Toniolo and Linder, Equation (3b), real

Percentage Accurate: 93.6% → 99.7%

Time: 16.9s

Alternatives: 18

Speedup: 1.4×

Specification

Math

\[\begin{array}{l} \\ \frac{\sin ky}{\sqrt{{\sin kx}^{2} + {\sin ky}^{2}}} \cdot \sin th \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))

C

double code(double kx, double ky, double th) {
	return (sin(ky) / sqrt((pow(sin(kx), 2.0) + pow(sin(ky), 2.0)))) * sin(th);
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    code = (sin(ky) / sqrt(((sin(kx) ** 2.0d0) + (sin(ky) ** 2.0d0)))) * sin(th)
end function

Java

public static double code(double kx, double ky, double th) {
	return (Math.sin(ky) / Math.sqrt((Math.pow(Math.sin(kx), 2.0) + Math.pow(Math.sin(ky), 2.0)))) * Math.sin(th);
}

Python

def code(kx, ky, th):
	return (math.sin(ky) / math.sqrt((math.pow(math.sin(kx), 2.0) + math.pow(math.sin(ky), 2.0)))) * math.sin(th)

Julia

function code(kx, ky, th)
	return Float64(Float64(sin(ky) / sqrt(Float64((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))) * sin(th))
end

MATLAB

function tmp = code(kx, ky, th)
	tmp = (sin(ky) / sqrt(((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))) * sin(th);
end

Wolfram

code[kx_, ky_, th_] := N[(N[(N[Sin[ky], $MachinePrecision] / N[Sqrt[N[(N[Power[N[Sin[kx], $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[Sin[ky], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[th], $MachinePrecision]), $MachinePrecision]

Initial Program: 93.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\sin ky}{\sqrt{{\sin kx}^{2} + {\sin ky}^{2}}} \cdot \sin th \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))

C

double code(double kx, double ky, double th) {
	return (sin(ky) / sqrt((pow(sin(kx), 2.0) + pow(sin(ky), 2.0)))) * sin(th);
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    code = (sin(ky) / sqrt(((sin(kx) ** 2.0d0) + (sin(ky) ** 2.0d0)))) * sin(th)
end function

Java

public static double code(double kx, double ky, double th) {
	return (Math.sin(ky) / Math.sqrt((Math.pow(Math.sin(kx), 2.0) + Math.pow(Math.sin(ky), 2.0)))) * Math.sin(th);
}

Python

def code(kx, ky, th):
	return (math.sin(ky) / math.sqrt((math.pow(math.sin(kx), 2.0) + math.pow(math.sin(ky), 2.0)))) * math.sin(th)

Julia

function code(kx, ky, th)
	return Float64(Float64(sin(ky) / sqrt(Float64((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))) * sin(th))
end

MATLAB

function tmp = code(kx, ky, th)
	tmp = (sin(ky) / sqrt(((sin(kx) ^ 2.0) + (sin(ky) ^ 2.0)))) * sin(th);
end

Wolfram

code[kx_, ky_, th_] := N[(N[(N[Sin[ky], $MachinePrecision] / N[Sqrt[N[(N[Power[N[Sin[kx], $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[Sin[ky], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[th], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{\sin ky}{\mathsf{hypot}\left(\sin ky, \sin kx\right)} \cdot \sin th \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th)))

C

double code(double kx, double ky, double th) {
	return (sin(ky) / hypot(sin(ky), sin(kx))) * sin(th);
}

Java

public static double code(double kx, double ky, double th) {
	return (Math.sin(ky) / Math.hypot(Math.sin(ky), Math.sin(kx))) * Math.sin(th);
}

Python

def code(kx, ky, th):
	return (math.sin(ky) / math.hypot(math.sin(ky), math.sin(kx))) * math.sin(th)

Julia

function code(kx, ky, th)
	return Float64(Float64(sin(ky) / hypot(sin(ky), sin(kx))) * sin(th))
end

MATLAB

function tmp = code(kx, ky, th)
	tmp = (sin(ky) / hypot(sin(ky), sin(kx))) * sin(th);
end

Wolfram

code[kx_, ky_, th_] := N[(N[(N[Sin[ky], $MachinePrecision] / N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * N[Sin[th], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 46.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.02:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 10^{-15}:\\ \;\;\;\;\sin th \cdot \left|\frac{\sin ky}{\sin kx}\right|\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.02)
   (fabs (sin th))
   (if (<= (sin ky) 1e-15)
     (* (sin th) (fabs (/ (sin ky) (sin kx))))
     (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.02) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 1e-15) {
		tmp = sin(th) * fabs((sin(ky) / sin(kx)));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.02d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 1d-15) then
        tmp = sin(th) * abs((sin(ky) / sin(kx)))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.02) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 1e-15) {
		tmp = Math.sin(th) * Math.abs((Math.sin(ky) / Math.sin(kx)));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.02:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 1e-15:
		tmp = math.sin(th) * math.fabs((math.sin(ky) / math.sin(kx)))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.02)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 1e-15)
		tmp = Float64(sin(th) * abs(Float64(sin(ky) / sin(kx))));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.02)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 1e-15)
		tmp = sin(th) * abs((sin(ky) / sin(kx)));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.02], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 1e-15], N[(N[Sin[th], $MachinePrecision] * N[Abs[N[(N[Sin[ky], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 47.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.06:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\sin th \cdot \frac{\sin ky}{\sin kx}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.06)
   (fabs (sin th))
   (if (<= (sin ky) 2e-69) (* (sin th) (/ (sin ky) (sin kx))) (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.06) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 2e-69) {
		tmp = sin(th) * (sin(ky) / sin(kx));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.06d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 2d-69) then
        tmp = sin(th) * (sin(ky) / sin(kx))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.06) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 2e-69) {
		tmp = Math.sin(th) * (Math.sin(ky) / Math.sin(kx));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.06:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 2e-69:
		tmp = math.sin(th) * (math.sin(ky) / math.sin(kx))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.06)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = Float64(sin(th) * Float64(sin(ky) / sin(kx)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.06)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = sin(th) * (sin(ky) / sin(kx));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.06], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 2e-69], N[(N[Sin[th], $MachinePrecision] * N[(N[Sin[ky], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 47.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.06:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\sin ky \cdot \frac{\sin th}{\sin kx}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.06)
   (fabs (sin th))
   (if (<= (sin ky) 2e-69) (* (sin ky) (/ (sin th) (sin kx))) (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.06) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 2e-69) {
		tmp = sin(ky) * (sin(th) / sin(kx));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.06d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 2d-69) then
        tmp = sin(ky) * (sin(th) / sin(kx))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.06) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 2e-69) {
		tmp = Math.sin(ky) * (Math.sin(th) / Math.sin(kx));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.06:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 2e-69:
		tmp = math.sin(ky) * (math.sin(th) / math.sin(kx))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.06)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = Float64(sin(ky) * Float64(sin(th) / sin(kx)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.06)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = sin(ky) * (sin(th) / sin(kx));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.06], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 2e-69], N[(N[Sin[ky], $MachinePrecision] * N[(N[Sin[th], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin kx \leq -0.048:\\ \;\;\;\;\left(ky \cdot \sin th\right) \cdot \sqrt{\frac{1}{0.5 - 0.5 \cdot \cos \left(kx \cdot 2\right)}}\\ \mathbf{elif}\;\sin kx \leq 5 \cdot 10^{-80}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\frac{\sin ky}{\frac{\sin kx}{\sin th}}\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin kx) -0.048)
   (* (* ky (sin th)) (sqrt (/ 1.0 (- 0.5 (* 0.5 (cos (* kx 2.0)))))))
   (if (<= (sin kx) 5e-80) (sin th) (/ (sin ky) (/ (sin kx) (sin th))))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(kx) <= -0.048) {
		tmp = (ky * sin(th)) * sqrt((1.0 / (0.5 - (0.5 * cos((kx * 2.0))))));
	} else if (sin(kx) <= 5e-80) {
		tmp = sin(th);
	} else {
		tmp = sin(ky) / (sin(kx) / sin(th));
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(kx) <= (-0.048d0)) then
        tmp = (ky * sin(th)) * sqrt((1.0d0 / (0.5d0 - (0.5d0 * cos((kx * 2.0d0))))))
    else if (sin(kx) <= 5d-80) then
        tmp = sin(th)
    else
        tmp = sin(ky) / (sin(kx) / sin(th))
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(kx) <= -0.048) {
		tmp = (ky * Math.sin(th)) * Math.sqrt((1.0 / (0.5 - (0.5 * Math.cos((kx * 2.0))))));
	} else if (Math.sin(kx) <= 5e-80) {
		tmp = Math.sin(th);
	} else {
		tmp = Math.sin(ky) / (Math.sin(kx) / Math.sin(th));
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(kx) <= -0.048:
		tmp = (ky * math.sin(th)) * math.sqrt((1.0 / (0.5 - (0.5 * math.cos((kx * 2.0))))))
	elif math.sin(kx) <= 5e-80:
		tmp = math.sin(th)
	else:
		tmp = math.sin(ky) / (math.sin(kx) / math.sin(th))
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(kx) <= -0.048)
		tmp = Float64(Float64(ky * sin(th)) * sqrt(Float64(1.0 / Float64(0.5 - Float64(0.5 * cos(Float64(kx * 2.0)))))));
	elseif (sin(kx) <= 5e-80)
		tmp = sin(th);
	else
		tmp = Float64(sin(ky) / Float64(sin(kx) / sin(th)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(kx) <= -0.048)
		tmp = (ky * sin(th)) * sqrt((1.0 / (0.5 - (0.5 * cos((kx * 2.0))))));
	elseif (sin(kx) <= 5e-80)
		tmp = sin(th);
	else
		tmp = sin(ky) / (sin(kx) / sin(th));
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[kx], $MachinePrecision], -0.048], N[(N[(ky * N[Sin[th], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / N[(0.5 - N[(0.5 * N[Cos[N[(kx * 2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[Sin[kx], $MachinePrecision], 5e-80], N[Sin[th], $MachinePrecision], N[(N[Sin[ky], $MachinePrecision] / N[(N[Sin[kx], $MachinePrecision] / N[Sin[th], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 99.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \sin ky \cdot \frac{\sin th}{\mathsf{hypot}\left(\sin ky, \sin kx\right)} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx)))))

C

double code(double kx, double ky, double th) {
	return sin(ky) * (sin(th) / hypot(sin(ky), sin(kx)));
}

Java

public static double code(double kx, double ky, double th) {
	return Math.sin(ky) * (Math.sin(th) / Math.hypot(Math.sin(ky), Math.sin(kx)));
}

Python

def code(kx, ky, th):
	return math.sin(ky) * (math.sin(th) / math.hypot(math.sin(ky), math.sin(kx)))

Julia

function code(kx, ky, th)
	return Float64(sin(ky) * Float64(sin(th) / hypot(sin(ky), sin(kx))))
end

MATLAB

function tmp = code(kx, ky, th)
	tmp = sin(ky) * (sin(th) / hypot(sin(ky), sin(kx)));
end

Wolfram

code[kx_, ky_, th_] := N[(N[Sin[ky], $MachinePrecision] * N[(N[Sin[th], $MachinePrecision] / N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 7: 56.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;th \leq 0.68:\\ \;\;\;\;\frac{\sin ky}{\mathsf{hypot}\left(\sin ky, \sin kx\right) \cdot \left(\frac{1}{th} + th \cdot 0.16666666666666666\right)}\\ \mathbf{elif}\;th \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\sin th \cdot \left|\frac{\sin ky}{\sin kx}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= th 0.68)
   (/
    (sin ky)
    (* (hypot (sin ky) (sin kx)) (+ (/ 1.0 th) (* th 0.16666666666666666))))
   (if (<= th 4.5e+56) (sin th) (* (sin th) (fabs (/ (sin ky) (sin kx)))))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.68) {
		tmp = sin(ky) / (hypot(sin(ky), sin(kx)) * ((1.0 / th) + (th * 0.16666666666666666)));
	} else if (th <= 4.5e+56) {
		tmp = sin(th);
	} else {
		tmp = sin(th) * fabs((sin(ky) / sin(kx)));
	}
	return tmp;
}

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.68) {
		tmp = Math.sin(ky) / (Math.hypot(Math.sin(ky), Math.sin(kx)) * ((1.0 / th) + (th * 0.16666666666666666)));
	} else if (th <= 4.5e+56) {
		tmp = Math.sin(th);
	} else {
		tmp = Math.sin(th) * Math.abs((Math.sin(ky) / Math.sin(kx)));
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if th <= 0.68:
		tmp = math.sin(ky) / (math.hypot(math.sin(ky), math.sin(kx)) * ((1.0 / th) + (th * 0.16666666666666666)))
	elif th <= 4.5e+56:
		tmp = math.sin(th)
	else:
		tmp = math.sin(th) * math.fabs((math.sin(ky) / math.sin(kx)))
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (th <= 0.68)
		tmp = Float64(sin(ky) / Float64(hypot(sin(ky), sin(kx)) * Float64(Float64(1.0 / th) + Float64(th * 0.16666666666666666))));
	elseif (th <= 4.5e+56)
		tmp = sin(th);
	else
		tmp = Float64(sin(th) * abs(Float64(sin(ky) / sin(kx))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (th <= 0.68)
		tmp = sin(ky) / (hypot(sin(ky), sin(kx)) * ((1.0 / th) + (th * 0.16666666666666666)));
	elseif (th <= 4.5e+56)
		tmp = sin(th);
	else
		tmp = sin(th) * abs((sin(ky) / sin(kx)));
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[th, 0.68], N[(N[Sin[ky], $MachinePrecision] / N[(N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision] * N[(N[(1.0 / th), $MachinePrecision] + N[(th * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[th, 4.5e+56], N[Sin[th], $MachinePrecision], N[(N[Sin[th], $MachinePrecision] * N[Abs[N[(N[Sin[ky], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 8: 47.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.01:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\sin th \cdot \frac{ky}{\sin kx}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.01)
   (fabs (sin th))
   (if (<= (sin ky) 2e-69) (* (sin th) (/ ky (sin kx))) (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.01) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 2e-69) {
		tmp = sin(th) * (ky / sin(kx));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.01d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 2d-69) then
        tmp = sin(th) * (ky / sin(kx))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.01) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 2e-69) {
		tmp = Math.sin(th) * (ky / Math.sin(kx));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.01:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 2e-69:
		tmp = math.sin(th) * (ky / math.sin(kx))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.01)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = Float64(sin(th) * Float64(ky / sin(kx)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.01)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = sin(th) * (ky / sin(kx));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.01], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 2e-69], N[(N[Sin[th], $MachinePrecision] * N[(ky / N[Sin[kx], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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

Alternative 9: 47.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.01:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 2 \cdot 10^{-69}:\\ \;\;\;\;\frac{ky}{\frac{\sin kx}{\sin th}}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.01)
   (fabs (sin th))
   (if (<= (sin ky) 2e-69) (/ ky (/ (sin kx) (sin th))) (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.01) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 2e-69) {
		tmp = ky / (sin(kx) / sin(th));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.01d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 2d-69) then
        tmp = ky / (sin(kx) / sin(th))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.01) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 2e-69) {
		tmp = ky / (Math.sin(kx) / Math.sin(th));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.01:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 2e-69:
		tmp = ky / (math.sin(kx) / math.sin(th))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.01)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = Float64(ky / Float64(sin(kx) / sin(th)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.01)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 2e-69)
		tmp = ky / (sin(kx) / sin(th));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.01], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 2e-69], N[(ky / N[(N[Sin[kx], $MachinePrecision] / N[Sin[th], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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

Alternative 10: 55.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;th \leq 0.006:\\ \;\;\;\;\sin ky \cdot \frac{th}{\mathsf{hypot}\left(\sin ky, \sin kx\right)}\\ \mathbf{elif}\;th \leq 4.5 \cdot 10^{+56}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\sin th \cdot \left|\frac{\sin ky}{\sin kx}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= th 0.006)
   (* (sin ky) (/ th (hypot (sin ky) (sin kx))))
   (if (<= th 4.5e+56) (sin th) (* (sin th) (fabs (/ (sin ky) (sin kx)))))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.006) {
		tmp = sin(ky) * (th / hypot(sin(ky), sin(kx)));
	} else if (th <= 4.5e+56) {
		tmp = sin(th);
	} else {
		tmp = sin(th) * fabs((sin(ky) / sin(kx)));
	}
	return tmp;
}

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.006) {
		tmp = Math.sin(ky) * (th / Math.hypot(Math.sin(ky), Math.sin(kx)));
	} else if (th <= 4.5e+56) {
		tmp = Math.sin(th);
	} else {
		tmp = Math.sin(th) * Math.abs((Math.sin(ky) / Math.sin(kx)));
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if th <= 0.006:
		tmp = math.sin(ky) * (th / math.hypot(math.sin(ky), math.sin(kx)))
	elif th <= 4.5e+56:
		tmp = math.sin(th)
	else:
		tmp = math.sin(th) * math.fabs((math.sin(ky) / math.sin(kx)))
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (th <= 0.006)
		tmp = Float64(sin(ky) * Float64(th / hypot(sin(ky), sin(kx))));
	elseif (th <= 4.5e+56)
		tmp = sin(th);
	else
		tmp = Float64(sin(th) * abs(Float64(sin(ky) / sin(kx))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (th <= 0.006)
		tmp = sin(ky) * (th / hypot(sin(ky), sin(kx)));
	elseif (th <= 4.5e+56)
		tmp = sin(th);
	else
		tmp = sin(th) * abs((sin(ky) / sin(kx)));
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[th, 0.006], N[(N[Sin[ky], $MachinePrecision] * N[(th / N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[th, 4.5e+56], N[Sin[th], $MachinePrecision], N[(N[Sin[th], $MachinePrecision] * N[Abs[N[(N[Sin[ky], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 11: 56.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;th \leq 0.0052:\\ \;\;\;\;\frac{\sin ky}{\mathsf{hypot}\left(\sin ky, \sin kx\right)} \cdot th\\ \mathbf{elif}\;th \leq 5.4 \cdot 10^{+56}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\sin th \cdot \left|\frac{\sin ky}{\sin kx}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= th 0.0052)
   (* (/ (sin ky) (hypot (sin ky) (sin kx))) th)
   (if (<= th 5.4e+56) (sin th) (* (sin th) (fabs (/ (sin ky) (sin kx)))))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.0052) {
		tmp = (sin(ky) / hypot(sin(ky), sin(kx))) * th;
	} else if (th <= 5.4e+56) {
		tmp = sin(th);
	} else {
		tmp = sin(th) * fabs((sin(ky) / sin(kx)));
	}
	return tmp;
}

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (th <= 0.0052) {
		tmp = (Math.sin(ky) / Math.hypot(Math.sin(ky), Math.sin(kx))) * th;
	} else if (th <= 5.4e+56) {
		tmp = Math.sin(th);
	} else {
		tmp = Math.sin(th) * Math.abs((Math.sin(ky) / Math.sin(kx)));
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if th <= 0.0052:
		tmp = (math.sin(ky) / math.hypot(math.sin(ky), math.sin(kx))) * th
	elif th <= 5.4e+56:
		tmp = math.sin(th)
	else:
		tmp = math.sin(th) * math.fabs((math.sin(ky) / math.sin(kx)))
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (th <= 0.0052)
		tmp = Float64(Float64(sin(ky) / hypot(sin(ky), sin(kx))) * th);
	elseif (th <= 5.4e+56)
		tmp = sin(th);
	else
		tmp = Float64(sin(th) * abs(Float64(sin(ky) / sin(kx))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (th <= 0.0052)
		tmp = (sin(ky) / hypot(sin(ky), sin(kx))) * th;
	elseif (th <= 5.4e+56)
		tmp = sin(th);
	else
		tmp = sin(th) * abs((sin(ky) / sin(kx)));
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[th, 0.0052], N[(N[(N[Sin[ky], $MachinePrecision] / N[Sqrt[N[Sin[ky], $MachinePrecision] ^ 2 + N[Sin[kx], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision] * th), $MachinePrecision], If[LessEqual[th, 5.4e+56], N[Sin[th], $MachinePrecision], N[(N[Sin[th], $MachinePrecision] * N[Abs[N[(N[Sin[ky], $MachinePrecision] / N[Sin[kx], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 12: 40.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\sin ky \leq -0.02:\\ \;\;\;\;\left|\sin th\right|\\ \mathbf{elif}\;\sin ky \leq 5 \cdot 10^{-85}:\\ \;\;\;\;\frac{ky}{\frac{kx}{\sin th}}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= (sin ky) -0.02)
   (fabs (sin th))
   (if (<= (sin ky) 5e-85) (/ ky (/ kx (sin th))) (sin th))))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (sin(ky) <= -0.02) {
		tmp = fabs(sin(th));
	} else if (sin(ky) <= 5e-85) {
		tmp = ky / (kx / sin(th));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (sin(ky) <= (-0.02d0)) then
        tmp = abs(sin(th))
    else if (sin(ky) <= 5d-85) then
        tmp = ky / (kx / sin(th))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (Math.sin(ky) <= -0.02) {
		tmp = Math.abs(Math.sin(th));
	} else if (Math.sin(ky) <= 5e-85) {
		tmp = ky / (kx / Math.sin(th));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if math.sin(ky) <= -0.02:
		tmp = math.fabs(math.sin(th))
	elif math.sin(ky) <= 5e-85:
		tmp = ky / (kx / math.sin(th))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (sin(ky) <= -0.02)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 5e-85)
		tmp = Float64(ky / Float64(kx / sin(th)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (sin(ky) <= -0.02)
		tmp = abs(sin(th));
	elseif (sin(ky) <= 5e-85)
		tmp = ky / (kx / sin(th));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[N[Sin[ky], $MachinePrecision], -0.02], N[Abs[N[Sin[th], $MachinePrecision]], $MachinePrecision], If[LessEqual[N[Sin[ky], $MachinePrecision], 5e-85], N[(ky / N[(kx / N[Sin[th], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]]

Derivation

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

Alternative 13: 26.9% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;kx \leq 1.1 \cdot 10^{-24}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\left(\sin th + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= kx 1.1e-24) (sin th) (+ (+ (sin th) 1.0) -1.0)))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 1.1e-24) {
		tmp = sin(th);
	} else {
		tmp = (sin(th) + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (kx <= 1.1d-24) then
        tmp = sin(th)
    else
        tmp = (sin(th) + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 1.1e-24) {
		tmp = Math.sin(th);
	} else {
		tmp = (Math.sin(th) + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if kx <= 1.1e-24:
		tmp = math.sin(th)
	else:
		tmp = (math.sin(th) + 1.0) + -1.0
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (kx <= 1.1e-24)
		tmp = sin(th);
	else
		tmp = Float64(Float64(sin(th) + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (kx <= 1.1e-24)
		tmp = sin(th);
	else
		tmp = (sin(th) + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[kx, 1.1e-24], N[Sin[th], $MachinePrecision], N[(N[(N[Sin[th], $MachinePrecision] + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

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

Alternative 14: 26.8% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;ky \leq 3.6 \cdot 10^{-85}:\\ \;\;\;\;\frac{ky}{\frac{kx}{\sin th}}\\ \mathbf{else}:\\ \;\;\;\;\sin th\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= ky 3.6e-85) (/ ky (/ kx (sin th))) (sin th)))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (ky <= 3.6e-85) {
		tmp = ky / (kx / sin(th));
	} else {
		tmp = sin(th);
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (ky <= 3.6d-85) then
        tmp = ky / (kx / sin(th))
    else
        tmp = sin(th)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (ky <= 3.6e-85) {
		tmp = ky / (kx / Math.sin(th));
	} else {
		tmp = Math.sin(th);
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if ky <= 3.6e-85:
		tmp = ky / (kx / math.sin(th))
	else:
		tmp = math.sin(th)
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (ky <= 3.6e-85)
		tmp = Float64(ky / Float64(kx / sin(th)));
	else
		tmp = sin(th);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (ky <= 3.6e-85)
		tmp = ky / (kx / sin(th));
	else
		tmp = sin(th);
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[ky, 3.6e-85], N[(ky / N[(kx / N[Sin[th], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Sin[th], $MachinePrecision]]

Derivation

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

Alternative 15: 26.1% accurate, 6.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;kx \leq 1.4 \cdot 10^{-15}:\\ \;\;\;\;\sin th\\ \mathbf{else}:\\ \;\;\;\;\left(th + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= kx 1.4e-15) (sin th) (+ (+ th 1.0) -1.0)))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 1.4e-15) {
		tmp = sin(th);
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (kx <= 1.4d-15) then
        tmp = sin(th)
    else
        tmp = (th + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 1.4e-15) {
		tmp = Math.sin(th);
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if kx <= 1.4e-15:
		tmp = math.sin(th)
	else:
		tmp = (th + 1.0) + -1.0
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (kx <= 1.4e-15)
		tmp = sin(th);
	else
		tmp = Float64(Float64(th + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (kx <= 1.4e-15)
		tmp = sin(th);
	else
		tmp = (th + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[kx, 1.4e-15], N[Sin[th], $MachinePrecision], N[(N[(th + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

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

Alternative 16: 16.9% accurate, 64.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;kx \leq 3.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{1}{\frac{1}{th} + th \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\left(th + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= kx 3.3e-16)
   (/ 1.0 (+ (/ 1.0 th) (* th 0.16666666666666666)))
   (+ (+ th 1.0) -1.0)))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 3.3e-16) {
		tmp = 1.0 / ((1.0 / th) + (th * 0.16666666666666666));
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (kx <= 3.3d-16) then
        tmp = 1.0d0 / ((1.0d0 / th) + (th * 0.16666666666666666d0))
    else
        tmp = (th + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 3.3e-16) {
		tmp = 1.0 / ((1.0 / th) + (th * 0.16666666666666666));
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if kx <= 3.3e-16:
		tmp = 1.0 / ((1.0 / th) + (th * 0.16666666666666666))
	else:
		tmp = (th + 1.0) + -1.0
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (kx <= 3.3e-16)
		tmp = Float64(1.0 / Float64(Float64(1.0 / th) + Float64(th * 0.16666666666666666)));
	else
		tmp = Float64(Float64(th + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (kx <= 3.3e-16)
		tmp = 1.0 / ((1.0 / th) + (th * 0.16666666666666666));
	else
		tmp = (th + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[kx, 3.3e-16], N[(1.0 / N[(N[(1.0 / th), $MachinePrecision] + N[(th * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(th + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

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

Alternative 17: 16.5% accurate, 100.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;kx \leq 6 \cdot 10^{-25}:\\ \;\;\;\;th\\ \mathbf{else}:\\ \;\;\;\;\left(th + 1\right) + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (kx ky th)
 :precision binary64
 (if (<= kx 6e-25) th (+ (+ th 1.0) -1.0)))

C

double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 6e-25) {
		tmp = th;
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    real(8) :: tmp
    if (kx <= 6d-25) then
        tmp = th
    else
        tmp = (th + 1.0d0) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double kx, double ky, double th) {
	double tmp;
	if (kx <= 6e-25) {
		tmp = th;
	} else {
		tmp = (th + 1.0) + -1.0;
	}
	return tmp;
}

Python

def code(kx, ky, th):
	tmp = 0
	if kx <= 6e-25:
		tmp = th
	else:
		tmp = (th + 1.0) + -1.0
	return tmp

Julia

function code(kx, ky, th)
	tmp = 0.0
	if (kx <= 6e-25)
		tmp = th;
	else
		tmp = Float64(Float64(th + 1.0) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(kx, ky, th)
	tmp = 0.0;
	if (kx <= 6e-25)
		tmp = th;
	else
		tmp = (th + 1.0) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[kx_, ky_, th_] := If[LessEqual[kx, 6e-25], th, N[(N[(th + 1.0), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

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

Alternative 18: 14.0% accurate, 709.0× speedup

Math

\[\begin{array}{l} \\ th \end{array} \]

FPCore

(FPCore (kx ky th) :precision binary64 th)

C

double code(double kx, double ky, double th) {
	return th;
}

Fortran

real(8) function code(kx, ky, th)
    real(8), intent (in) :: kx
    real(8), intent (in) :: ky
    real(8), intent (in) :: th
    code = th
end function

Java

public static double code(double kx, double ky, double th) {
	return th;
}

Python

def code(kx, ky, th):
	return th

Julia

function code(kx, ky, th)
	return th
end

MATLAB

function tmp = code(kx, ky, th)
	tmp = th;
end

Wolfram

code[kx_, ky_, th_] := th

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  :precision binary64
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))