math.cos on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 13

Speedup: 1.0×

• 48.5% 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, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 3: 73.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.00185:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;0.5 \cdot \left(e^{im} + e^{-im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(1 + im \cdot \left(0.5 + im \cdot \left(0.25 + im \cdot 0.08333333333333333\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.00185)
   (cos re)
   (if (<= im 1.3e+103)
     (* 0.5 (+ (exp im) (exp (- im))))
     (*
      (cos re)
      (+ 1.0 (* im (+ 0.5 (* im (+ 0.25 (* im 0.08333333333333333))))))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.00185) {
		tmp = cos(re);
	} else if (im <= 1.3e+103) {
		tmp = 0.5 * (exp(im) + exp(-im));
	} else {
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 0.00185d0) then
        tmp = cos(re)
    else if (im <= 1.3d+103) then
        tmp = 0.5d0 * (exp(im) + exp(-im))
    else
        tmp = cos(re) * (1.0d0 + (im * (0.5d0 + (im * (0.25d0 + (im * 0.08333333333333333d0))))))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 0.00185) {
		tmp = Math.cos(re);
	} else if (im <= 1.3e+103) {
		tmp = 0.5 * (Math.exp(im) + Math.exp(-im));
	} else {
		tmp = Math.cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 0.00185:
		tmp = math.cos(re)
	elif im <= 1.3e+103:
		tmp = 0.5 * (math.exp(im) + math.exp(-im))
	else:
		tmp = math.cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.00185)
		tmp = cos(re);
	elseif (im <= 1.3e+103)
		tmp = Float64(0.5 * Float64(exp(im) + exp(Float64(-im))));
	else
		tmp = Float64(cos(re) * Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * Float64(0.25 + Float64(im * 0.08333333333333333)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 0.00185)
		tmp = cos(re);
	elseif (im <= 1.3e+103)
		tmp = 0.5 * (exp(im) + exp(-im));
	else
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.00185], N[Cos[re], $MachinePrecision], If[LessEqual[im, 1.3e+103], N[(0.5 * N[(N[Exp[im], $MachinePrecision] + N[Exp[(-im)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(1.0 + N[(im * N[(0.5 + N[(im * N[(0.25 + N[(im * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 86.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.0068:\\ \;\;\;\;\left(\cos re \cdot 0.5\right) \cdot \mathsf{fma}\left(im, im, 2\right)\\ \mathbf{elif}\;im \leq 10^{+103}:\\ \;\;\;\;0.5 \cdot \left(e^{im} + e^{-im}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(1 + im \cdot \left(0.5 + im \cdot \left(0.25 + im \cdot 0.08333333333333333\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.0068)
   (* (* (cos re) 0.5) (fma im im 2.0))
   (if (<= im 1e+103)
     (* 0.5 (+ (exp im) (exp (- im))))
     (*
      (cos re)
      (+ 1.0 (* im (+ 0.5 (* im (+ 0.25 (* im 0.08333333333333333))))))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.0068) {
		tmp = (cos(re) * 0.5) * fma(im, im, 2.0);
	} else if (im <= 1e+103) {
		tmp = 0.5 * (exp(im) + exp(-im));
	} else {
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.0068)
		tmp = Float64(Float64(cos(re) * 0.5) * fma(im, im, 2.0));
	elseif (im <= 1e+103)
		tmp = Float64(0.5 * Float64(exp(im) + exp(Float64(-im))));
	else
		tmp = Float64(cos(re) * Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * Float64(0.25 + Float64(im * 0.08333333333333333)))))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.0068], N[(N[(N[Cos[re], $MachinePrecision] * 0.5), $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1e+103], N[(0.5 * N[(N[Exp[im], $MachinePrecision] + N[Exp[(-im)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(1.0 + N[(im * N[(0.5 + N[(im * N[(0.25 + N[(im * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 75.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 6: 73.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.3:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;0.5 + 0.5 \cdot e^{im}\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(1 + im \cdot \left(0.5 + im \cdot \left(0.25 + im \cdot 0.08333333333333333\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.3)
   (cos re)
   (if (<= im 1.3e+103)
     (+ 0.5 (* 0.5 (exp im)))
     (*
      (cos re)
      (+ 1.0 (* im (+ 0.5 (* im (+ 0.25 (* im 0.08333333333333333))))))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.3) {
		tmp = cos(re);
	} else if (im <= 1.3e+103) {
		tmp = 0.5 + (0.5 * exp(im));
	} else {
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.3d0) then
        tmp = cos(re)
    else if (im <= 1.3d+103) then
        tmp = 0.5d0 + (0.5d0 * exp(im))
    else
        tmp = cos(re) * (1.0d0 + (im * (0.5d0 + (im * (0.25d0 + (im * 0.08333333333333333d0))))))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.3) {
		tmp = Math.cos(re);
	} else if (im <= 1.3e+103) {
		tmp = 0.5 + (0.5 * Math.exp(im));
	} else {
		tmp = Math.cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.3:
		tmp = math.cos(re)
	elif im <= 1.3e+103:
		tmp = 0.5 + (0.5 * math.exp(im))
	else:
		tmp = math.cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.3)
		tmp = cos(re);
	elseif (im <= 1.3e+103)
		tmp = Float64(0.5 + Float64(0.5 * exp(im)));
	else
		tmp = Float64(cos(re) * Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * Float64(0.25 + Float64(im * 0.08333333333333333)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.3)
		tmp = cos(re);
	elseif (im <= 1.3e+103)
		tmp = 0.5 + (0.5 * exp(im));
	else
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.3], N[Cos[re], $MachinePrecision], If[LessEqual[im, 1.3e+103], N[(0.5 + N[(0.5 * N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(1.0 + N[(im * N[(0.5 + N[(im * N[(0.25 + N[(im * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 7: 72.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.6:\\ \;\;\;\;\cos re\\ \mathbf{elif}\;im \leq 2.8 \cdot 10^{+154}:\\ \;\;\;\;0.5 + 0.5 \cdot e^{im}\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left(1 + im \cdot \left(0.5 + im \cdot 0.25\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.6)
   (cos re)
   (if (<= im 2.8e+154)
     (+ 0.5 (* 0.5 (exp im)))
     (* (cos re) (+ 1.0 (* im (+ 0.5 (* im 0.25))))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.6) {
		tmp = cos(re);
	} else if (im <= 2.8e+154) {
		tmp = 0.5 + (0.5 * exp(im));
	} else {
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * 0.25))));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.6d0) then
        tmp = cos(re)
    else if (im <= 2.8d+154) then
        tmp = 0.5d0 + (0.5d0 * exp(im))
    else
        tmp = cos(re) * (1.0d0 + (im * (0.5d0 + (im * 0.25d0))))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.6) {
		tmp = Math.cos(re);
	} else if (im <= 2.8e+154) {
		tmp = 0.5 + (0.5 * Math.exp(im));
	} else {
		tmp = Math.cos(re) * (1.0 + (im * (0.5 + (im * 0.25))));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.6:
		tmp = math.cos(re)
	elif im <= 2.8e+154:
		tmp = 0.5 + (0.5 * math.exp(im))
	else:
		tmp = math.cos(re) * (1.0 + (im * (0.5 + (im * 0.25))))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.6)
		tmp = cos(re);
	elseif (im <= 2.8e+154)
		tmp = Float64(0.5 + Float64(0.5 * exp(im)));
	else
		tmp = Float64(cos(re) * Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * 0.25)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.6)
		tmp = cos(re);
	elseif (im <= 2.8e+154)
		tmp = 0.5 + (0.5 * exp(im));
	else
		tmp = cos(re) * (1.0 + (im * (0.5 + (im * 0.25))));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.6], N[Cos[re], $MachinePrecision], If[LessEqual[im, 2.8e+154], N[(0.5 + N[(0.5 * N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(1.0 + N[(im * N[(0.5 + N[(im * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 8: 69.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 2.9:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;0.5 + 0.5 \cdot e^{im}\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 2.9) (cos re) (+ 0.5 (* 0.5 (exp im)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 2.9) {
		tmp = cos(re);
	} else {
		tmp = 0.5 + (0.5 * exp(im));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 2.9d0) then
        tmp = cos(re)
    else
        tmp = 0.5d0 + (0.5d0 * exp(im))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 2.9) {
		tmp = Math.cos(re);
	} else {
		tmp = 0.5 + (0.5 * Math.exp(im));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 2.9:
		tmp = math.cos(re)
	else:
		tmp = 0.5 + (0.5 * math.exp(im))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 2.9)
		tmp = cos(re);
	else
		tmp = Float64(0.5 + Float64(0.5 * exp(im)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 2.9)
		tmp = cos(re);
	else
		tmp = 0.5 + (0.5 * exp(im));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 2.9], N[Cos[re], $MachinePrecision], N[(0.5 + N[(0.5 * N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 9: 63.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 15:\\ \;\;\;\;\cos re\\ \mathbf{else}:\\ \;\;\;\;1 + im \cdot \left(0.5 + im \cdot \left(0.25 + im \cdot 0.08333333333333333\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 15.0)
   (cos re)
   (+ 1.0 (* im (+ 0.5 (* im (+ 0.25 (* im 0.08333333333333333))))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 15.0) {
		tmp = cos(re);
	} else {
		tmp = 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 15.0d0) then
        tmp = cos(re)
    else
        tmp = 1.0d0 + (im * (0.5d0 + (im * (0.25d0 + (im * 0.08333333333333333d0)))))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 15.0) {
		tmp = Math.cos(re);
	} else {
		tmp = 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 15.0:
		tmp = math.cos(re)
	else:
		tmp = 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 15.0)
		tmp = cos(re);
	else
		tmp = Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * Float64(0.25 + Float64(im * 0.08333333333333333))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 15.0)
		tmp = cos(re);
	else
		tmp = 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 15.0], N[Cos[re], $MachinePrecision], N[(1.0 + N[(im * N[(0.5 + N[(im * N[(0.25 + N[(im * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 10: 44.5% accurate, 23.7× speedup

Math

\[\begin{array}{l} \\ 1 + im \cdot \left(0.5 + im \cdot \left(0.25 + im \cdot 0.08333333333333333\right)\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (+ 1.0 (* im (+ 0.5 (* im (+ 0.25 (* im 0.08333333333333333)))))))

C

double code(double re, double im) {
	return 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 1.0d0 + (im * (0.5d0 + (im * (0.25d0 + (im * 0.08333333333333333d0)))))
end function

Java

public static double code(double re, double im) {
	return 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
}

Python

def code(re, im):
	return 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))))

Julia

function code(re, im)
	return Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * Float64(0.25 + Float64(im * 0.08333333333333333))))))
end

MATLAB

function tmp = code(re, im)
	tmp = 1.0 + (im * (0.5 + (im * (0.25 + (im * 0.08333333333333333)))));
end

Wolfram

code[re_, im_] := N[(1.0 + N[(im * N[(0.5 + N[(im * N[(0.25 + N[(im * 0.08333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 47.0% accurate, 34.2× speedup

Math

\[\begin{array}{l} \\ 1 + im \cdot \left(0.5 + im \cdot 0.25\right) \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (+ 1.0 (* im (+ 0.5 (* im 0.25)))))

C

double code(double re, double im) {
	return 1.0 + (im * (0.5 + (im * 0.25)));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 1.0d0 + (im * (0.5d0 + (im * 0.25d0)))
end function

Java

public static double code(double re, double im) {
	return 1.0 + (im * (0.5 + (im * 0.25)));
}

Python

def code(re, im):
	return 1.0 + (im * (0.5 + (im * 0.25)))

Julia

function code(re, im)
	return Float64(1.0 + Float64(im * Float64(0.5 + Float64(im * 0.25))))
end

MATLAB

function tmp = code(re, im)
	tmp = 1.0 + (im * (0.5 + (im * 0.25)));
end

Wolfram

code[re_, im_] := N[(1.0 + N[(im * N[(0.5 + N[(im * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 28.8% accurate, 61.6× speedup

Math

\[\begin{array}{l} \\ 1 + 0.5 \cdot im \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (+ 1.0 (* 0.5 im)))

C

double code(double re, double im) {
	return 1.0 + (0.5 * im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 1.0d0 + (0.5d0 * im)
end function

Java

public static double code(double re, double im) {
	return 1.0 + (0.5 * im);
}

Python

def code(re, im):
	return 1.0 + (0.5 * im)

Julia

function code(re, im)
	return Float64(1.0 + Float64(0.5 * im))
end

MATLAB

function tmp = code(re, im)
	tmp = 1.0 + (0.5 * im);
end

Wolfram

code[re_, im_] := N[(1.0 + N[(0.5 * im), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 13: 28.9% accurate, 308.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (re im) :precision binary64 1.0)

C

double code(double re, double im) {
	return 1.0;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 1.0d0
end function

Java

public static double code(double re, double im) {
	return 1.0;
}

Python

def code(re, im):
	return 1.0

Julia

function code(re, im)
	return 1.0
end

MATLAB

function tmp = code(re, im)
	tmp = 1.0;
end

Wolfram

code[re_, im_] := 1.0

Derivation

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

Reproduce

herbie shell --seed 2023350 
(FPCore (re im)
  :name "math.cos on complex, real part"
  :precision binary64
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))