VandenBroeck and Keller, Equation (24)

Percentage Accurate: 99.7% → 99.8%

Time: 9.2s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (B x) :precision binary64 (- (/ 1.0 (sin B)) (/ x (tan B))))

C

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

Fortran

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

Java

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

Python

def code(B, x):
	return (1.0 / math.sin(B)) - (x / math.tan(B))

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12.5:\\ \;\;\;\;\cos B \cdot \frac{-x}{\sin B}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} + -1}{\frac{\tan B}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= x -12.5)
   (* (cos B) (/ (- x) (sin B)))
   (if (<= x 1.7e+16)
     (- (/ 1.0 (sin B)) (/ x B))
     (/ (+ (/ 1.0 x) -1.0) (/ (tan B) x)))))

C

double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = cos(B) * (-x / sin(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-12.5d0)) then
        tmp = cos(b) * (-x / sin(b))
    else if (x <= 1.7d+16) then
        tmp = (1.0d0 / sin(b)) - (x / b)
    else
        tmp = ((1.0d0 / x) + (-1.0d0)) / (tan(b) / x)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = Math.cos(B) * (-x / Math.sin(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (Math.tan(B) / x);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if x <= -12.5:
		tmp = math.cos(B) * (-x / math.sin(B))
	elif x <= 1.7e+16:
		tmp = (1.0 / math.sin(B)) - (x / B)
	else:
		tmp = ((1.0 / x) + -1.0) / (math.tan(B) / x)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (x <= -12.5)
		tmp = Float64(cos(B) * Float64(Float64(-x) / sin(B)));
	elseif (x <= 1.7e+16)
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	else
		tmp = Float64(Float64(Float64(1.0 / x) + -1.0) / Float64(tan(B) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (x <= -12.5)
		tmp = cos(B) * (-x / sin(B));
	elseif (x <= 1.7e+16)
		tmp = (1.0 / sin(B)) - (x / B);
	else
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[x, -12.5], N[(N[Cos[B], $MachinePrecision] * N[((-x) / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+16], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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Alternative 3: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12.5:\\ \;\;\;\;x \cdot \frac{-\cos B}{\sin B}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} + -1}{\frac{\tan B}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= x -12.5)
   (* x (/ (- (cos B)) (sin B)))
   (if (<= x 1.7e+16)
     (- (/ 1.0 (sin B)) (/ x B))
     (/ (+ (/ 1.0 x) -1.0) (/ (tan B) x)))))

C

double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = x * (-cos(B) / sin(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-12.5d0)) then
        tmp = x * (-cos(b) / sin(b))
    else if (x <= 1.7d+16) then
        tmp = (1.0d0 / sin(b)) - (x / b)
    else
        tmp = ((1.0d0 / x) + (-1.0d0)) / (tan(b) / x)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = x * (-Math.cos(B) / Math.sin(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (Math.tan(B) / x);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if x <= -12.5:
		tmp = x * (-math.cos(B) / math.sin(B))
	elif x <= 1.7e+16:
		tmp = (1.0 / math.sin(B)) - (x / B)
	else:
		tmp = ((1.0 / x) + -1.0) / (math.tan(B) / x)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (x <= -12.5)
		tmp = Float64(x * Float64(Float64(-cos(B)) / sin(B)));
	elseif (x <= 1.7e+16)
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	else
		tmp = Float64(Float64(Float64(1.0 / x) + -1.0) / Float64(tan(B) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (x <= -12.5)
		tmp = x * (-cos(B) / sin(B));
	elseif (x <= 1.7e+16)
		tmp = (1.0 / sin(B)) - (x / B);
	else
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[x, -12.5], N[(x * N[((-N[Cos[B], $MachinePrecision]) / N[Sin[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+16], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12.5:\\ \;\;\;\;\frac{-x}{\frac{\sin B}{\cos B}}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} + -1}{\frac{\tan B}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= x -12.5)
   (/ (- x) (/ (sin B) (cos B)))
   (if (<= x 1.7e+16)
     (- (/ 1.0 (sin B)) (/ x B))
     (/ (+ (/ 1.0 x) -1.0) (/ (tan B) x)))))

C

double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = -x / (sin(B) / cos(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-12.5d0)) then
        tmp = -x / (sin(b) / cos(b))
    else if (x <= 1.7d+16) then
        tmp = (1.0d0 / sin(b)) - (x / b)
    else
        tmp = ((1.0d0 / x) + (-1.0d0)) / (tan(b) / x)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = -x / (Math.sin(B) / Math.cos(B));
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (Math.tan(B) / x);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if x <= -12.5:
		tmp = -x / (math.sin(B) / math.cos(B))
	elif x <= 1.7e+16:
		tmp = (1.0 / math.sin(B)) - (x / B)
	else:
		tmp = ((1.0 / x) + -1.0) / (math.tan(B) / x)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (x <= -12.5)
		tmp = Float64(Float64(-x) / Float64(sin(B) / cos(B)));
	elseif (x <= 1.7e+16)
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	else
		tmp = Float64(Float64(Float64(1.0 / x) + -1.0) / Float64(tan(B) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (x <= -12.5)
		tmp = -x / (sin(B) / cos(B));
	elseif (x <= 1.7e+16)
		tmp = (1.0 / sin(B)) - (x / B);
	else
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[x, -12.5], N[((-x) / N[(N[Sin[B], $MachinePrecision] / N[Cos[B], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+16], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -12.5:\\ \;\;\;\;\frac{x \cdot \left(-\cos B\right)}{\sin B}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{x} + -1}{\frac{\tan B}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= x -12.5)
   (/ (* x (- (cos B))) (sin B))
   (if (<= x 1.7e+16)
     (- (/ 1.0 (sin B)) (/ x B))
     (/ (+ (/ 1.0 x) -1.0) (/ (tan B) x)))))

C

double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = (x * -cos(B)) / sin(B);
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-12.5d0)) then
        tmp = (x * -cos(b)) / sin(b)
    else if (x <= 1.7d+16) then
        tmp = (1.0d0 / sin(b)) - (x / b)
    else
        tmp = ((1.0d0 / x) + (-1.0d0)) / (tan(b) / x)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (x <= -12.5) {
		tmp = (x * -Math.cos(B)) / Math.sin(B);
	} else if (x <= 1.7e+16) {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	} else {
		tmp = ((1.0 / x) + -1.0) / (Math.tan(B) / x);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if x <= -12.5:
		tmp = (x * -math.cos(B)) / math.sin(B)
	elif x <= 1.7e+16:
		tmp = (1.0 / math.sin(B)) - (x / B)
	else:
		tmp = ((1.0 / x) + -1.0) / (math.tan(B) / x)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (x <= -12.5)
		tmp = Float64(Float64(x * Float64(-cos(B))) / sin(B));
	elseif (x <= 1.7e+16)
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	else
		tmp = Float64(Float64(Float64(1.0 / x) + -1.0) / Float64(tan(B) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (x <= -12.5)
		tmp = (x * -cos(B)) / sin(B);
	elseif (x <= 1.7e+16)
		tmp = (1.0 / sin(B)) - (x / B);
	else
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[x, -12.5], N[(N[(x * (-N[Cos[B], $MachinePrecision])), $MachinePrecision] / N[Sin[B], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7e+16], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 98.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.21 \lor \neg \left(x \leq 1.7 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{\frac{1}{x} + -1}{\frac{\tan B}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} - \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (or (<= x -0.21) (not (<= x 1.7e+16)))
   (/ (+ (/ 1.0 x) -1.0) (/ (tan B) x))
   (- (/ 1.0 (sin B)) (/ x B))))

C

double code(double B, double x) {
	double tmp;
	if ((x <= -0.21) || !(x <= 1.7e+16)) {
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	} else {
		tmp = (1.0 / sin(B)) - (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-0.21d0)) .or. (.not. (x <= 1.7d+16))) then
        tmp = ((1.0d0 / x) + (-1.0d0)) / (tan(b) / x)
    else
        tmp = (1.0d0 / sin(b)) - (x / b)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if ((x <= -0.21) || !(x <= 1.7e+16)) {
		tmp = ((1.0 / x) + -1.0) / (Math.tan(B) / x);
	} else {
		tmp = (1.0 / Math.sin(B)) - (x / B);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if (x <= -0.21) or not (x <= 1.7e+16):
		tmp = ((1.0 / x) + -1.0) / (math.tan(B) / x)
	else:
		tmp = (1.0 / math.sin(B)) - (x / B)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if ((x <= -0.21) || !(x <= 1.7e+16))
		tmp = Float64(Float64(Float64(1.0 / x) + -1.0) / Float64(tan(B) / x));
	else
		tmp = Float64(Float64(1.0 / sin(B)) - Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if ((x <= -0.21) || ~((x <= 1.7e+16)))
		tmp = ((1.0 / x) + -1.0) / (tan(B) / x);
	else
		tmp = (1.0 / sin(B)) - (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[Or[LessEqual[x, -0.21], N[Not[LessEqual[x, 1.7e+16]], $MachinePrecision]], N[(N[(N[(1.0 / x), $MachinePrecision] + -1.0), $MachinePrecision] / N[(N[Tan[B], $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] - N[(x / B), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 63.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 0.076:\\ \;\;\;\;B \cdot \left(0.16666666666666666 + x \cdot 0.3333333333333333\right) + \frac{1 - x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B} + \frac{x}{B}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= B 0.076)
   (+ (* B (+ 0.16666666666666666 (* x 0.3333333333333333))) (/ (- 1.0 x) B))
   (+ (/ 1.0 (sin B)) (/ x B))))

C

double code(double B, double x) {
	double tmp;
	if (B <= 0.076) {
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	} else {
		tmp = (1.0 / sin(B)) + (x / B);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (b <= 0.076d0) then
        tmp = (b * (0.16666666666666666d0 + (x * 0.3333333333333333d0))) + ((1.0d0 - x) / b)
    else
        tmp = (1.0d0 / sin(b)) + (x / b)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (B <= 0.076) {
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	} else {
		tmp = (1.0 / Math.sin(B)) + (x / B);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if B <= 0.076:
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B)
	else:
		tmp = (1.0 / math.sin(B)) + (x / B)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (B <= 0.076)
		tmp = Float64(Float64(B * Float64(0.16666666666666666 + Float64(x * 0.3333333333333333))) + Float64(Float64(1.0 - x) / B));
	else
		tmp = Float64(Float64(1.0 / sin(B)) + Float64(x / B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (B <= 0.076)
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	else
		tmp = (1.0 / sin(B)) + (x / B);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[B, 0.076], N[(N[(B * N[(0.16666666666666666 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision] + N[(x / B), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 75.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(B, x):
	return (1.0 / math.sin(B)) - (x / B)

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 9: 63.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;B \leq 0.35:\\ \;\;\;\;B \cdot \left(0.16666666666666666 + x \cdot 0.3333333333333333\right) + \frac{1 - x}{B}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sin B}\\ \end{array} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (if (<= B 0.35)
   (+ (* B (+ 0.16666666666666666 (* x 0.3333333333333333))) (/ (- 1.0 x) B))
   (/ 1.0 (sin B))))

C

double code(double B, double x) {
	double tmp;
	if (B <= 0.35) {
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	} else {
		tmp = 1.0 / sin(B);
	}
	return tmp;
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    real(8) :: tmp
    if (b <= 0.35d0) then
        tmp = (b * (0.16666666666666666d0 + (x * 0.3333333333333333d0))) + ((1.0d0 - x) / b)
    else
        tmp = 1.0d0 / sin(b)
    end if
    code = tmp
end function

Java

public static double code(double B, double x) {
	double tmp;
	if (B <= 0.35) {
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	} else {
		tmp = 1.0 / Math.sin(B);
	}
	return tmp;
}

Python

def code(B, x):
	tmp = 0
	if B <= 0.35:
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B)
	else:
		tmp = 1.0 / math.sin(B)
	return tmp

Julia

function code(B, x)
	tmp = 0.0
	if (B <= 0.35)
		tmp = Float64(Float64(B * Float64(0.16666666666666666 + Float64(x * 0.3333333333333333))) + Float64(Float64(1.0 - x) / B));
	else
		tmp = Float64(1.0 / sin(B));
	end
	return tmp
end

MATLAB

function tmp_2 = code(B, x)
	tmp = 0.0;
	if (B <= 0.35)
		tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
	else
		tmp = 1.0 / sin(B);
	end
	tmp_2 = tmp;
end

Wolfram

code[B_, x_] := If[LessEqual[B, 0.35], N[(N[(B * N[(0.16666666666666666 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[Sin[B], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 51.3% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ B \cdot \left(0.16666666666666666 + x \cdot 0.3333333333333333\right) + \frac{1 - x}{B} \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (+ (* B (+ 0.16666666666666666 (* x 0.3333333333333333))) (/ (- 1.0 x) B)))

C

double code(double B, double x) {
	return (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    code = (b * (0.16666666666666666d0 + (x * 0.3333333333333333d0))) + ((1.0d0 - x) / b)
end function

Java

public static double code(double B, double x) {
	return (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
}

Python

def code(B, x):
	return (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B)

Julia

function code(B, x)
	return Float64(Float64(B * Float64(0.16666666666666666 + Float64(x * 0.3333333333333333))) + Float64(Float64(1.0 - x) / B))
end

MATLAB

function tmp = code(B, x)
	tmp = (B * (0.16666666666666666 + (x * 0.3333333333333333))) + ((1.0 - x) / B);
end

Wolfram

code[B_, x_] := N[(N[(B * N[(0.16666666666666666 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 51.3% accurate, 23.3× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{B} + B \cdot 0.16666666666666666 \end{array} \]

FPCore

(FPCore (B x)
 :precision binary64
 (+ (/ (- 1.0 x) B) (* B 0.16666666666666666)))

C

double code(double B, double x) {
	return ((1.0 - x) / B) + (B * 0.16666666666666666);
}

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    code = ((1.0d0 - x) / b) + (b * 0.16666666666666666d0)
end function

Java

public static double code(double B, double x) {
	return ((1.0 - x) / B) + (B * 0.16666666666666666);
}

Python

def code(B, x):
	return ((1.0 - x) / B) + (B * 0.16666666666666666)

Julia

function code(B, x)
	return Float64(Float64(Float64(1.0 - x) / B) + Float64(B * 0.16666666666666666))
end

MATLAB

function tmp = code(B, x)
	tmp = ((1.0 - x) / B) + (B * 0.16666666666666666);
end

Wolfram

code[B_, x_] := N[(N[(N[(1.0 - x), $MachinePrecision] / B), $MachinePrecision] + N[(B * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 51.1% accurate, 42.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 13: 27.0% accurate, 52.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 14: 2.5% accurate, 70.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(b, x)
    real(8), intent (in) :: b
    real(8), intent (in) :: x
    code = x / b
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (- (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))