math.sin on complex, imaginary part

Percentage Accurate: 53.4% → 99.9%

Time: 9.0s

Alternatives: 11

Speedup: 2.9×

• 48.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp((0.0 - 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((0.0d0 - im)) - exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp((0.0 - im)) - Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp((0.0 - im)) - math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(0.0 - im)) - exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp((0.0 - im)) - exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] - N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))

C

double code(double re, double im) {
	return (0.5 * cos(re)) * (exp((0.0 - 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((0.0d0 - im)) - exp(im))
end function

Java

public static double code(double re, double im) {
	return (0.5 * Math.cos(re)) * (Math.exp((0.0 - im)) - Math.exp(im));
}

Python

def code(re, im):
	return (0.5 * math.cos(re)) * (math.exp((0.0 - im)) - math.exp(im))

Julia

function code(re, im)
	return Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(0.0 - im)) - exp(im)))
end

MATLAB

function tmp = code(re, im)
	tmp = (0.5 * cos(re)) * (exp((0.0 - im)) - exp(im));
end

Wolfram

code[re_, im_] := N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] - N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -0.2:\\ \;\;\;\;0.5 \cdot \left(t_0 \cdot \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2 + \left(-0.3333333333333333 \cdot {im_m}^{3} + -0.016666666666666666 \cdot {im_m}^{5}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (let* ((t_0 (- (exp (- im_m)) (exp im_m))))
   (*
    im_s
    (if (<= t_0 -0.2)
      (* 0.5 (* t_0 (cos re)))
      (*
       0.5
       (*
        (cos re)
        (+
         (* im_m -2.0)
         (+
          (* -0.3333333333333333 (pow im_m 3.0))
          (* -0.016666666666666666 (pow im_m 5.0))))))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double t_0 = exp(-im_m) - exp(im_m);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = 0.5 * (t_0 * cos(re));
	} else {
		tmp = 0.5 * (cos(re) * ((im_m * -2.0) + ((-0.3333333333333333 * pow(im_m, 3.0)) + (-0.016666666666666666 * pow(im_m, 5.0)))));
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(-im_m) - exp(im_m)
    if (t_0 <= (-0.2d0)) then
        tmp = 0.5d0 * (t_0 * cos(re))
    else
        tmp = 0.5d0 * (cos(re) * ((im_m * (-2.0d0)) + (((-0.3333333333333333d0) * (im_m ** 3.0d0)) + ((-0.016666666666666666d0) * (im_m ** 5.0d0)))))
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double t_0 = Math.exp(-im_m) - Math.exp(im_m);
	double tmp;
	if (t_0 <= -0.2) {
		tmp = 0.5 * (t_0 * Math.cos(re));
	} else {
		tmp = 0.5 * (Math.cos(re) * ((im_m * -2.0) + ((-0.3333333333333333 * Math.pow(im_m, 3.0)) + (-0.016666666666666666 * Math.pow(im_m, 5.0)))));
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	t_0 = math.exp(-im_m) - math.exp(im_m)
	tmp = 0
	if t_0 <= -0.2:
		tmp = 0.5 * (t_0 * math.cos(re))
	else:
		tmp = 0.5 * (math.cos(re) * ((im_m * -2.0) + ((-0.3333333333333333 * math.pow(im_m, 3.0)) + (-0.016666666666666666 * math.pow(im_m, 5.0)))))
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	t_0 = Float64(exp(Float64(-im_m)) - exp(im_m))
	tmp = 0.0
	if (t_0 <= -0.2)
		tmp = Float64(0.5 * Float64(t_0 * cos(re)));
	else
		tmp = Float64(0.5 * Float64(cos(re) * Float64(Float64(im_m * -2.0) + Float64(Float64(-0.3333333333333333 * (im_m ^ 3.0)) + Float64(-0.016666666666666666 * (im_m ^ 5.0))))));
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	t_0 = exp(-im_m) - exp(im_m);
	tmp = 0.0;
	if (t_0 <= -0.2)
		tmp = 0.5 * (t_0 * cos(re));
	else
		tmp = 0.5 * (cos(re) * ((im_m * -2.0) + ((-0.3333333333333333 * (im_m ^ 3.0)) + (-0.016666666666666666 * (im_m ^ 5.0)))));
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := Block[{t$95$0 = N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, -0.2], N[(0.5 * N[(t$95$0 * N[Cos[re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(N[(im$95$m * -2.0), $MachinePrecision] + N[(N[(-0.3333333333333333 * N[Power[im$95$m, 3.0], $MachinePrecision]), $MachinePrecision] + N[(-0.016666666666666666 * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 2: 99.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -0.002:\\ \;\;\;\;0.5 \cdot \left(t_0 \cdot \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (let* ((t_0 (- (exp (- im_m)) (exp im_m))))
   (*
    im_s
    (if (<= t_0 -0.002)
      (* 0.5 (* t_0 (cos re)))
      (* 0.5 (* (cos re) (* im_m -2.0)))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double t_0 = exp(-im_m) - exp(im_m);
	double tmp;
	if (t_0 <= -0.002) {
		tmp = 0.5 * (t_0 * cos(re));
	} else {
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(-im_m) - exp(im_m)
    if (t_0 <= (-0.002d0)) then
        tmp = 0.5d0 * (t_0 * cos(re))
    else
        tmp = 0.5d0 * (cos(re) * (im_m * (-2.0d0)))
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double t_0 = Math.exp(-im_m) - Math.exp(im_m);
	double tmp;
	if (t_0 <= -0.002) {
		tmp = 0.5 * (t_0 * Math.cos(re));
	} else {
		tmp = 0.5 * (Math.cos(re) * (im_m * -2.0));
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	t_0 = math.exp(-im_m) - math.exp(im_m)
	tmp = 0
	if t_0 <= -0.002:
		tmp = 0.5 * (t_0 * math.cos(re))
	else:
		tmp = 0.5 * (math.cos(re) * (im_m * -2.0))
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	t_0 = Float64(exp(Float64(-im_m)) - exp(im_m))
	tmp = 0.0
	if (t_0 <= -0.002)
		tmp = Float64(0.5 * Float64(t_0 * cos(re)));
	else
		tmp = Float64(0.5 * Float64(cos(re) * Float64(im_m * -2.0)));
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	t_0 = exp(-im_m) - exp(im_m);
	tmp = 0.0;
	if (t_0 <= -0.002)
		tmp = 0.5 * (t_0 * cos(re));
	else
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := Block[{t$95$0 = N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, -0.002], N[(0.5 * N[(t$95$0 * N[Cos[re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 3: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \left(0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(im_m \cdot \left(\cos re \cdot -2\right)\right)\right)\right) \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (* im_s (* 0.5 (log1p (expm1 (* im_m (* (cos re) -2.0)))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	return im_s * (0.5 * log1p(expm1((im_m * (cos(re) * -2.0)))));
}

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	return im_s * (0.5 * Math.log1p(Math.expm1((im_m * (Math.cos(re) * -2.0)))));
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	return im_s * (0.5 * math.log1p(math.expm1((im_m * (math.cos(re) * -2.0)))))

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	return Float64(im_s * Float64(0.5 * log1p(expm1(Float64(im_m * Float64(cos(re) * -2.0))))))
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * N[(0.5 * N[Log[1 + N[(Exp[N[(im$95$m * N[(N[Cos[re], $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 4: 97.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.122:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2 + -0.3333333333333333 \cdot {im_m}^{3}\right)\right)\\ \mathbf{elif}\;im_m \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;0.5 \cdot \left(e^{-im_m} - e^{im_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im_m}^{5} \cdot -0.008333333333333333\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 0.122)
    (*
     0.5
     (* (cos re) (+ (* im_m -2.0) (* -0.3333333333333333 (pow im_m 3.0)))))
    (if (<= im_m 4.5e+61)
      (* 0.5 (- (exp (- im_m)) (exp im_m)))
      (* (cos re) (* (pow im_m 5.0) -0.008333333333333333))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.122) {
		tmp = 0.5 * (cos(re) * ((im_m * -2.0) + (-0.3333333333333333 * pow(im_m, 3.0))));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * (exp(-im_m) - exp(im_m));
	} else {
		tmp = cos(re) * (pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 0.122d0) then
        tmp = 0.5d0 * (cos(re) * ((im_m * (-2.0d0)) + ((-0.3333333333333333d0) * (im_m ** 3.0d0))))
    else if (im_m <= 4.5d+61) then
        tmp = 0.5d0 * (exp(-im_m) - exp(im_m))
    else
        tmp = cos(re) * ((im_m ** 5.0d0) * (-0.008333333333333333d0))
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.122) {
		tmp = 0.5 * (Math.cos(re) * ((im_m * -2.0) + (-0.3333333333333333 * Math.pow(im_m, 3.0))));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * (Math.exp(-im_m) - Math.exp(im_m));
	} else {
		tmp = Math.cos(re) * (Math.pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 0.122:
		tmp = 0.5 * (math.cos(re) * ((im_m * -2.0) + (-0.3333333333333333 * math.pow(im_m, 3.0))))
	elif im_m <= 4.5e+61:
		tmp = 0.5 * (math.exp(-im_m) - math.exp(im_m))
	else:
		tmp = math.cos(re) * (math.pow(im_m, 5.0) * -0.008333333333333333)
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 0.122)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(Float64(im_m * -2.0) + Float64(-0.3333333333333333 * (im_m ^ 3.0)))));
	elseif (im_m <= 4.5e+61)
		tmp = Float64(0.5 * Float64(exp(Float64(-im_m)) - exp(im_m)));
	else
		tmp = Float64(cos(re) * Float64((im_m ^ 5.0) * -0.008333333333333333));
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	tmp = 0.0;
	if (im_m <= 0.122)
		tmp = 0.5 * (cos(re) * ((im_m * -2.0) + (-0.3333333333333333 * (im_m ^ 3.0))));
	elseif (im_m <= 4.5e+61)
		tmp = 0.5 * (exp(-im_m) - exp(im_m));
	else
		tmp = cos(re) * ((im_m ^ 5.0) * -0.008333333333333333);
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 0.122], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(N[(im$95$m * -2.0), $MachinePrecision] + N[(-0.3333333333333333 * N[Power[im$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im$95$m, 4.5e+61], N[(0.5 * N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 5: 96.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 480:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2\right)\right)\\ \mathbf{elif}\;im_m \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(im_m \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im_m}^{5} \cdot -0.008333333333333333\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 480.0)
    (* 0.5 (* (cos re) (* im_m -2.0)))
    (if (<= im_m 4.5e+61)
      (* 0.5 (log1p (expm1 (* im_m -2.0))))
      (* (cos re) (* (pow im_m 5.0) -0.008333333333333333))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 480.0) {
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * log1p(expm1((im_m * -2.0)));
	} else {
		tmp = cos(re) * (pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 480.0) {
		tmp = 0.5 * (Math.cos(re) * (im_m * -2.0));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * Math.log1p(Math.expm1((im_m * -2.0)));
	} else {
		tmp = Math.cos(re) * (Math.pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 480.0:
		tmp = 0.5 * (math.cos(re) * (im_m * -2.0))
	elif im_m <= 4.5e+61:
		tmp = 0.5 * math.log1p(math.expm1((im_m * -2.0)))
	else:
		tmp = math.cos(re) * (math.pow(im_m, 5.0) * -0.008333333333333333)
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 480.0)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(im_m * -2.0)));
	elseif (im_m <= 4.5e+61)
		tmp = Float64(0.5 * log1p(expm1(Float64(im_m * -2.0))));
	else
		tmp = Float64(cos(re) * Float64((im_m ^ 5.0) * -0.008333333333333333));
	end
	return Float64(im_s * tmp)
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 480.0], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im$95$m, 4.5e+61], N[(0.5 * N[Log[1 + N[(Exp[N[(im$95$m * -2.0), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 6: 96.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.0027:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2\right)\right)\\ \mathbf{elif}\;im_m \leq 4.5 \cdot 10^{+61}:\\ \;\;\;\;0.5 \cdot \left(e^{-im_m} - e^{im_m}\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im_m}^{5} \cdot -0.008333333333333333\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 0.0027)
    (* 0.5 (* (cos re) (* im_m -2.0)))
    (if (<= im_m 4.5e+61)
      (* 0.5 (- (exp (- im_m)) (exp im_m)))
      (* (cos re) (* (pow im_m 5.0) -0.008333333333333333))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.0027) {
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * (exp(-im_m) - exp(im_m));
	} else {
		tmp = cos(re) * (pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 0.0027d0) then
        tmp = 0.5d0 * (cos(re) * (im_m * (-2.0d0)))
    else if (im_m <= 4.5d+61) then
        tmp = 0.5d0 * (exp(-im_m) - exp(im_m))
    else
        tmp = cos(re) * ((im_m ** 5.0d0) * (-0.008333333333333333d0))
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.0027) {
		tmp = 0.5 * (Math.cos(re) * (im_m * -2.0));
	} else if (im_m <= 4.5e+61) {
		tmp = 0.5 * (Math.exp(-im_m) - Math.exp(im_m));
	} else {
		tmp = Math.cos(re) * (Math.pow(im_m, 5.0) * -0.008333333333333333);
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 0.0027:
		tmp = 0.5 * (math.cos(re) * (im_m * -2.0))
	elif im_m <= 4.5e+61:
		tmp = 0.5 * (math.exp(-im_m) - math.exp(im_m))
	else:
		tmp = math.cos(re) * (math.pow(im_m, 5.0) * -0.008333333333333333)
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 0.0027)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(im_m * -2.0)));
	elseif (im_m <= 4.5e+61)
		tmp = Float64(0.5 * Float64(exp(Float64(-im_m)) - exp(im_m)));
	else
		tmp = Float64(cos(re) * Float64((im_m ^ 5.0) * -0.008333333333333333));
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	tmp = 0.0;
	if (im_m <= 0.0027)
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	elseif (im_m <= 4.5e+61)
		tmp = 0.5 * (exp(-im_m) - exp(im_m));
	else
		tmp = cos(re) * ((im_m ^ 5.0) * -0.008333333333333333);
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 0.0027], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im$95$m, 4.5e+61], N[(0.5 * N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 7: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 470:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(im_m \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 470.0)
    (* 0.5 (* (cos re) (* im_m -2.0)))
    (* 0.5 (log1p (expm1 (* im_m -2.0)))))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 470.0) {
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	} else {
		tmp = 0.5 * log1p(expm1((im_m * -2.0)));
	}
	return im_s * tmp;
}

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 470.0) {
		tmp = 0.5 * (Math.cos(re) * (im_m * -2.0));
	} else {
		tmp = 0.5 * Math.log1p(Math.expm1((im_m * -2.0)));
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 470.0:
		tmp = 0.5 * (math.cos(re) * (im_m * -2.0))
	else:
		tmp = 0.5 * math.log1p(math.expm1((im_m * -2.0)))
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 470.0)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(im_m * -2.0)));
	else
		tmp = Float64(0.5 * log1p(expm1(Float64(im_m * -2.0))));
	end
	return Float64(im_s * tmp)
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 470.0], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[Log[1 + N[(Exp[N[(im$95$m * -2.0), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 80.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 5.2:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(im_m \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{im_m}^{5} \cdot -0.008333333333333333\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 5.2)
    (* 0.5 (* (cos re) (* im_m -2.0)))
    (* (pow im_m 5.0) -0.008333333333333333))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 5.2) {
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	} else {
		tmp = pow(im_m, 5.0) * -0.008333333333333333;
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 5.2d0) then
        tmp = 0.5d0 * (cos(re) * (im_m * (-2.0d0)))
    else
        tmp = (im_m ** 5.0d0) * (-0.008333333333333333d0)
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 5.2) {
		tmp = 0.5 * (Math.cos(re) * (im_m * -2.0));
	} else {
		tmp = Math.pow(im_m, 5.0) * -0.008333333333333333;
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 5.2:
		tmp = 0.5 * (math.cos(re) * (im_m * -2.0))
	else:
		tmp = math.pow(im_m, 5.0) * -0.008333333333333333
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 5.2)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(im_m * -2.0)));
	else
		tmp = Float64((im_m ^ 5.0) * -0.008333333333333333);
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	tmp = 0.0;
	if (im_m <= 5.2)
		tmp = 0.5 * (cos(re) * (im_m * -2.0));
	else
		tmp = (im_m ^ 5.0) * -0.008333333333333333;
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 5.2], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 57.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.12:\\ \;\;\;\;0.5 \cdot \left(im_m \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;{im_m}^{5} \cdot -0.008333333333333333\\ \end{array} \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m)
 :precision binary64
 (*
  im_s
  (if (<= im_m 0.12)
    (* 0.5 (* im_m -2.0))
    (* (pow im_m 5.0) -0.008333333333333333))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.12) {
		tmp = 0.5 * (im_m * -2.0);
	} else {
		tmp = pow(im_m, 5.0) * -0.008333333333333333;
	}
	return im_s * tmp;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    real(8) :: tmp
    if (im_m <= 0.12d0) then
        tmp = 0.5d0 * (im_m * (-2.0d0))
    else
        tmp = (im_m ** 5.0d0) * (-0.008333333333333333d0)
    end if
    code = im_s * tmp
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	double tmp;
	if (im_m <= 0.12) {
		tmp = 0.5 * (im_m * -2.0);
	} else {
		tmp = Math.pow(im_m, 5.0) * -0.008333333333333333;
	}
	return im_s * tmp;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	tmp = 0
	if im_m <= 0.12:
		tmp = 0.5 * (im_m * -2.0)
	else:
		tmp = math.pow(im_m, 5.0) * -0.008333333333333333
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	tmp = 0.0
	if (im_m <= 0.12)
		tmp = Float64(0.5 * Float64(im_m * -2.0));
	else
		tmp = Float64((im_m ^ 5.0) * -0.008333333333333333);
	end
	return Float64(im_s * tmp)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp_2 = code(im_s, re, im_m)
	tmp = 0.0;
	if (im_m <= 0.12)
		tmp = 0.5 * (im_m * -2.0);
	else
		tmp = (im_m ^ 5.0) * -0.008333333333333333;
	end
	tmp_2 = im_s * tmp;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * If[LessEqual[im$95$m, 0.12], N[(0.5 * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision], N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 30.0% accurate, 61.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \left(0.5 \cdot \left(im_m \cdot -2\right)\right) \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m) :precision binary64 (* im_s (* 0.5 (* im_m -2.0))))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	return im_s * (0.5 * (im_m * -2.0));
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    code = im_s * (0.5d0 * (im_m * (-2.0d0)))
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	return im_s * (0.5 * (im_m * -2.0));
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	return im_s * (0.5 * (im_m * -2.0))

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	return Float64(im_s * Float64(0.5 * Float64(im_m * -2.0)))
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp = code(im_s, re, im_m)
	tmp = im_s * (0.5 * (im_m * -2.0));
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * N[(0.5 * N[(im$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 11: 3.6% accurate, 309.0× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot -1 \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m) :precision binary64 (* im_s -1.0))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	return im_s * -1.0;
}

Fortran

im_m = abs(im)
im_s = copysign(1.0d0, im)
real(8) function code(im_s, re, im_m)
    real(8), intent (in) :: im_s
    real(8), intent (in) :: re
    real(8), intent (in) :: im_m
    code = im_s * (-1.0d0)
end function

Java

im_m = Math.abs(im);
im_s = Math.copySign(1.0, im);
public static double code(double im_s, double re, double im_m) {
	return im_s * -1.0;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	return im_s * -1.0

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	return Float64(im_s * -1.0)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp = code(im_s, re, im_m)
	tmp = im_s * -1.0;
end

Wolfram

im_m = N[Abs[im], $MachinePrecision]
im_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[im$95$s_, re_, im$95$m_] := N[(im$95$s * -1.0), $MachinePrecision]

Derivation

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

Developer target: 99.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|im\right| < 1:\\ \;\;\;\;-\cos re \cdot \left(\left(im + \left(\left(0.16666666666666666 \cdot im\right) \cdot im\right) \cdot im\right) + \left(\left(\left(\left(0.008333333333333333 \cdot im\right) \cdot im\right) \cdot im\right) \cdot im\right) \cdot im\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (< (fabs im) 1.0)
   (-
    (*
     (cos re)
     (+
      (+ im (* (* (* 0.16666666666666666 im) im) im))
      (* (* (* (* (* 0.008333333333333333 im) im) im) im) im))))
   (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im)))))

C

double code(double re, double im) {
	double tmp;
	if (fabs(im) < 1.0) {
		tmp = -(cos(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)));
	} else {
		tmp = (0.5 * cos(re)) * (exp((0.0 - im)) - 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 (abs(im) < 1.0d0) then
        tmp = -(cos(re) * ((im + (((0.16666666666666666d0 * im) * im) * im)) + (((((0.008333333333333333d0 * im) * im) * im) * im) * im)))
    else
        tmp = (0.5d0 * cos(re)) * (exp((0.0d0 - im)) - exp(im))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (Math.abs(im) < 1.0) {
		tmp = -(Math.cos(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)));
	} else {
		tmp = (0.5 * Math.cos(re)) * (Math.exp((0.0 - im)) - Math.exp(im));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if math.fabs(im) < 1.0:
		tmp = -(math.cos(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)))
	else:
		tmp = (0.5 * math.cos(re)) * (math.exp((0.0 - im)) - math.exp(im))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (abs(im) < 1.0)
		tmp = Float64(-Float64(cos(re) * Float64(Float64(im + Float64(Float64(Float64(0.16666666666666666 * im) * im) * im)) + Float64(Float64(Float64(Float64(Float64(0.008333333333333333 * im) * im) * im) * im) * im))));
	else
		tmp = Float64(Float64(0.5 * cos(re)) * Float64(exp(Float64(0.0 - im)) - exp(im)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (abs(im) < 1.0)
		tmp = -(cos(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)));
	else
		tmp = (0.5 * cos(re)) * (exp((0.0 - im)) - exp(im));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[Less[N[Abs[im], $MachinePrecision], 1.0], (-N[(N[Cos[re], $MachinePrecision] * N[(N[(im + N[(N[(N[(0.16666666666666666 * im), $MachinePrecision] * im), $MachinePrecision] * im), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(0.008333333333333333 * im), $MachinePrecision] * im), $MachinePrecision] * im), $MachinePrecision] * im), $MachinePrecision] * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), N[(N[(0.5 * N[Cos[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[N[(0.0 - im), $MachinePrecision]], $MachinePrecision] - N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023350 
(FPCore (re im)
  :name "math.sin on complex, imaginary part"
  :precision binary64

  :herbie-target
  (if (< (fabs im) 1.0) (- (* (cos re) (+ (+ im (* (* (* 0.16666666666666666 im) im) im)) (* (* (* (* (* 0.008333333333333333 im) im) im) im) im)))) (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))

  (* (* 0.5 (cos re)) (- (exp (- 0.0 im)) (exp im))))