math.cos on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 5.6s

Alternatives: 11

Speedup: 1.0×

• 49.5% 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: 84.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(e^{-im} + e^{im}\right)\\ t_1 := 0.5 \cdot {im}^{2}\\ \mathbf{if}\;im \leq 0.014:\\ \;\;\;\;\cos re \cdot \left(t_1 + 1\right)\\ \mathbf{elif}\;im \leq 4.2 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;im \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;{im}^{2} \cdot \left(0.5 + -0.25 \cdot {re}^{2}\right)\\ \mathbf{elif}\;im \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ (exp (- im)) (exp im)))) (t_1 (* 0.5 (pow im 2.0))))
   (if (<= im 0.014)
     (* (cos re) (+ t_1 1.0))
     (if (<= im 4.2e+64)
       t_0
       (if (<= im 2.7e+76)
         (* (pow im 2.0) (+ 0.5 (* -0.25 (pow re 2.0))))
         (if (<= im 1.32e+154) t_0 (* (cos re) t_1)))))))

C

double code(double re, double im) {
	double t_0 = 0.5 * (exp(-im) + exp(im));
	double t_1 = 0.5 * pow(im, 2.0);
	double tmp;
	if (im <= 0.014) {
		tmp = cos(re) * (t_1 + 1.0);
	} else if (im <= 4.2e+64) {
		tmp = t_0;
	} else if (im <= 2.7e+76) {
		tmp = pow(im, 2.0) * (0.5 + (-0.25 * pow(re, 2.0)));
	} else if (im <= 1.32e+154) {
		tmp = t_0;
	} else {
		tmp = cos(re) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (exp(-im) + exp(im))
    t_1 = 0.5d0 * (im ** 2.0d0)
    if (im <= 0.014d0) then
        tmp = cos(re) * (t_1 + 1.0d0)
    else if (im <= 4.2d+64) then
        tmp = t_0
    else if (im <= 2.7d+76) then
        tmp = (im ** 2.0d0) * (0.5d0 + ((-0.25d0) * (re ** 2.0d0)))
    else if (im <= 1.32d+154) then
        tmp = t_0
    else
        tmp = cos(re) * t_1
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = 0.5 * (Math.exp(-im) + Math.exp(im));
	double t_1 = 0.5 * Math.pow(im, 2.0);
	double tmp;
	if (im <= 0.014) {
		tmp = Math.cos(re) * (t_1 + 1.0);
	} else if (im <= 4.2e+64) {
		tmp = t_0;
	} else if (im <= 2.7e+76) {
		tmp = Math.pow(im, 2.0) * (0.5 + (-0.25 * Math.pow(re, 2.0)));
	} else if (im <= 1.32e+154) {
		tmp = t_0;
	} else {
		tmp = Math.cos(re) * t_1;
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = 0.5 * (math.exp(-im) + math.exp(im))
	t_1 = 0.5 * math.pow(im, 2.0)
	tmp = 0
	if im <= 0.014:
		tmp = math.cos(re) * (t_1 + 1.0)
	elif im <= 4.2e+64:
		tmp = t_0
	elif im <= 2.7e+76:
		tmp = math.pow(im, 2.0) * (0.5 + (-0.25 * math.pow(re, 2.0)))
	elif im <= 1.32e+154:
		tmp = t_0
	else:
		tmp = math.cos(re) * t_1
	return tmp

Julia

function code(re, im)
	t_0 = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)))
	t_1 = Float64(0.5 * (im ^ 2.0))
	tmp = 0.0
	if (im <= 0.014)
		tmp = Float64(cos(re) * Float64(t_1 + 1.0));
	elseif (im <= 4.2e+64)
		tmp = t_0;
	elseif (im <= 2.7e+76)
		tmp = Float64((im ^ 2.0) * Float64(0.5 + Float64(-0.25 * (re ^ 2.0))));
	elseif (im <= 1.32e+154)
		tmp = t_0;
	else
		tmp = Float64(cos(re) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = 0.5 * (exp(-im) + exp(im));
	t_1 = 0.5 * (im ^ 2.0);
	tmp = 0.0;
	if (im <= 0.014)
		tmp = cos(re) * (t_1 + 1.0);
	elseif (im <= 4.2e+64)
		tmp = t_0;
	elseif (im <= 2.7e+76)
		tmp = (im ^ 2.0) * (0.5 + (-0.25 * (re ^ 2.0)));
	elseif (im <= 1.32e+154)
		tmp = t_0;
	else
		tmp = cos(re) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[im, 0.014], N[(N[Cos[re], $MachinePrecision] * N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 4.2e+64], t$95$0, If[LessEqual[im, 2.7e+76], N[(N[Power[im, 2.0], $MachinePrecision] * N[(0.5 + N[(-0.25 * N[Power[re, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.32e+154], t$95$0, N[(N[Cos[re], $MachinePrecision] * t$95$1), $MachinePrecision]]]]]]]

Derivation

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1. Add Preprocessing

Alternative 3: 81.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.014:\\ \;\;\;\;\mathsf{fma}\left(0.5 \cdot im, im, \cos re\right)\\ \mathbf{elif}\;im \leq 1.5 \cdot 10^{+154}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(0.5 \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.014)
   (fma (* 0.5 im) im (cos re))
   (if (<= im 1.5e+154)
     (* 0.5 (+ (exp (- im)) (exp im)))
     (* (cos re) (* 0.5 (pow im 2.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.014) {
		tmp = fma((0.5 * im), im, cos(re));
	} else if (im <= 1.5e+154) {
		tmp = 0.5 * (exp(-im) + exp(im));
	} else {
		tmp = cos(re) * (0.5 * pow(im, 2.0));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.014)
		tmp = fma(Float64(0.5 * im), im, cos(re));
	elseif (im <= 1.5e+154)
		tmp = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)));
	else
		tmp = Float64(cos(re) * Float64(0.5 * (im ^ 2.0)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.014], N[(N[(0.5 * im), $MachinePrecision] * im + N[Cos[re], $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.5e+154], N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 4: 84.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot {im}^{2}\\ \mathbf{if}\;im \leq 0.0092:\\ \;\;\;\;\cos re \cdot \left(t_0 + 1\right)\\ \mathbf{elif}\;im \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (let* ((t_0 (* 0.5 (pow im 2.0))))
   (if (<= im 0.0092)
     (* (cos re) (+ t_0 1.0))
     (if (<= im 1.32e+154)
       (* 0.5 (+ (exp (- im)) (exp im)))
       (* (cos re) t_0)))))

C

double code(double re, double im) {
	double t_0 = 0.5 * pow(im, 2.0);
	double tmp;
	if (im <= 0.0092) {
		tmp = cos(re) * (t_0 + 1.0);
	} else if (im <= 1.32e+154) {
		tmp = 0.5 * (exp(-im) + exp(im));
	} else {
		tmp = cos(re) * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (im ** 2.0d0)
    if (im <= 0.0092d0) then
        tmp = cos(re) * (t_0 + 1.0d0)
    else if (im <= 1.32d+154) then
        tmp = 0.5d0 * (exp(-im) + exp(im))
    else
        tmp = cos(re) * t_0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double t_0 = 0.5 * Math.pow(im, 2.0);
	double tmp;
	if (im <= 0.0092) {
		tmp = Math.cos(re) * (t_0 + 1.0);
	} else if (im <= 1.32e+154) {
		tmp = 0.5 * (Math.exp(-im) + Math.exp(im));
	} else {
		tmp = Math.cos(re) * t_0;
	}
	return tmp;
}

Python

def code(re, im):
	t_0 = 0.5 * math.pow(im, 2.0)
	tmp = 0
	if im <= 0.0092:
		tmp = math.cos(re) * (t_0 + 1.0)
	elif im <= 1.32e+154:
		tmp = 0.5 * (math.exp(-im) + math.exp(im))
	else:
		tmp = math.cos(re) * t_0
	return tmp

Julia

function code(re, im)
	t_0 = Float64(0.5 * (im ^ 2.0))
	tmp = 0.0
	if (im <= 0.0092)
		tmp = Float64(cos(re) * Float64(t_0 + 1.0));
	elseif (im <= 1.32e+154)
		tmp = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)));
	else
		tmp = Float64(cos(re) * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	t_0 = 0.5 * (im ^ 2.0);
	tmp = 0.0;
	if (im <= 0.0092)
		tmp = cos(re) * (t_0 + 1.0);
	elseif (im <= 1.32e+154)
		tmp = 0.5 * (exp(-im) + exp(im));
	else
		tmp = cos(re) * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := Block[{t$95$0 = N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[im, 0.0092], N[(N[Cos[re], $MachinePrecision] * N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.32e+154], N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * t$95$0), $MachinePrecision]]]]

Derivation

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1. Add Preprocessing

Alternative 5: 78.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.0078:\\ \;\;\;\;\mathsf{fma}\left(0.5 \cdot im, im, \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(e^{-im} + e^{im}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.0078)
   (fma (* 0.5 im) im (cos re))
   (* 0.5 (+ (exp (- im)) (exp im)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.0078) {
		tmp = fma((0.5 * im), im, cos(re));
	} else {
		tmp = 0.5 * (exp(-im) + exp(im));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.0078)
		tmp = fma(Float64(0.5 * im), im, cos(re));
	else
		tmp = Float64(0.5 * Float64(exp(Float64(-im)) + exp(im)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.0078], N[(N[(0.5 * im), $MachinePrecision] * im + N[Cos[re], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 6: 69.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(0.5 \cdot im, im, \cos re\right) \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (fma (* 0.5 im) im (cos re)))

C

double code(double re, double im) {
	return fma((0.5 * im), im, cos(re));
}

Julia

function code(re, im)
	return fma(Float64(0.5 * im), im, cos(re))
end

Wolfram

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

Derivation

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

Alternative 7: 61.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.25 \cdot 10^{+15}:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 4.9 \cdot 10^{+127}:\\ \;\;\;\;0.25 + {re}^{2} \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot {im}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.25e+15)
   (cos re)
   (if (<= im 4.9e+127) (+ 0.25 (* (pow re 2.0) 0.25)) (* 0.5 (pow im 2.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.25e+15) {
		tmp = cos(re);
	} else if (im <= 4.9e+127) {
		tmp = 0.25 + (pow(re, 2.0) * 0.25);
	} else {
		tmp = 0.5 * pow(im, 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.25d+15) then
        tmp = cos(re)
    else if (im <= 4.9d+127) then
        tmp = 0.25d0 + ((re ** 2.0d0) * 0.25d0)
    else
        tmp = 0.5d0 * (im ** 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.25e+15) {
		tmp = Math.cos(re);
	} else if (im <= 4.9e+127) {
		tmp = 0.25 + (Math.pow(re, 2.0) * 0.25);
	} else {
		tmp = 0.5 * Math.pow(im, 2.0);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.25e+15:
		tmp = math.cos(re)
	elif im <= 4.9e+127:
		tmp = 0.25 + (math.pow(re, 2.0) * 0.25)
	else:
		tmp = 0.5 * math.pow(im, 2.0)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.25e+15)
		tmp = cos(re);
	elseif (im <= 4.9e+127)
		tmp = Float64(0.25 + Float64((re ^ 2.0) * 0.25));
	else
		tmp = Float64(0.5 * (im ^ 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.25e+15)
		tmp = cos(re);
	elseif (im <= 4.9e+127)
		tmp = 0.25 + ((re ^ 2.0) * 0.25);
	else
		tmp = 0.5 * (im ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.25e+15], N[Cos[re], $MachinePrecision], If[LessEqual[im, 4.9e+127], N[(0.25 + N[(N[Power[re, 2.0], $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 8: 61.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 7.5 \cdot 10^{+15}:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.9 \cdot 10^{+128}:\\ \;\;\;\;0.25 + {re}^{2} \cdot 0.25\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot {im}^{2} + 1\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 7.5e+15)
   (cos re)
   (if (<= im 2.9e+128)
     (+ 0.25 (* (pow re 2.0) 0.25))
     (+ (* 0.5 (pow im 2.0)) 1.0))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 7.5e+15) {
		tmp = cos(re);
	} else if (im <= 2.9e+128) {
		tmp = 0.25 + (pow(re, 2.0) * 0.25);
	} else {
		tmp = (0.5 * pow(im, 2.0)) + 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 <= 7.5d+15) then
        tmp = cos(re)
    else if (im <= 2.9d+128) then
        tmp = 0.25d0 + ((re ** 2.0d0) * 0.25d0)
    else
        tmp = (0.5d0 * (im ** 2.0d0)) + 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 7.5e+15) {
		tmp = Math.cos(re);
	} else if (im <= 2.9e+128) {
		tmp = 0.25 + (Math.pow(re, 2.0) * 0.25);
	} else {
		tmp = (0.5 * Math.pow(im, 2.0)) + 1.0;
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 7.5e+15:
		tmp = math.cos(re)
	elif im <= 2.9e+128:
		tmp = 0.25 + (math.pow(re, 2.0) * 0.25)
	else:
		tmp = (0.5 * math.pow(im, 2.0)) + 1.0
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 7.5e+15)
		tmp = cos(re);
	elseif (im <= 2.9e+128)
		tmp = Float64(0.25 + Float64((re ^ 2.0) * 0.25));
	else
		tmp = Float64(Float64(0.5 * (im ^ 2.0)) + 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 7.5e+15)
		tmp = cos(re);
	elseif (im <= 2.9e+128)
		tmp = 0.25 + ((re ^ 2.0) * 0.25);
	else
		tmp = (0.5 * (im ^ 2.0)) + 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 7.5e+15], N[Cos[re], $MachinePrecision], If[LessEqual[im, 2.9e+128], N[(0.25 + N[(N[Power[re, 2.0], $MachinePrecision] * 0.25), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]]]

Derivation

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

Alternative 9: 60.2% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 1.85 \cdot 10^{+85}:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot {im}^{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 1.85e+85) (cos re) (* 0.5 (pow im 2.0))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 1.85e+85) {
		tmp = cos(re);
	} else {
		tmp = 0.5 * pow(im, 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 1.85d+85) then
        tmp = cos(re)
    else
        tmp = 0.5d0 * (im ** 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 1.85e+85) {
		tmp = Math.cos(re);
	} else {
		tmp = 0.5 * Math.pow(im, 2.0);
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 1.85e+85:
		tmp = math.cos(re)
	else:
		tmp = 0.5 * math.pow(im, 2.0)
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 1.85e+85)
		tmp = cos(re);
	else
		tmp = Float64(0.5 * (im ^ 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 1.85e+85)
		tmp = cos(re);
	else
		tmp = 0.5 * (im ^ 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 1.85e+85], N[Cos[re], $MachinePrecision], N[(0.5 * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 51.0% 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

Alternative 11: 8.1% accurate, 308.0× speedup

Math

\[\begin{array}{l} \\ 0.25 \end{array} \]

FPCore

(FPCore (re im) :precision binary64 0.25)

C

double code(double re, double im) {
	return 0.25;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 0.25d0
end function

Java

public static double code(double re, double im) {
	return 0.25;
}

Python

def code(re, im):
	return 0.25

Julia

function code(re, im)
	return 0.25
end

MATLAB

function tmp = code(re, im)
	tmp = 0.25;
end

Wolfram

code[re_, im_] := 0.25

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))