tmp = -(x / B)
	else:
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -3.15e-34)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 1.9e-121)
		tmp = Float64(-Float64(x / B));
	else
		tmp = Float64(Float64(B * 0.16666666666666666) + Float64(Float64(1.0 - x) / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -3.15e-34)
		tmp = (-1.0 - x) / B;
	elseif (F <= 1.9e-121)
		tmp = -(x / B);
	else
		tmp = (B * 0.16666666666666666) + ((1.0 - x) / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -3.15e-34], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 1.9e-121], (-N[(x / B), $MachinePrecision]), N[(N[(B * 0.16666666666666666), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 23: 43.5% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.7e-32)
   (/ (- -1.0 x) B)
   (if (<= F 1.9e-121) (- (/ x B)) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.7e-32) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.9e-121) {
		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 <= (-1.7d-32)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 1.9d-121) 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 <= -1.7e-32) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.7e-32:
		tmp = (-1.0 - x) / B
	elif F <= 1.9e-121:
		tmp = -(x / B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.7e-32)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 1.9e-121)
		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 <= -1.7e-32)
		tmp = (-1.0 - x) / B;
	elseif (F <= 1.9e-121)
		tmp = -(x / B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.7e-32], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 1.9e-121], (-N[(x / B), $MachinePrecision]), N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 24: 36.7% accurate, 45.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq 1.9 \cdot 10^{-121}:\\ \;\;\;\;-\frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F 1.9e-121) (- (/ x B)) (/ (- 1.0 x) B)))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= 1.9e-121) {
		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 <= 1.9d-121) 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 <= 1.9e-121) {
		tmp = -(x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= 1.9e-121:
		tmp = -(x / B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= 1.9e-121)
		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 <= 1.9e-121)
		tmp = -(x / B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, 1.9e-121], (-N[(x / B), $MachinePrecision]), N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]

Derivation

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

Alternative 25: 29.7% accurate, 81.0× speedup

Math

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

FPCore

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

C

double code(double F, double B, double x) {
	return -(x / 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 = -(x / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023347 
(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))))))