VandenBroeck and Keller, Equation (23)

Percentage Accurate: 76.1% → 99.6%

Time: 19.2s

Alternatives: 20

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: 76.1% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 58000000:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.5e+62)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 58000000.0)
       (- (* (/ 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 <= -1.5e+62) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 58000000.0) {
		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 <= (-1.5d+62)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 58000000.0d0) 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 <= -1.5e+62) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 58000000.0) {
		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 <= -1.5e+62:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 58000000.0:
		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 <= -1.5e+62)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 58000000.0)
		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 <= -1.5e+62)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 58000000.0)
		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, -1.5e+62], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 58000000.0], 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

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1. Add Preprocessing

Alternative 2: 99.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -1.3:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 1.36:\\ \;\;\;\;x \cdot \frac{-1}{\tan B} + \frac{F}{\sin B \cdot \sqrt{2 + x \cdot 2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -1.3)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 1.36)
       (+ (* x (/ -1.0 (tan B))) (/ F (* (sin B) (sqrt (+ 2.0 (* x 2.0))))))
       (- (/ 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 <= -1.3) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 1.36) {
		tmp = (x * (-1.0 / tan(B))) + (F / (sin(B) * sqrt((2.0 + (x * 2.0)))));
	} 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 <= (-1.3d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 1.36d0) then
        tmp = (x * ((-1.0d0) / tan(b))) + (f / (sin(b) * sqrt((2.0d0 + (x * 2.0d0)))))
    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 <= -1.3) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 1.36) {
		tmp = (x * (-1.0 / Math.tan(B))) + (F / (Math.sin(B) * Math.sqrt((2.0 + (x * 2.0)))));
	} 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 <= -1.3:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 1.36:
		tmp = (x * (-1.0 / math.tan(B))) + (F / (math.sin(B) * math.sqrt((2.0 + (x * 2.0)))))
	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 <= -1.3)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 1.36)
		tmp = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64(F / Float64(sin(B) * sqrt(Float64(2.0 + Float64(x * 2.0))))));
	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 <= -1.3)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 1.36)
		tmp = (x * (-1.0 / tan(B))) + (F / (sin(B) * sqrt((2.0 + (x * 2.0)))));
	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, -1.3], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 1.36], N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(F / N[(N[Sin[B], $MachinePrecision] * N[Sqrt[N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 3: 92.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{-1}{\tan B} + {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B}\\ t_1 := \frac{1}{\sin B}\\ t_2 := \left(F \cdot t_1\right) \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ t_3 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.00019:\\ \;\;\;\;\frac{-1}{\sin B} - t_3\\ \mathbf{elif}\;F \leq -4.15 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;F \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 6.6 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;F \leq 26500000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 - t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0
         (+
          (* x (/ -1.0 (tan B)))
          (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B))))
        (t_1 (/ 1.0 (sin B)))
        (t_2 (- (* (* F t_1) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B)))
        (t_3 (/ x (tan B))))
   (if (<= F -0.00019)
     (- (/ -1.0 (sin B)) t_3)
     (if (<= F -4.15e-32)
       t_2
       (if (<= F 3.8e-76)
         t_0
         (if (<= F 6.6e-31) t_2 (if (<= F 26500000.0) t_0 (- t_1 t_3))))))))

C

double code(double F, double B, double x) {
	double t_0 = (x * (-1.0 / tan(B))) + (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B));
	double t_1 = 1.0 / sin(B);
	double t_2 = ((F * t_1) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	double t_3 = x / tan(B);
	double tmp;
	if (F <= -0.00019) {
		tmp = (-1.0 / sin(B)) - t_3;
	} else if (F <= -4.15e-32) {
		tmp = t_2;
	} else if (F <= 3.8e-76) {
		tmp = t_0;
	} else if (F <= 6.6e-31) {
		tmp = t_2;
	} else if (F <= 26500000.0) {
		tmp = t_0;
	} else {
		tmp = t_1 - t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = (x * ((-1.0d0) / tan(b))) + (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b))
    t_1 = 1.0d0 / sin(b)
    t_2 = ((f * t_1) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    t_3 = x / tan(b)
    if (f <= (-0.00019d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_3
    else if (f <= (-4.15d-32)) then
        tmp = t_2
    else if (f <= 3.8d-76) then
        tmp = t_0
    else if (f <= 6.6d-31) then
        tmp = t_2
    else if (f <= 26500000.0d0) then
        tmp = t_0
    else
        tmp = t_1 - t_3
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = (x * (-1.0 / Math.tan(B))) + (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B));
	double t_1 = 1.0 / Math.sin(B);
	double t_2 = ((F * t_1) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	double t_3 = x / Math.tan(B);
	double tmp;
	if (F <= -0.00019) {
		tmp = (-1.0 / Math.sin(B)) - t_3;
	} else if (F <= -4.15e-32) {
		tmp = t_2;
	} else if (F <= 3.8e-76) {
		tmp = t_0;
	} else if (F <= 6.6e-31) {
		tmp = t_2;
	} else if (F <= 26500000.0) {
		tmp = t_0;
	} else {
		tmp = t_1 - t_3;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = (x * (-1.0 / math.tan(B))) + (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B))
	t_1 = 1.0 / math.sin(B)
	t_2 = ((F * t_1) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	t_3 = x / math.tan(B)
	tmp = 0
	if F <= -0.00019:
		tmp = (-1.0 / math.sin(B)) - t_3
	elif F <= -4.15e-32:
		tmp = t_2
	elif F <= 3.8e-76:
		tmp = t_0
	elif F <= 6.6e-31:
		tmp = t_2
	elif F <= 26500000.0:
		tmp = t_0
	else:
		tmp = t_1 - t_3
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(x * Float64(-1.0 / tan(B))) + Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)))
	t_1 = Float64(1.0 / sin(B))
	t_2 = Float64(Float64(Float64(F * t_1) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B))
	t_3 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -0.00019)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_3);
	elseif (F <= -4.15e-32)
		tmp = t_2;
	elseif (F <= 3.8e-76)
		tmp = t_0;
	elseif (F <= 6.6e-31)
		tmp = t_2;
	elseif (F <= 26500000.0)
		tmp = t_0;
	else
		tmp = Float64(t_1 - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = (x * (-1.0 / tan(B))) + (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B));
	t_1 = 1.0 / sin(B);
	t_2 = ((F * t_1) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	t_3 = x / tan(B);
	tmp = 0.0;
	if (F <= -0.00019)
		tmp = (-1.0 / sin(B)) - t_3;
	elseif (F <= -4.15e-32)
		tmp = t_2;
	elseif (F <= 3.8e-76)
		tmp = t_0;
	elseif (F <= 6.6e-31)
		tmp = t_2;
	elseif (F <= 26500000.0)
		tmp = t_0;
	else
		tmp = t_1 - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(N[(x * N[(-1.0 / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(F * t$95$1), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -0.00019], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[F, -4.15e-32], t$95$2, If[LessEqual[F, 3.8e-76], t$95$0, If[LessEqual[F, 6.6e-31], t$95$2, If[LessEqual[F, 26500000.0], t$95$0, N[(t$95$1 - t$95$3), $MachinePrecision]]]]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 89.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -0.0006:\\ \;\;\;\;\frac{-1}{\sin B} - t_1\\ \mathbf{elif}\;F \leq -6 \cdot 10^{-84}:\\ \;\;\;\;\left(F \cdot t_0\right) \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 1.1 \cdot 10^{-174}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{elif}\;F \leq 26500000:\\ \;\;\;\;\frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;t_0 - t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B))) (t_1 (/ x (tan B))))
   (if (<= F -0.0006)
     (- (/ -1.0 (sin B)) t_1)
     (if (<= F -6e-84)
       (- (* (* F t_0) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B))
       (if (<= F 1.1e-174)
         (/ (- x) (tan B))
         (if (<= F 26500000.0)
           (-
            (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5))
            (/ x B))
           (- t_0 t_1)))))))

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 <= -0.0006) {
		tmp = (-1.0 / sin(B)) - t_1;
	} else if (F <= -6e-84) {
		tmp = ((F * t_0) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 1.1e-174) {
		tmp = -x / tan(B);
	} else if (F <= 26500000.0) {
		tmp = ((F / sin(B)) * pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	} else {
		tmp = t_0 - 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 = 1.0d0 / sin(b)
    t_1 = x / tan(b)
    if (f <= (-0.0006d0)) then
        tmp = ((-1.0d0) / sin(b)) - t_1
    else if (f <= (-6d-84)) then
        tmp = ((f * t_0) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    else if (f <= 1.1d-174) then
        tmp = -x / tan(b)
    else if (f <= 26500000.0d0) then
        tmp = ((f / sin(b)) * ((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0))) - (x / b)
    else
        tmp = t_0 - t_1
    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 <= -0.0006) {
		tmp = (-1.0 / Math.sin(B)) - t_1;
	} else if (F <= -6e-84) {
		tmp = ((F * t_0) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	} else if (F <= 1.1e-174) {
		tmp = -x / Math.tan(B);
	} else if (F <= 26500000.0) {
		tmp = ((F / Math.sin(B)) * Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B);
	} else {
		tmp = t_0 - t_1;
	}
	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 <= -0.0006:
		tmp = (-1.0 / math.sin(B)) - t_1
	elif F <= -6e-84:
		tmp = ((F * t_0) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	elif F <= 1.1e-174:
		tmp = -x / math.tan(B)
	elif F <= 26500000.0:
		tmp = ((F / math.sin(B)) * math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5)) - (x / B)
	else:
		tmp = t_0 - t_1
	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 <= -0.0006)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_1);
	elseif (F <= -6e-84)
		tmp = Float64(Float64(Float64(F * t_0) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B));
	elseif (F <= 1.1e-174)
		tmp = Float64(Float64(-x) / tan(B));
	elseif (F <= 26500000.0)
		tmp = Float64(Float64(Float64(F / sin(B)) * (Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5)) - Float64(x / B));
	else
		tmp = Float64(t_0 - t_1);
	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 <= -0.0006)
		tmp = (-1.0 / sin(B)) - t_1;
	elseif (F <= -6e-84)
		tmp = ((F * t_0) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	elseif (F <= 1.1e-174)
		tmp = -x / tan(B);
	elseif (F <= 26500000.0)
		tmp = ((F / sin(B)) * ((((F * F) + 2.0) + (x * 2.0)) ^ -0.5)) - (x / B);
	else
		tmp = t_0 - t_1;
	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, -0.0006], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[F, -6e-84], N[(N[(N[(F * t$95$0), $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, 1.1e-174], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 26500000.0], 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], N[(t$95$0 - t$95$1), $MachinePrecision]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 89.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\sin B}\\ t_1 := \left(F \cdot t_0\right) \cdot \sqrt{\frac{1}{2 + x \cdot 2}} - \frac{x}{B}\\ t_2 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -5.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{-1}{\sin B} - t_2\\ \mathbf{elif}\;F \leq -5.4 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 9 \cdot 10^{-175}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{elif}\;F \leq 0.022:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 - t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ 1.0 (sin B)))
        (t_1 (- (* (* F t_0) (sqrt (/ 1.0 (+ 2.0 (* x 2.0))))) (/ x B)))
        (t_2 (/ x (tan B))))
   (if (<= F -5.5e-5)
     (- (/ -1.0 (sin B)) t_2)
     (if (<= F -5.4e-83)
       t_1
       (if (<= F 9e-175)
         (/ (- x) (tan B))
         (if (<= F 0.022) t_1 (- t_0 t_2)))))))

C

double code(double F, double B, double x) {
	double t_0 = 1.0 / sin(B);
	double t_1 = ((F * t_0) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	double t_2 = x / tan(B);
	double tmp;
	if (F <= -5.5e-5) {
		tmp = (-1.0 / sin(B)) - t_2;
	} else if (F <= -5.4e-83) {
		tmp = t_1;
	} else if (F <= 9e-175) {
		tmp = -x / tan(B);
	} else if (F <= 0.022) {
		tmp = t_1;
	} else {
		tmp = t_0 - 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 = 1.0d0 / sin(b)
    t_1 = ((f * t_0) * sqrt((1.0d0 / (2.0d0 + (x * 2.0d0))))) - (x / b)
    t_2 = x / tan(b)
    if (f <= (-5.5d-5)) then
        tmp = ((-1.0d0) / sin(b)) - t_2
    else if (f <= (-5.4d-83)) then
        tmp = t_1
    else if (f <= 9d-175) then
        tmp = -x / tan(b)
    else if (f <= 0.022d0) then
        tmp = t_1
    else
        tmp = t_0 - t_2
    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 = ((F * t_0) * Math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	double t_2 = x / Math.tan(B);
	double tmp;
	if (F <= -5.5e-5) {
		tmp = (-1.0 / Math.sin(B)) - t_2;
	} else if (F <= -5.4e-83) {
		tmp = t_1;
	} else if (F <= 9e-175) {
		tmp = -x / Math.tan(B);
	} else if (F <= 0.022) {
		tmp = t_1;
	} else {
		tmp = t_0 - t_2;
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = 1.0 / math.sin(B)
	t_1 = ((F * t_0) * math.sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B)
	t_2 = x / math.tan(B)
	tmp = 0
	if F <= -5.5e-5:
		tmp = (-1.0 / math.sin(B)) - t_2
	elif F <= -5.4e-83:
		tmp = t_1
	elif F <= 9e-175:
		tmp = -x / math.tan(B)
	elif F <= 0.022:
		tmp = t_1
	else:
		tmp = t_0 - t_2
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(1.0 / sin(B))
	t_1 = Float64(Float64(Float64(F * t_0) * sqrt(Float64(1.0 / Float64(2.0 + Float64(x * 2.0))))) - Float64(x / B))
	t_2 = Float64(x / tan(B))
	tmp = 0.0
	if (F <= -5.5e-5)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_2);
	elseif (F <= -5.4e-83)
		tmp = t_1;
	elseif (F <= 9e-175)
		tmp = Float64(Float64(-x) / tan(B));
	elseif (F <= 0.022)
		tmp = t_1;
	else
		tmp = Float64(t_0 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = 1.0 / sin(B);
	t_1 = ((F * t_0) * sqrt((1.0 / (2.0 + (x * 2.0))))) - (x / B);
	t_2 = x / tan(B);
	tmp = 0.0;
	if (F <= -5.5e-5)
		tmp = (-1.0 / sin(B)) - t_2;
	elseif (F <= -5.4e-83)
		tmp = t_1;
	elseif (F <= 9e-175)
		tmp = -x / tan(B);
	elseif (F <= 0.022)
		tmp = t_1;
	else
		tmp = t_0 - t_2;
	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[(F * t$95$0), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -5.5e-5], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[F, -5.4e-83], t$95$1, If[LessEqual[F, 9e-175], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 0.022], t$95$1, N[(t$95$0 - t$95$2), $MachinePrecision]]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 6: 72.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{\tan B}\\ t_1 := \left(F \cdot \frac{1}{\sin B}\right) \cdot \frac{1}{F} - \frac{x}{B}\\ \mathbf{if}\;F \leq -7.2 \cdot 10^{-33}:\\ \;\;\;\;\frac{-1}{\sin B} - \frac{x}{\tan B}\\ \mathbf{elif}\;F \leq 4.3 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 5 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;F \leq 1.92 \cdot 10^{+164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;F \leq 1.85 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{\frac{\sin B}{\cos B}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ (- x) (tan B)))
        (t_1 (- (* (* F (/ 1.0 (sin B))) (/ 1.0 F)) (/ x B))))
   (if (<= F -7.2e-33)
     (- (/ -1.0 (sin B)) (/ x (tan B)))
     (if (<= F 4.3e+18)
       t_0
       (if (<= F 5e+105)
         t_1
         (if (<= F 1.92e+164)
           t_0
           (if (<= F 1.85e+236) t_1 (/ (- x) (/ (sin B) (cos B))))))))))

C

double code(double F, double B, double x) {
	double t_0 = -x / tan(B);
	double t_1 = ((F * (1.0 / sin(B))) * (1.0 / F)) - (x / B);
	double tmp;
	if (F <= -7.2e-33) {
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	} else if (F <= 4.3e+18) {
		tmp = t_0;
	} else if (F <= 5e+105) {
		tmp = t_1;
	} else if (F <= 1.92e+164) {
		tmp = t_0;
	} else if (F <= 1.85e+236) {
		tmp = t_1;
	} else {
		tmp = -x / (sin(B) / cos(B));
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = -x / tan(b)
    t_1 = ((f * (1.0d0 / sin(b))) * (1.0d0 / f)) - (x / b)
    if (f <= (-7.2d-33)) then
        tmp = ((-1.0d0) / sin(b)) - (x / tan(b))
    else if (f <= 4.3d+18) then
        tmp = t_0
    else if (f <= 5d+105) then
        tmp = t_1
    else if (f <= 1.92d+164) then
        tmp = t_0
    else if (f <= 1.85d+236) then
        tmp = t_1
    else
        tmp = -x / (sin(b) / cos(b))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = -x / Math.tan(B);
	double t_1 = ((F * (1.0 / Math.sin(B))) * (1.0 / F)) - (x / B);
	double tmp;
	if (F <= -7.2e-33) {
		tmp = (-1.0 / Math.sin(B)) - (x / Math.tan(B));
	} else if (F <= 4.3e+18) {
		tmp = t_0;
	} else if (F <= 5e+105) {
		tmp = t_1;
	} else if (F <= 1.92e+164) {
		tmp = t_0;
	} else if (F <= 1.85e+236) {
		tmp = t_1;
	} else {
		tmp = -x / (Math.sin(B) / Math.cos(B));
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = -x / math.tan(B)
	t_1 = ((F * (1.0 / math.sin(B))) * (1.0 / F)) - (x / B)
	tmp = 0
	if F <= -7.2e-33:
		tmp = (-1.0 / math.sin(B)) - (x / math.tan(B))
	elif F <= 4.3e+18:
		tmp = t_0
	elif F <= 5e+105:
		tmp = t_1
	elif F <= 1.92e+164:
		tmp = t_0
	elif F <= 1.85e+236:
		tmp = t_1
	else:
		tmp = -x / (math.sin(B) / math.cos(B))
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(Float64(-x) / tan(B))
	t_1 = Float64(Float64(Float64(F * Float64(1.0 / sin(B))) * Float64(1.0 / F)) - Float64(x / B))
	tmp = 0.0
	if (F <= -7.2e-33)
		tmp = Float64(Float64(-1.0 / sin(B)) - Float64(x / tan(B)));
	elseif (F <= 4.3e+18)
		tmp = t_0;
	elseif (F <= 5e+105)
		tmp = t_1;
	elseif (F <= 1.92e+164)
		tmp = t_0;
	elseif (F <= 1.85e+236)
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) / Float64(sin(B) / cos(B)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = -x / tan(B);
	t_1 = ((F * (1.0 / sin(B))) * (1.0 / F)) - (x / B);
	tmp = 0.0;
	if (F <= -7.2e-33)
		tmp = (-1.0 / sin(B)) - (x / tan(B));
	elseif (F <= 4.3e+18)
		tmp = t_0;
	elseif (F <= 5e+105)
		tmp = t_1;
	elseif (F <= 1.92e+164)
		tmp = t_0;
	elseif (F <= 1.85e+236)
		tmp = t_1;
	else
		tmp = -x / (sin(B) / cos(B));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(F * N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -7.2e-33], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / N[Tan[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[F, 4.3e+18], t$95$0, If[LessEqual[F, 5e+105], t$95$1, If[LessEqual[F, 1.92e+164], t$95$0, If[LessEqual[F, 1.85e+236], t$95$1, N[((-x) / N[(N[Sin[B], $MachinePrecision] / N[Cos[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 7: 85.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\tan B}\\ \mathbf{if}\;F \leq -2.65 \cdot 10^{-34}:\\ \;\;\;\;\frac{-1}{\sin B} - t_0\\ \mathbf{elif}\;F \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (/ x (tan B))))
   (if (<= F -2.65e-34)
     (- (/ -1.0 (sin B)) t_0)
     (if (<= F 2.5e-84) (/ (- x) (tan 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 <= -2.65e-34) {
		tmp = (-1.0 / sin(B)) - t_0;
	} else if (F <= 2.5e-84) {
		tmp = -x / tan(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 <= (-2.65d-34)) then
        tmp = ((-1.0d0) / sin(b)) - t_0
    else if (f <= 2.5d-84) then
        tmp = -x / tan(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 <= -2.65e-34) {
		tmp = (-1.0 / Math.sin(B)) - t_0;
	} else if (F <= 2.5e-84) {
		tmp = -x / Math.tan(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 <= -2.65e-34:
		tmp = (-1.0 / math.sin(B)) - t_0
	elif F <= 2.5e-84:
		tmp = -x / math.tan(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 <= -2.65e-34)
		tmp = Float64(Float64(-1.0 / sin(B)) - t_0);
	elseif (F <= 2.5e-84)
		tmp = Float64(Float64(-x) / tan(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 <= -2.65e-34)
		tmp = (-1.0 / sin(B)) - t_0;
	elseif (F <= 2.5e-84)
		tmp = -x / tan(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, -2.65e-34], N[(N[(-1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[F, 2.5e-84], N[((-x) / N[Tan[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: 59.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := F \cdot \frac{1}{\sin B}\\ \mathbf{if}\;F \leq -1.15:\\ \;\;\;\;t_0 \cdot \frac{-1}{F} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 4.3 \cdot 10^{+18} \lor \neg \left(F \leq 4.3 \cdot 10^{+105} \lor \neg \left(F \leq 1.92 \cdot 10^{+164}\right) \land F \leq 1.12 \cdot 10^{+236}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{1}{F} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (let* ((t_0 (* F (/ 1.0 (sin B)))))
   (if (<= F -1.15)
     (- (* t_0 (/ -1.0 F)) (/ x B))
     (if (or (<= F 4.3e+18)
             (not
              (or (<= F 4.3e+105)
                  (and (not (<= F 1.92e+164)) (<= F 1.12e+236)))))
       (/ (- x) (tan B))
       (- (* t_0 (/ 1.0 F)) (/ x B))))))

C

double code(double F, double B, double x) {
	double t_0 = F * (1.0 / sin(B));
	double tmp;
	if (F <= -1.15) {
		tmp = (t_0 * (-1.0 / F)) - (x / B);
	} else if ((F <= 4.3e+18) || !((F <= 4.3e+105) || (!(F <= 1.92e+164) && (F <= 1.12e+236)))) {
		tmp = -x / tan(B);
	} else {
		tmp = (t_0 * (1.0 / F)) - (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) :: tmp
    t_0 = f * (1.0d0 / sin(b))
    if (f <= (-1.15d0)) then
        tmp = (t_0 * ((-1.0d0) / f)) - (x / b)
    else if ((f <= 4.3d+18) .or. (.not. (f <= 4.3d+105) .or. (.not. (f <= 1.92d+164)) .and. (f <= 1.12d+236))) then
        tmp = -x / tan(b)
    else
        tmp = (t_0 * (1.0d0 / f)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double t_0 = F * (1.0 / Math.sin(B));
	double tmp;
	if (F <= -1.15) {
		tmp = (t_0 * (-1.0 / F)) - (x / B);
	} else if ((F <= 4.3e+18) || !((F <= 4.3e+105) || (!(F <= 1.92e+164) && (F <= 1.12e+236)))) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (t_0 * (1.0 / F)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	t_0 = F * (1.0 / math.sin(B))
	tmp = 0
	if F <= -1.15:
		tmp = (t_0 * (-1.0 / F)) - (x / B)
	elif (F <= 4.3e+18) or not ((F <= 4.3e+105) or (not (F <= 1.92e+164) and (F <= 1.12e+236))):
		tmp = -x / math.tan(B)
	else:
		tmp = (t_0 * (1.0 / F)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	t_0 = Float64(F * Float64(1.0 / sin(B)))
	tmp = 0.0
	if (F <= -1.15)
		tmp = Float64(Float64(t_0 * Float64(-1.0 / F)) - Float64(x / B));
	elseif ((F <= 4.3e+18) || !((F <= 4.3e+105) || (!(F <= 1.92e+164) && (F <= 1.12e+236))))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(t_0 * Float64(1.0 / F)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	t_0 = F * (1.0 / sin(B));
	tmp = 0.0;
	if (F <= -1.15)
		tmp = (t_0 * (-1.0 / F)) - (x / B);
	elseif ((F <= 4.3e+18) || ~(((F <= 4.3e+105) || (~((F <= 1.92e+164)) && (F <= 1.12e+236)))))
		tmp = -x / tan(B);
	else
		tmp = (t_0 * (1.0 / F)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := Block[{t$95$0 = N[(F * N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[F, -1.15], N[(N[(t$95$0 * N[(-1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 4.3e+18], N[Not[Or[LessEqual[F, 4.3e+105], And[N[Not[LessEqual[F, 1.92e+164]], $MachinePrecision], LessEqual[F, 1.12e+236]]]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * N[(1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 9: 62.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-126} \lor \neg \left(x \leq 3.55 \cdot 10^{-186}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;{\left(\left(F \cdot F + 2\right) + x \cdot 2\right)}^{-0.5} \cdot \frac{F}{B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (or (<= x -5.8e-126) (not (<= x 3.55e-186)))
   (/ (- x) (tan B))
   (- (* (pow (+ (+ (* F F) 2.0) (* x 2.0)) -0.5) (/ F B)) (/ x B))))

C

double code(double F, double B, double x) {
	double tmp;
	if ((x <= -5.8e-126) || !(x <= 3.55e-186)) {
		tmp = -x / tan(B);
	} else {
		tmp = (pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / 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 ((x <= (-5.8d-126)) .or. (.not. (x <= 3.55d-186))) then
        tmp = -x / tan(b)
    else
        tmp = (((((f * f) + 2.0d0) + (x * 2.0d0)) ** (-0.5d0)) * (f / b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if ((x <= -5.8e-126) || !(x <= 3.55e-186)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (Math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B);
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if (x <= -5.8e-126) or not (x <= 3.55e-186):
		tmp = -x / math.tan(B)
	else:
		tmp = (math.pow((((F * F) + 2.0) + (x * 2.0)), -0.5) * (F / B)) - (x / B)
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if ((x <= -5.8e-126) || !(x <= 3.55e-186))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64((Float64(Float64(Float64(F * F) + 2.0) + Float64(x * 2.0)) ^ -0.5) * Float64(F / B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if ((x <= -5.8e-126) || ~((x <= 3.55e-186)))
		tmp = -x / tan(B);
	else
		tmp = (((((F * F) + 2.0) + (x * 2.0)) ^ -0.5) * (F / B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[Or[LessEqual[x, -5.8e-126], N[Not[LessEqual[x, 3.55e-186]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], 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]]

Derivation

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

Alternative 10: 59.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.15:\\ \;\;\;\;\left(F \cdot \frac{1}{\sin B}\right) \cdot \frac{-1}{F} - \frac{x}{B}\\ \mathbf{elif}\;F \leq 4.6 \cdot 10^{+18} \lor \neg \left(F \leq 3.25 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.15)
   (- (* (* F (/ 1.0 (sin B))) (/ -1.0 F)) (/ x B))
   (if (or (<= F 4.6e+18) (not (<= F 3.25e+237)))
     (/ (- x) (tan B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.15) {
		tmp = ((F * (1.0 / sin(B))) * (-1.0 / F)) - (x / B);
	} else if ((F <= 4.6e+18) || !(F <= 3.25e+237)) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-1.15d0)) then
        tmp = ((f * (1.0d0 / sin(b))) * ((-1.0d0) / f)) - (x / b)
    else if ((f <= 4.6d+18) .or. (.not. (f <= 3.25d+237))) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.15) {
		tmp = ((F * (1.0 / Math.sin(B))) * (-1.0 / F)) - (x / B);
	} else if ((F <= 4.6e+18) || !(F <= 3.25e+237)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.15:
		tmp = ((F * (1.0 / math.sin(B))) * (-1.0 / F)) - (x / B)
	elif (F <= 4.6e+18) or not (F <= 3.25e+237):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.15)
		tmp = Float64(Float64(Float64(F * Float64(1.0 / sin(B))) * Float64(-1.0 / F)) - Float64(x / B));
	elseif ((F <= 4.6e+18) || !(F <= 3.25e+237))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.15)
		tmp = ((F * (1.0 / sin(B))) * (-1.0 / F)) - (x / B);
	elseif ((F <= 4.6e+18) || ~((F <= 3.25e+237)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.15], N[(N[(N[(F * N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / F), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 4.6e+18], N[Not[LessEqual[F, 3.25e+237]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 11: 59.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-126} \lor \neg \left(x \leq 2.55 \cdot 10^{-185}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5} - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (or (<= x -5.8e-126) (not (<= x 2.55e-185)))
   (/ (- x) (tan B))
   (/ (- (* F (sqrt 0.5)) x) B)))

C

double code(double F, double B, double x) {
	double tmp;
	if ((x <= -5.8e-126) || !(x <= 2.55e-185)) {
		tmp = -x / tan(B);
	} else {
		tmp = ((F * sqrt(0.5)) - 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 ((x <= (-5.8d-126)) .or. (.not. (x <= 2.55d-185))) then
        tmp = -x / tan(b)
    else
        tmp = ((f * sqrt(0.5d0)) - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if ((x <= -5.8e-126) || !(x <= 2.55e-185)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = ((F * Math.sqrt(0.5)) - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if (x <= -5.8e-126) or not (x <= 2.55e-185):
		tmp = -x / math.tan(B)
	else:
		tmp = ((F * math.sqrt(0.5)) - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if ((x <= -5.8e-126) || !(x <= 2.55e-185))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(Float64(F * sqrt(0.5)) - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if ((x <= -5.8e-126) || ~((x <= 2.55e-185)))
		tmp = -x / tan(B);
	else
		tmp = ((F * sqrt(0.5)) - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[Or[LessEqual[x, -5.8e-126], N[Not[LessEqual[x, 2.55e-185]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision] / B), $MachinePrecision]]

Derivation

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

Alternative 12: 57.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.18 \cdot 10^{+61}:\\ \;\;\;\;\left(\frac{-1}{B} - B \cdot 0.16666666666666666\right) - \frac{x}{B}\\ \mathbf{elif}\;F \leq 5.2 \cdot 10^{+18} \lor \neg \left(F \leq 5.8 \cdot 10^{+236}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.18e+61)
   (- (- (/ -1.0 B) (* B 0.16666666666666666)) (/ x B))
   (if (or (<= F 5.2e+18) (not (<= F 5.8e+236)))
     (/ (- x) (tan B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.18e+61) {
		tmp = ((-1.0 / B) - (B * 0.16666666666666666)) - (x / B);
	} else if ((F <= 5.2e+18) || !(F <= 5.8e+236)) {
		tmp = -x / tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-1.18d+61)) then
        tmp = (((-1.0d0) / b) - (b * 0.16666666666666666d0)) - (x / b)
    else if ((f <= 5.2d+18) .or. (.not. (f <= 5.8d+236))) then
        tmp = -x / tan(b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.18e+61) {
		tmp = ((-1.0 / B) - (B * 0.16666666666666666)) - (x / B);
	} else if ((F <= 5.2e+18) || !(F <= 5.8e+236)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.18e+61:
		tmp = ((-1.0 / B) - (B * 0.16666666666666666)) - (x / B)
	elif (F <= 5.2e+18) or not (F <= 5.8e+236):
		tmp = -x / math.tan(B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.18e+61)
		tmp = Float64(Float64(Float64(-1.0 / B) - Float64(B * 0.16666666666666666)) - Float64(x / B));
	elseif ((F <= 5.2e+18) || !(F <= 5.8e+236))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -1.18e+61)
		tmp = ((-1.0 / B) - (B * 0.16666666666666666)) - (x / B);
	elseif ((F <= 5.2e+18) || ~((F <= 5.8e+236)))
		tmp = -x / tan(B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.18e+61], N[(N[(N[(-1.0 / B), $MachinePrecision] - N[(B * 0.16666666666666666), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[F, 5.2e+18], N[Not[LessEqual[F, 5.8e+236]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 13: 58.5% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{-167} \lor \neg \left(x \leq 6.4 \cdot 10^{-186}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{F}{\frac{B}{\sqrt{0.5}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (or (<= x -3.3e-167) (not (<= x 6.4e-186)))
   (/ (- x) (tan B))
   (/ F (/ B (sqrt 0.5)))))

C

double code(double F, double B, double x) {
	double tmp;
	if ((x <= -3.3e-167) || !(x <= 6.4e-186)) {
		tmp = -x / tan(B);
	} else {
		tmp = F / (B / sqrt(0.5));
	}
	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 ((x <= (-3.3d-167)) .or. (.not. (x <= 6.4d-186))) then
        tmp = -x / tan(b)
    else
        tmp = f / (b / sqrt(0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if ((x <= -3.3e-167) || !(x <= 6.4e-186)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = F / (B / Math.sqrt(0.5));
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if (x <= -3.3e-167) or not (x <= 6.4e-186):
		tmp = -x / math.tan(B)
	else:
		tmp = F / (B / math.sqrt(0.5))
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if ((x <= -3.3e-167) || !(x <= 6.4e-186))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(F / Float64(B / sqrt(0.5)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if ((x <= -3.3e-167) || ~((x <= 6.4e-186)))
		tmp = -x / tan(B);
	else
		tmp = F / (B / sqrt(0.5));
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[Or[LessEqual[x, -3.3e-167], N[Not[LessEqual[x, 6.4e-186]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(F / N[(B / N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 14: 58.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-171} \lor \neg \left(x \leq 2.1 \cdot 10^{-189}\right):\\ \;\;\;\;\frac{-x}{\tan B}\\ \mathbf{else}:\\ \;\;\;\;\frac{F \cdot \sqrt{0.5}}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (or (<= x -7e-171) (not (<= x 2.1e-189)))
   (/ (- x) (tan B))
   (/ (* F (sqrt 0.5)) B)))

C

double code(double F, double B, double x) {
	double tmp;
	if ((x <= -7e-171) || !(x <= 2.1e-189)) {
		tmp = -x / tan(B);
	} else {
		tmp = (F * sqrt(0.5)) / 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 ((x <= (-7d-171)) .or. (.not. (x <= 2.1d-189))) then
        tmp = -x / tan(b)
    else
        tmp = (f * sqrt(0.5d0)) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if ((x <= -7e-171) || !(x <= 2.1e-189)) {
		tmp = -x / Math.tan(B);
	} else {
		tmp = (F * Math.sqrt(0.5)) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if (x <= -7e-171) or not (x <= 2.1e-189):
		tmp = -x / math.tan(B)
	else:
		tmp = (F * math.sqrt(0.5)) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if ((x <= -7e-171) || !(x <= 2.1e-189))
		tmp = Float64(Float64(-x) / tan(B));
	else
		tmp = Float64(Float64(F * sqrt(0.5)) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if ((x <= -7e-171) || ~((x <= 2.1e-189)))
		tmp = -x / tan(B);
	else
		tmp = (F * sqrt(0.5)) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[Or[LessEqual[x, -7e-171], N[Not[LessEqual[x, 2.1e-189]], $MachinePrecision]], N[((-x) / N[Tan[B], $MachinePrecision]), $MachinePrecision], N[(N[(F * N[Sqrt[0.5], $MachinePrecision]), $MachinePrecision] / B), $MachinePrecision]]

Derivation

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

Alternative 15: 44.8% accurate, 18.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -6.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;B \cdot \left(x \cdot -0.16666666666666666 - x \cdot -0.5\right) - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -6.7e-49)
   (/ (- -1.0 x) B)
   (if (<= F 2.2e-40)
     (- (* B (- (* x -0.16666666666666666) (* x -0.5))) (/ x B))
     (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.7e-49) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 2.2e-40) {
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-6.7d-49)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 2.2d-40) then
        tmp = (b * ((x * (-0.16666666666666666d0)) - (x * (-0.5d0)))) - (x / b)
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -6.7e-49) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 2.2e-40) {
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -6.7e-49:
		tmp = (-1.0 - x) / B
	elif F <= 2.2e-40:
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B)
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -6.7e-49)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 2.2e-40)
		tmp = Float64(Float64(B * Float64(Float64(x * -0.16666666666666666) - Float64(x * -0.5))) - Float64(x / B));
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -6.7e-49)
		tmp = (-1.0 - x) / B;
	elseif (F <= 2.2e-40)
		tmp = (B * ((x * -0.16666666666666666) - (x * -0.5))) - (x / B);
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -6.7e-49], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 2.2e-40], N[(N[(B * N[(N[(x * -0.16666666666666666), $MachinePrecision] - N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 16: 37.3% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -2.4 \cdot 10^{+147}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{elif}\;F \leq 2.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -2.4e+147)
   (/ -1.0 B)
   (if (<= F 2.5e-84) (/ (- x) B) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.4e+147) {
		tmp = -1.0 / B;
	} else if (F <= 2.5e-84) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= (-2.4d+147)) then
        tmp = (-1.0d0) / b
    else if (f <= 2.5d-84) then
        tmp = -x / b
    else
        tmp = (1.0d0 - x) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= -2.4e+147) {
		tmp = -1.0 / B;
	} else if (F <= 2.5e-84) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -2.4e+147:
		tmp = -1.0 / B
	elif F <= 2.5e-84:
		tmp = -x / B
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -2.4e+147)
		tmp = Float64(-1.0 / B);
	elseif (F <= 2.5e-84)
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(Float64(1.0 - x) / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= -2.4e+147)
		tmp = -1.0 / B;
	elseif (F <= 2.5e-84)
		tmp = -x / B;
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -2.4e+147], N[(-1.0 / B), $MachinePrecision], If[LessEqual[F, 2.5e-84], N[((-x) / B), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 17: 44.6% accurate, 35.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{-1 - x}{B}\\ \mathbf{elif}\;F \leq 7.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (<= F -1.4e-46)
   (/ (- -1.0 x) B)
   (if (<= F 7.6e-86) (/ (- x) B) (/ (- 1.0 x) B))))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= -1.4e-46) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 7.6e-86) {
		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 <= (-1.4d-46)) then
        tmp = ((-1.0d0) - x) / b
    else if (f <= 7.6d-86) 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 <= -1.4e-46) {
		tmp = (-1.0 - x) / B;
	} else if (F <= 7.6e-86) {
		tmp = -x / B;
	} else {
		tmp = (1.0 - x) / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= -1.4e-46:
		tmp = (-1.0 - x) / B
	elif F <= 7.6e-86:
		tmp = -x / B
	else:
		tmp = (1.0 - x) / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= -1.4e-46)
		tmp = Float64(Float64(-1.0 - x) / B);
	elseif (F <= 7.6e-86)
		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 <= -1.4e-46)
		tmp = (-1.0 - x) / B;
	elseif (F <= 7.6e-86)
		tmp = -x / B;
	else
		tmp = (1.0 - x) / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, -1.4e-46], N[(N[(-1.0 - x), $MachinePrecision] / B), $MachinePrecision], If[LessEqual[F, 7.6e-86], N[((-x) / B), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]]]

Derivation

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

Alternative 18: 31.9% accurate, 39.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75 \cdot 10^{-81} \lor \neg \left(x \leq 4.2 \cdot 10^{-195}\right):\\ \;\;\;\;\frac{-x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x)
 :precision binary64
 (if (or (<= x -3.75e-81) (not (<= x 4.2e-195))) (/ (- x) B) (/ -1.0 B)))

C

double code(double F, double B, double x) {
	double tmp;
	if ((x <= -3.75e-81) || !(x <= 4.2e-195)) {
		tmp = -x / B;
	} else {
		tmp = -1.0 / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-3.75d-81)) .or. (.not. (x <= 4.2d-195))) then
        tmp = -x / b
    else
        tmp = (-1.0d0) / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if ((x <= -3.75e-81) || !(x <= 4.2e-195)) {
		tmp = -x / B;
	} else {
		tmp = -1.0 / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if (x <= -3.75e-81) or not (x <= 4.2e-195):
		tmp = -x / B
	else:
		tmp = -1.0 / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if ((x <= -3.75e-81) || !(x <= 4.2e-195))
		tmp = Float64(Float64(-x) / B);
	else
		tmp = Float64(-1.0 / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if ((x <= -3.75e-81) || ~((x <= 4.2e-195)))
		tmp = -x / B;
	else
		tmp = -1.0 / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[Or[LessEqual[x, -3.75e-81], N[Not[LessEqual[x, 4.2e-195]], $MachinePrecision]], N[((-x) / B), $MachinePrecision], N[(-1.0 / B), $MachinePrecision]]

Derivation

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

Alternative 19: 17.9% accurate, 64.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;F \leq 4.1 \cdot 10^{-60}:\\ \;\;\;\;\frac{-1}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (F B x) :precision binary64 (if (<= F 4.1e-60) (/ -1.0 B) (/ 1.0 B)))

C

double code(double F, double B, double x) {
	double tmp;
	if (F <= 4.1e-60) {
		tmp = -1.0 / B;
	} else {
		tmp = 1.0 / B;
	}
	return tmp;
}

Fortran

real(8) function code(f, b, x)
    real(8), intent (in) :: f
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (f <= 4.1d-60) then
        tmp = (-1.0d0) / b
    else
        tmp = 1.0d0 / b
    end if
    code = tmp
end function

Java

public static double code(double F, double B, double x) {
	double tmp;
	if (F <= 4.1e-60) {
		tmp = -1.0 / B;
	} else {
		tmp = 1.0 / B;
	}
	return tmp;
}

Python

def code(F, B, x):
	tmp = 0
	if F <= 4.1e-60:
		tmp = -1.0 / B
	else:
		tmp = 1.0 / B
	return tmp

Julia

function code(F, B, x)
	tmp = 0.0
	if (F <= 4.1e-60)
		tmp = Float64(-1.0 / B);
	else
		tmp = Float64(1.0 / B);
	end
	return tmp
end

MATLAB

function tmp_2 = code(F, B, x)
	tmp = 0.0;
	if (F <= 4.1e-60)
		tmp = -1.0 / B;
	else
		tmp = 1.0 / B;
	end
	tmp_2 = tmp;
end

Wolfram

code[F_, B_, x_] := If[LessEqual[F, 4.1e-60], N[(-1.0 / B), $MachinePrecision], N[(1.0 / B), $MachinePrecision]]

Derivation

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

Alternative 20: 10.5% accurate, 108.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2024010 
(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))))))