math.cos on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 12

Speedup: 1.0×

• 50.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp(-im) + exp(im));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp(-im) + exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp(-im) + Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp(-im) + math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(-im)) + exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp(-im) + exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 86.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 415:\\ \;\;\;\;\left(0.5 \cdot \cos re\right) \cdot \mathsf{fma}\left(im, im, 2\right)\\ \mathbf{elif}\;im \leq 5 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left({im}^{6} \cdot 0.001388888888888889\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \sqrt{{im}^{12} \cdot 1.9290123456790124 \cdot 10^{-6}}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 415.0)
   (* (* 0.5 (cos re)) (fma im im 2.0))
   (if (<= im 5e+22)
     (log1p (expm1 (* (pow im 6.0) 0.001388888888888889)))
     (* (cos re) (sqrt (* (pow im 12.0) 1.9290123456790124e-6))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 415.0) {
		tmp = (0.5 * cos(re)) * fma(im, im, 2.0);
	} else if (im <= 5e+22) {
		tmp = log1p(expm1((pow(im, 6.0) * 0.001388888888888889)));
	} else {
		tmp = cos(re) * sqrt((pow(im, 12.0) * 1.9290123456790124e-6));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 415.0)
		tmp = Float64(Float64(0.5 * cos(re)) * fma(im, im, 2.0));
	elseif (im <= 5e+22)
		tmp = log1p(expm1(Float64((im ^ 6.0) * 0.001388888888888889)));
	else
		tmp = Float64(cos(re) * sqrt(Float64((im ^ 12.0) * 1.9290123456790124e-6)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 415.0], N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 5e+22], N[Log[1 + N[(Exp[N[(N[Power[im, 6.0], $MachinePrecision] * 0.001388888888888889), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 1.9290123456790124e-6), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \cos re\\ \mathbf{if}\;im \leq 415:\\ \;\;\;\;t_0 \cdot \mathsf{fma}\left(im, im, 2\right)\\ \mathbf{elif}\;im \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\mathsf{log1p}\left(\mathsf{expm1}\left({im}^{6} \cdot 0.001388888888888889\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (cos re))))
   (if (<= im 415.0)
     (* t_0 (fma im im 2.0))
     (if (<= im 1.5e+50)
       (log1p (expm1 (* (pow im 6.0) 0.001388888888888889)))
       (* t_0 (+ 2.0 (* (pow im 6.0) 0.002777777777777778)))))))

C

double code(double re, double im) {
	double t_0 = 0.5 * cos(re);
	double tmp;
	if (im <= 415.0) {
		tmp = t_0 * fma(im, im, 2.0);
	} else if (im <= 1.5e+50) {
		tmp = log1p(expm1((pow(im, 6.0) * 0.001388888888888889)));
	} else {
		tmp = t_0 * (2.0 + (pow(im, 6.0) * 0.002777777777777778));
	}
	return tmp;
}

Julia

function code(re, im)
	t_0 = Float64(0.5 * cos(re))
	tmp = 0.0
	if (im <= 415.0)
		tmp = Float64(t_0 * fma(im, im, 2.0));
	elseif (im <= 1.5e+50)
		tmp = log1p(expm1(Float64((im ^ 6.0) * 0.001388888888888889)));
	else
		tmp = Float64(t_0 * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778)));
	end
	return tmp
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[im, 415.0], N[(t$95$0 * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.5e+50], N[Log[1 + N[(Exp[N[(N[Power[im, 6.0], $MachinePrecision] * 0.001388888888888889), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision], N[(t$95$0 * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 4: 71.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\sqrt{{im}^{12} \cdot 1.9290123456790124 \cdot 10^{-6}}\\ \mathbf{else}:\\ \;\;\;\;0.001388888888888889 \cdot \left(\cos re \cdot {im}^{6}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.8e+17)
   (cos re)
   (if (<= im 1.5e+50)
     (sqrt (* (pow im 12.0) 1.9290123456790124e-6))
     (* 0.001388888888888889 (* (cos re) (pow im 6.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.8e+17) {
		tmp = cos(re);
	} else if (im <= 1.5e+50) {
		tmp = sqrt((pow(im, 12.0) * 1.9290123456790124e-6));
	} else {
		tmp = 0.001388888888888889 * (cos(re) * pow(im, 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.8d+17) then
        tmp = cos(re)
    else if (im <= 1.5d+50) then
        tmp = sqrt(((im ** 12.0d0) * 1.9290123456790124d-6))
    else
        tmp = 0.001388888888888889d0 * (cos(re) * (im ** 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.8e+17) {
		tmp = Math.cos(re);
	} else if (im <= 1.5e+50) {
		tmp = Math.sqrt((Math.pow(im, 12.0) * 1.9290123456790124e-6));
	} else {
		tmp = 0.001388888888888889 * (Math.cos(re) * Math.pow(im, 6.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.8e+17:
		tmp = math.cos(re)
	elif im <= 1.5e+50:
		tmp = math.sqrt((math.pow(im, 12.0) * 1.9290123456790124e-6))
	else:
		tmp = 0.001388888888888889 * (math.cos(re) * math.pow(im, 6.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.8e+17)
		tmp = cos(re);
	elseif (im <= 1.5e+50)
		tmp = sqrt(Float64((im ^ 12.0) * 1.9290123456790124e-6));
	else
		tmp = Float64(0.001388888888888889 * Float64(cos(re) * (im ^ 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.8e+17)
		tmp = cos(re);
	elseif (im <= 1.5e+50)
		tmp = sqrt(((im ^ 12.0) * 1.9290123456790124e-6));
	else
		tmp = 0.001388888888888889 * (cos(re) * (im ^ 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.8e+17], N[Cos[re], $MachinePrecision], If[LessEqual[im, 1.5e+50], N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 1.9290123456790124e-6), $MachinePrecision]], $MachinePrecision], N[(0.001388888888888889 * N[(N[Cos[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 71.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.1 \cdot 10^{+17}:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\sqrt{{im}^{12} \cdot 1.9290123456790124 \cdot 10^{-6}} + 1\\ \mathbf{else}:\\ \;\;\;\;0.001388888888888889 \cdot \left(\cos re \cdot {im}^{6}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.1e+17)
   (cos re)
   (if (<= im 1.5e+50)
     (+ (sqrt (* (pow im 12.0) 1.9290123456790124e-6)) 1.0)
     (* 0.001388888888888889 (* (cos re) (pow im 6.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.1e+17) {
		tmp = cos(re);
	} else if (im <= 1.5e+50) {
		tmp = sqrt((pow(im, 12.0) * 1.9290123456790124e-6)) + 1.0;
	} else {
		tmp = 0.001388888888888889 * (cos(re) * pow(im, 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.1d+17) then
        tmp = cos(re)
    else if (im <= 1.5d+50) then
        tmp = sqrt(((im ** 12.0d0) * 1.9290123456790124d-6)) + 1.0d0
    else
        tmp = 0.001388888888888889d0 * (cos(re) * (im ** 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.1e+17) {
		tmp = Math.cos(re);
	} else if (im <= 1.5e+50) {
		tmp = Math.sqrt((Math.pow(im, 12.0) * 1.9290123456790124e-6)) + 1.0;
	} else {
		tmp = 0.001388888888888889 * (Math.cos(re) * Math.pow(im, 6.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.1e+17:
		tmp = math.cos(re)
	elif im <= 1.5e+50:
		tmp = math.sqrt((math.pow(im, 12.0) * 1.9290123456790124e-6)) + 1.0
	else:
		tmp = 0.001388888888888889 * (math.cos(re) * math.pow(im, 6.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.1e+17)
		tmp = cos(re);
	elseif (im <= 1.5e+50)
		tmp = Float64(sqrt(Float64((im ^ 12.0) * 1.9290123456790124e-6)) + 1.0);
	else
		tmp = Float64(0.001388888888888889 * Float64(cos(re) * (im ^ 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.1e+17)
		tmp = cos(re);
	elseif (im <= 1.5e+50)
		tmp = sqrt(((im ^ 12.0) * 1.9290123456790124e-6)) + 1.0;
	else
		tmp = 0.001388888888888889 * (cos(re) * (im ^ 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.1e+17], N[Cos[re], $MachinePrecision], If[LessEqual[im, 1.5e+50], N[(N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 1.9290123456790124e-6), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision], N[(0.001388888888888889 * N[(N[Cos[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 85.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 3.5 \cdot 10^{+17}:\\ \;\;\;\;\left(0.5 \cdot \cos re\right) \cdot \mathsf{fma}\left(im, im, 2\right)\\ \mathbf{elif}\;im \leq 1.5 \cdot 10^{+50}:\\ \;\;\;\;\sqrt{{im}^{12} \cdot 1.9290123456790124 \cdot 10^{-6}} + 1\\ \mathbf{else}:\\ \;\;\;\;0.001388888888888889 \cdot \left(\cos re \cdot {im}^{6}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 3.5e+17)
   (* (* 0.5 (cos re)) (fma im im 2.0))
   (if (<= im 1.5e+50)
     (+ (sqrt (* (pow im 12.0) 1.9290123456790124e-6)) 1.0)
     (* 0.001388888888888889 (* (cos re) (pow im 6.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 3.5e+17) {
		tmp = (0.5 * cos(re)) * fma(im, im, 2.0);
	} else if (im <= 1.5e+50) {
		tmp = sqrt((pow(im, 12.0) * 1.9290123456790124e-6)) + 1.0;
	} else {
		tmp = 0.001388888888888889 * (cos(re) * pow(im, 6.0));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 3.5e+17)
		tmp = Float64(Float64(0.5 * cos(re)) * fma(im, im, 2.0));
	elseif (im <= 1.5e+50)
		tmp = Float64(sqrt(Float64((im ^ 12.0) * 1.9290123456790124e-6)) + 1.0);
	else
		tmp = Float64(0.001388888888888889 * Float64(cos(re) * (im ^ 6.0)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 3.5e+17], N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.5e+50], N[(N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 1.9290123456790124e-6), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision], N[(0.001388888888888889 * N[(N[Cos[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 7: 91.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (+ 2.0 (* (pow im 6.0) 0.002777777777777778))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (2.0 + (pow(im, 6.0) * 0.002777777777777778));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (2.0d0 + ((im ** 6.0d0) * 0.002777777777777778d0))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (2.0 + (Math.pow(im, 6.0) * 0.002777777777777778));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (2.0 + (math.pow(im, 6.0) * 0.002777777777777778))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (2.0 + ((im ^ 6.0) * 0.002777777777777778));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 8: 66.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 9 \cdot 10^{+16}:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{im}^{12} \cdot 1.9290123456790124 \cdot 10^{-6}}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 9e+16) (cos re) (sqrt (* (pow im 12.0) 1.9290123456790124e-6))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 9e+16) {
		tmp = cos(re);
	} else {
		tmp = sqrt((pow(im, 12.0) * 1.9290123456790124e-6));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 9d+16) then
        tmp = cos(re)
    else
        tmp = sqrt(((im ** 12.0d0) * 1.9290123456790124d-6))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 9e+16) {
		tmp = Math.cos(re);
	} else {
		tmp = Math.sqrt((Math.pow(im, 12.0) * 1.9290123456790124e-6));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 9e+16:
		tmp = math.cos(re)
	else:
		tmp = math.sqrt((math.pow(im, 12.0) * 1.9290123456790124e-6))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 9e+16)
		tmp = cos(re);
	else
		tmp = sqrt(Float64((im ^ 12.0) * 1.9290123456790124e-6));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 9e+16)
		tmp = cos(re);
	else
		tmp = sqrt(((im ^ 12.0) * 1.9290123456790124e-6));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 9e+16], N[Cos[re], $MachinePrecision], N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 1.9290123456790124e-6), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 9: 65.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.0076:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 3.85 \cdot 10^{+55}:\\ \;\;\;\;1 + {re}^{2} \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;{im}^{6} \cdot 0.001388888888888889 + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.0076)
   (cos re)
   (if (<= im 3.85e+55)
     (+ 1.0 (* (pow re 2.0) -0.5))
     (+ (* (pow im 6.0) 0.001388888888888889) 1.0))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.0076) {
		tmp = cos(re);
	} else if (im <= 3.85e+55) {
		tmp = 1.0 + (pow(re, 2.0) * -0.5);
	} else {
		tmp = (pow(im, 6.0) * 0.001388888888888889) + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 0.0076d0) then
        tmp = cos(re)
    else if (im <= 3.85d+55) then
        tmp = 1.0d0 + ((re ** 2.0d0) * (-0.5d0))
    else
        tmp = ((im ** 6.0d0) * 0.001388888888888889d0) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 0.0076) {
		tmp = Math.cos(re);
	} else if (im <= 3.85e+55) {
		tmp = 1.0 + (Math.pow(re, 2.0) * -0.5);
	} else {
		tmp = (Math.pow(im, 6.0) * 0.001388888888888889) + 1.0;
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 0.0076:
		tmp = math.cos(re)
	elif im <= 3.85e+55:
		tmp = 1.0 + (math.pow(re, 2.0) * -0.5)
	else:
		tmp = (math.pow(im, 6.0) * 0.001388888888888889) + 1.0
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.0076)
		tmp = cos(re);
	elseif (im <= 3.85e+55)
		tmp = Float64(1.0 + Float64((re ^ 2.0) * -0.5));
	else
		tmp = Float64(Float64((im ^ 6.0) * 0.001388888888888889) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 0.0076)
		tmp = cos(re);
	elseif (im <= 3.85e+55)
		tmp = 1.0 + ((re ^ 2.0) * -0.5);
	else
		tmp = ((im ^ 6.0) * 0.001388888888888889) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.0076], N[Cos[re], $MachinePrecision], If[LessEqual[im, 3.85e+55], N[(1.0 + N[(N[Power[re, 2.0], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[im, 6.0], $MachinePrecision] * 0.001388888888888889), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

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

Alternative 10: 65.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 7.8 \cdot 10^{+16}:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;{im}^{6} \cdot 0.001388888888888889 + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 7.8e+16) (cos re) (+ (* (pow im 6.0) 0.001388888888888889) 1.0)))

C

double code(double re, double im) {
	double tmp;
	if (im <= 7.8e+16) {
		tmp = cos(re);
	} else {
		tmp = (pow(im, 6.0) * 0.001388888888888889) + 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 7.8d+16) then
        tmp = cos(re)
    else
        tmp = ((im ** 6.0d0) * 0.001388888888888889d0) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 7.8e+16) {
		tmp = Math.cos(re);
	} else {
		tmp = (Math.pow(im, 6.0) * 0.001388888888888889) + 1.0;
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 7.8e+16:
		tmp = math.cos(re)
	else:
		tmp = (math.pow(im, 6.0) * 0.001388888888888889) + 1.0
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 7.8e+16)
		tmp = cos(re);
	else
		tmp = Float64(Float64((im ^ 6.0) * 0.001388888888888889) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 7.8e+16)
		tmp = cos(re);
	else
		tmp = ((im ^ 6.0) * 0.001388888888888889) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 7.8e+16], N[Cos[re], $MachinePrecision], N[(N[(N[Power[im, 6.0], $MachinePrecision] * 0.001388888888888889), $MachinePrecision] + 1.0), $MachinePrecision]]

Derivation

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

Alternative 11: 65.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;{im}^{6} \cdot 0.001388888888888889\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 1.5e+17) (cos re) (* (pow im 6.0) 0.001388888888888889)))

C

double code(double re, double im) {
	double tmp;
	if (im <= 1.5e+17) {
		tmp = cos(re);
	} else {
		tmp = pow(im, 6.0) * 0.001388888888888889;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 1.5d+17) then
        tmp = cos(re)
    else
        tmp = (im ** 6.0d0) * 0.001388888888888889d0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 1.5e+17) {
		tmp = Math.cos(re);
	} else {
		tmp = Math.pow(im, 6.0) * 0.001388888888888889;
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 1.5e+17:
		tmp = math.cos(re)
	else:
		tmp = math.pow(im, 6.0) * 0.001388888888888889
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 1.5e+17)
		tmp = cos(re);
	else
		tmp = Float64((im ^ 6.0) * 0.001388888888888889);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 1.5e+17)
		tmp = cos(re);
	else
		tmp = (im ^ 6.0) * 0.001388888888888889;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 1.5e+17], N[Cos[re], $MachinePrecision], N[(N[Power[im, 6.0], $MachinePrecision] * 0.001388888888888889), $MachinePrecision]]

Derivation

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

Alternative 12: 50.6% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \cos re \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (cos re))

C

double code(double re, double im) {
	return cos(re);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = cos(re)
end function

Java

public static double code(double re, double im) {
	return Math.cos(re);
}

Python

def code(re, im):
	return math.cos(re)

Julia

function code(re, im)
	return cos(re)
end

MATLAB

function tmp = code(re, im)
	tmp = cos(re);
end

Wolfram

code[re_, im_] := N[Cos[re], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024006 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))