math.sin on complex, imaginary part

Percentage Accurate: 54.8% → 99.6%

Time: 11.3s

Alternatives: 12

Speedup: 2.8×

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

Specification

Math

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

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: 54.8% 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: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m}\\ t_1 := \cos re \cdot -0.5\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 - e^{im_m} \leq -1000000000:\\ \;\;\;\;\left(e^{im_m} - t_0\right) \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(0.016666666666666666 \cdot {im_m}^{5} + \left(0.3333333333333333 \cdot {im_m}^{3} + im_m \cdot 2\right)\right)\\ \end{array} \end{array} \end{array} \]

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))) (t_1 (* (cos re) -0.5)))
   (*
    im_s
    (if (<= (- t_0 (exp im_m)) -1000000000.0)
      (* (- (exp im_m) t_0) t_1)
      (*
       t_1
       (+
        (* 0.016666666666666666 (pow im_m 5.0))
        (+ (* 0.3333333333333333 (pow im_m 3.0)) (* 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);
	double t_1 = cos(re) * -0.5;
	double tmp;
	if ((t_0 - exp(im_m)) <= -1000000000.0) {
		tmp = (exp(im_m) - t_0) * t_1;
	} else {
		tmp = t_1 * ((0.016666666666666666 * pow(im_m, 5.0)) + ((0.3333333333333333 * pow(im_m, 3.0)) + (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) :: t_1
    real(8) :: tmp
    t_0 = exp(-im_m)
    t_1 = cos(re) * (-0.5d0)
    if ((t_0 - exp(im_m)) <= (-1000000000.0d0)) then
        tmp = (exp(im_m) - t_0) * t_1
    else
        tmp = t_1 * ((0.016666666666666666d0 * (im_m ** 5.0d0)) + ((0.3333333333333333d0 * (im_m ** 3.0d0)) + (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);
	double t_1 = Math.cos(re) * -0.5;
	double tmp;
	if ((t_0 - Math.exp(im_m)) <= -1000000000.0) {
		tmp = (Math.exp(im_m) - t_0) * t_1;
	} else {
		tmp = t_1 * ((0.016666666666666666 * Math.pow(im_m, 5.0)) + ((0.3333333333333333 * Math.pow(im_m, 3.0)) + (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)
	t_1 = math.cos(re) * -0.5
	tmp = 0
	if (t_0 - math.exp(im_m)) <= -1000000000.0:
		tmp = (math.exp(im_m) - t_0) * t_1
	else:
		tmp = t_1 * ((0.016666666666666666 * math.pow(im_m, 5.0)) + ((0.3333333333333333 * math.pow(im_m, 3.0)) + (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 = exp(Float64(-im_m))
	t_1 = Float64(cos(re) * -0.5)
	tmp = 0.0
	if (Float64(t_0 - exp(im_m)) <= -1000000000.0)
		tmp = Float64(Float64(exp(im_m) - t_0) * t_1);
	else
		tmp = Float64(t_1 * Float64(Float64(0.016666666666666666 * (im_m ^ 5.0)) + Float64(Float64(0.3333333333333333 * (im_m ^ 3.0)) + 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);
	t_1 = cos(re) * -0.5;
	tmp = 0.0;
	if ((t_0 - exp(im_m)) <= -1000000000.0)
		tmp = (exp(im_m) - t_0) * t_1;
	else
		tmp = t_1 * ((0.016666666666666666 * (im_m ^ 5.0)) + ((0.3333333333333333 * (im_m ^ 3.0)) + (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[Exp[(-im$95$m)], $MachinePrecision]}, Block[{t$95$1 = N[(N[Cos[re], $MachinePrecision] * -0.5), $MachinePrecision]}, N[(im$95$s * If[LessEqual[N[(t$95$0 - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision], -1000000000.0], N[(N[(N[Exp[im$95$m], $MachinePrecision] - t$95$0), $MachinePrecision] * t$95$1), $MachinePrecision], N[(t$95$1 * N[(N[(0.016666666666666666 * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision] + N[(N[(0.3333333333333333 * N[Power[im$95$m, 3.0], $MachinePrecision]), $MachinePrecision] + N[(im$95$m * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

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

Alternative 2: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m}\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 - e^{im_m} \leq -0.01:\\ \;\;\;\;\left(e^{im_m} - t_0\right) \cdot \left(\cos re \cdot -0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \end{array} \end{array} \end{array} \]

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))))
   (*
    im_s
    (if (<= (- t_0 (exp im_m)) -0.01)
      (* (- (exp im_m) t_0) (* (cos re) -0.5))
      (* (cos re) (- (* (pow im_m 3.0) -0.16666666666666666) im_m))))))

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);
	double tmp;
	if ((t_0 - exp(im_m)) <= -0.01) {
		tmp = (exp(im_m) - t_0) * (cos(re) * -0.5);
	} else {
		tmp = cos(re) * ((pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	}
	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)
    if ((t_0 - exp(im_m)) <= (-0.01d0)) then
        tmp = (exp(im_m) - t_0) * (cos(re) * (-0.5d0))
    else
        tmp = cos(re) * (((im_m ** 3.0d0) * (-0.16666666666666666d0)) - im_m)
    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);
	double tmp;
	if ((t_0 - Math.exp(im_m)) <= -0.01) {
		tmp = (Math.exp(im_m) - t_0) * (Math.cos(re) * -0.5);
	} else {
		tmp = Math.cos(re) * ((Math.pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	}
	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)
	tmp = 0
	if (t_0 - math.exp(im_m)) <= -0.01:
		tmp = (math.exp(im_m) - t_0) * (math.cos(re) * -0.5)
	else:
		tmp = math.cos(re) * ((math.pow(im_m, 3.0) * -0.16666666666666666) - im_m)
	return im_s * tmp

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	t_0 = exp(Float64(-im_m))
	tmp = 0.0
	if (Float64(t_0 - exp(im_m)) <= -0.01)
		tmp = Float64(Float64(exp(im_m) - t_0) * Float64(cos(re) * -0.5));
	else
		tmp = Float64(cos(re) * Float64(Float64((im_m ^ 3.0) * -0.16666666666666666) - im_m));
	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);
	tmp = 0.0;
	if ((t_0 - exp(im_m)) <= -0.01)
		tmp = (exp(im_m) - t_0) * (cos(re) * -0.5);
	else
		tmp = cos(re) * (((im_m ^ 3.0) * -0.16666666666666666) - im_m);
	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[Exp[(-im$95$m)], $MachinePrecision]}, N[(im$95$s * If[LessEqual[N[(t$95$0 - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision], -0.01], N[(N[(N[Exp[im$95$m], $MachinePrecision] - t$95$0), $MachinePrecision] * N[(N[Cos[re], $MachinePrecision] * -0.5), $MachinePrecision]), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[(N[Power[im$95$m, 3.0], $MachinePrecision] * -0.16666666666666666), $MachinePrecision] - im$95$m), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 3: 96.7% accurate, 1.4× speedup

Math

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

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 5e-5)
    (* im_m (- (cos re)))
    (if (<= im_m 4.5e+61)
      (* (- (exp im_m) (exp (- im_m))) -0.5)
      (* -0.008333333333333333 (* (cos re) (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 tmp;
	if (im_m <= 5e-5) {
		tmp = im_m * -cos(re);
	} else if (im_m <= 4.5e+61) {
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	} else {
		tmp = -0.008333333333333333 * (cos(re) * 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) :: tmp
    if (im_m <= 5d-5) then
        tmp = im_m * -cos(re)
    else if (im_m <= 4.5d+61) then
        tmp = (exp(im_m) - exp(-im_m)) * (-0.5d0)
    else
        tmp = (-0.008333333333333333d0) * (cos(re) * (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 tmp;
	if (im_m <= 5e-5) {
		tmp = im_m * -Math.cos(re);
	} else if (im_m <= 4.5e+61) {
		tmp = (Math.exp(im_m) - Math.exp(-im_m)) * -0.5;
	} else {
		tmp = -0.008333333333333333 * (Math.cos(re) * 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):
	tmp = 0
	if im_m <= 5e-5:
		tmp = im_m * -math.cos(re)
	elif im_m <= 4.5e+61:
		tmp = (math.exp(im_m) - math.exp(-im_m)) * -0.5
	else:
		tmp = -0.008333333333333333 * (math.cos(re) * 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)
	tmp = 0.0
	if (im_m <= 5e-5)
		tmp = Float64(im_m * Float64(-cos(re)));
	elseif (im_m <= 4.5e+61)
		tmp = Float64(Float64(exp(im_m) - exp(Float64(-im_m))) * -0.5);
	else
		tmp = Float64(-0.008333333333333333 * Float64(cos(re) * (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)
	tmp = 0.0;
	if (im_m <= 5e-5)
		tmp = im_m * -cos(re);
	elseif (im_m <= 4.5e+61)
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	else
		tmp = -0.008333333333333333 * (cos(re) * (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_] := N[(im$95$s * If[LessEqual[im$95$m, 5e-5], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], If[LessEqual[im$95$m, 4.5e+61], N[(N[(N[Exp[im$95$m], $MachinePrecision] - N[Exp[(-im$95$m)], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision], N[(-0.008333333333333333 * N[(N[Cos[re], $MachinePrecision] * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 4: 96.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.0076:\\ \;\;\;\;\cos re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \mathbf{elif}\;im_m \leq 5 \cdot 10^{+61}:\\ \;\;\;\;\left(e^{im_m} - e^{-im_m}\right) \cdot -0.5\\ \mathbf{else}:\\ \;\;\;\;-0.008333333333333333 \cdot \left(\cos re \cdot {im_m}^{5}\right)\\ \end{array} \end{array} \]

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 0.0076)
    (* (cos re) (- (* (pow im_m 3.0) -0.16666666666666666) im_m))
    (if (<= im_m 5e+61)
      (* (- (exp im_m) (exp (- im_m))) -0.5)
      (* -0.008333333333333333 (* (cos re) (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 tmp;
	if (im_m <= 0.0076) {
		tmp = cos(re) * ((pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else if (im_m <= 5e+61) {
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	} else {
		tmp = -0.008333333333333333 * (cos(re) * 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) :: tmp
    if (im_m <= 0.0076d0) then
        tmp = cos(re) * (((im_m ** 3.0d0) * (-0.16666666666666666d0)) - im_m)
    else if (im_m <= 5d+61) then
        tmp = (exp(im_m) - exp(-im_m)) * (-0.5d0)
    else
        tmp = (-0.008333333333333333d0) * (cos(re) * (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 tmp;
	if (im_m <= 0.0076) {
		tmp = Math.cos(re) * ((Math.pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else if (im_m <= 5e+61) {
		tmp = (Math.exp(im_m) - Math.exp(-im_m)) * -0.5;
	} else {
		tmp = -0.008333333333333333 * (Math.cos(re) * 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):
	tmp = 0
	if im_m <= 0.0076:
		tmp = math.cos(re) * ((math.pow(im_m, 3.0) * -0.16666666666666666) - im_m)
	elif im_m <= 5e+61:
		tmp = (math.exp(im_m) - math.exp(-im_m)) * -0.5
	else:
		tmp = -0.008333333333333333 * (math.cos(re) * 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)
	tmp = 0.0
	if (im_m <= 0.0076)
		tmp = Float64(cos(re) * Float64(Float64((im_m ^ 3.0) * -0.16666666666666666) - im_m));
	elseif (im_m <= 5e+61)
		tmp = Float64(Float64(exp(im_m) - exp(Float64(-im_m))) * -0.5);
	else
		tmp = Float64(-0.008333333333333333 * Float64(cos(re) * (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)
	tmp = 0.0;
	if (im_m <= 0.0076)
		tmp = cos(re) * (((im_m ^ 3.0) * -0.16666666666666666) - im_m);
	elseif (im_m <= 5e+61)
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	else
		tmp = -0.008333333333333333 * (cos(re) * (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_] := N[(im$95$s * If[LessEqual[im$95$m, 0.0076], N[(N[Cos[re], $MachinePrecision] * N[(N[(N[Power[im$95$m, 3.0], $MachinePrecision] * -0.16666666666666666), $MachinePrecision] - im$95$m), $MachinePrecision]), $MachinePrecision], If[LessEqual[im$95$m, 5e+61], N[(N[(N[Exp[im$95$m], $MachinePrecision] - N[Exp[(-im$95$m)], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision], N[(-0.008333333333333333 * N[(N[Cos[re], $MachinePrecision] * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 5: 86.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.00018:\\ \;\;\;\;im_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{im_m} - e^{-im_m}\right) \cdot -0.5\\ \end{array} \end{array} \]

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 0.00018)
    (* im_m (- (cos re)))
    (* (- (exp im_m) (exp (- im_m))) -0.5))))

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 <= 0.00018) {
		tmp = im_m * -cos(re);
	} else {
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	}
	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 <= 0.00018d0) then
        tmp = im_m * -cos(re)
    else
        tmp = (exp(im_m) - exp(-im_m)) * (-0.5d0)
    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 <= 0.00018) {
		tmp = im_m * -Math.cos(re);
	} else {
		tmp = (Math.exp(im_m) - Math.exp(-im_m)) * -0.5;
	}
	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 <= 0.00018:
		tmp = im_m * -math.cos(re)
	else:
		tmp = (math.exp(im_m) - math.exp(-im_m)) * -0.5
	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 <= 0.00018)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = Float64(Float64(exp(im_m) - exp(Float64(-im_m))) * -0.5);
	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 <= 0.00018)
		tmp = im_m * -cos(re);
	else
		tmp = (exp(im_m) - exp(-im_m)) * -0.5;
	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, 0.00018], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], N[(N[(N[Exp[im$95$m], $MachinePrecision] - N[Exp[(-im$95$m)], $MachinePrecision]), $MachinePrecision] * -0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 6: 80.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 540:\\ \;\;\;\;im_m \cdot \left(-\cos re\right)\\ \mathbf{elif}\;im_m \leq 2.9 \cdot 10^{+59}:\\ \;\;\;\;0.5 \cdot \left(im_m \cdot {re}^{2}\right) - im_m\\ \mathbf{else}:\\ \;\;\;\;{im_m}^{5} \cdot -0.008333333333333333 - im_m\\ \end{array} \end{array} \]

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 540.0)
    (* im_m (- (cos re)))
    (if (<= im_m 2.9e+59)
      (- (* 0.5 (* im_m (pow re 2.0))) im_m)
      (- (* (pow im_m 5.0) -0.008333333333333333) im_m)))))

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 <= 540.0) {
		tmp = im_m * -cos(re);
	} else if (im_m <= 2.9e+59) {
		tmp = (0.5 * (im_m * pow(re, 2.0))) - im_m;
	} else {
		tmp = (pow(im_m, 5.0) * -0.008333333333333333) - im_m;
	}
	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 <= 540.0d0) then
        tmp = im_m * -cos(re)
    else if (im_m <= 2.9d+59) then
        tmp = (0.5d0 * (im_m * (re ** 2.0d0))) - im_m
    else
        tmp = ((im_m ** 5.0d0) * (-0.008333333333333333d0)) - im_m
    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 <= 540.0) {
		tmp = im_m * -Math.cos(re);
	} else if (im_m <= 2.9e+59) {
		tmp = (0.5 * (im_m * Math.pow(re, 2.0))) - im_m;
	} else {
		tmp = (Math.pow(im_m, 5.0) * -0.008333333333333333) - im_m;
	}
	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 <= 540.0:
		tmp = im_m * -math.cos(re)
	elif im_m <= 2.9e+59:
		tmp = (0.5 * (im_m * math.pow(re, 2.0))) - im_m
	else:
		tmp = (math.pow(im_m, 5.0) * -0.008333333333333333) - im_m
	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 <= 540.0)
		tmp = Float64(im_m * Float64(-cos(re)));
	elseif (im_m <= 2.9e+59)
		tmp = Float64(Float64(0.5 * Float64(im_m * (re ^ 2.0))) - im_m);
	else
		tmp = Float64(Float64((im_m ^ 5.0) * -0.008333333333333333) - im_m);
	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 <= 540.0)
		tmp = im_m * -cos(re);
	elseif (im_m <= 2.9e+59)
		tmp = (0.5 * (im_m * (re ^ 2.0))) - im_m;
	else
		tmp = ((im_m ^ 5.0) * -0.008333333333333333) - im_m;
	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, 540.0], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], If[LessEqual[im$95$m, 2.9e+59], N[(N[(0.5 * N[(im$95$m * N[Power[re, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - im$95$m), $MachinePrecision], N[(N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision] - im$95$m), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 7: 79.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 3.85 \cdot 10^{+55}:\\ \;\;\;\;im_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(0.016666666666666666 \cdot {im_m}^{5}\right)\\ \end{array} \end{array} \]

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 3.85e+55)
    (* im_m (- (cos re)))
    (* -0.5 (* 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 tmp;
	if (im_m <= 3.85e+55) {
		tmp = im_m * -cos(re);
	} else {
		tmp = -0.5 * (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) :: tmp
    if (im_m <= 3.85d+55) then
        tmp = im_m * -cos(re)
    else
        tmp = (-0.5d0) * (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 tmp;
	if (im_m <= 3.85e+55) {
		tmp = im_m * -Math.cos(re);
	} else {
		tmp = -0.5 * (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):
	tmp = 0
	if im_m <= 3.85e+55:
		tmp = im_m * -math.cos(re)
	else:
		tmp = -0.5 * (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)
	tmp = 0.0
	if (im_m <= 3.85e+55)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = Float64(-0.5 * 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)
	tmp = 0.0;
	if (im_m <= 3.85e+55)
		tmp = im_m * -cos(re);
	else
		tmp = -0.5 * (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_] := N[(im$95$s * If[LessEqual[im$95$m, 3.85e+55], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], N[(-0.5 * N[(0.016666666666666666 * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 79.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 3.85 \cdot 10^{+55}:\\ \;\;\;\;im_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;{im_m}^{5} \cdot -0.008333333333333333 - im_m\\ \end{array} \end{array} \]

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 3.85e+55)
    (* im_m (- (cos re)))
    (- (* (pow im_m 5.0) -0.008333333333333333) im_m))))

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 <= 3.85e+55) {
		tmp = im_m * -cos(re);
	} else {
		tmp = (pow(im_m, 5.0) * -0.008333333333333333) - im_m;
	}
	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 <= 3.85d+55) then
        tmp = im_m * -cos(re)
    else
        tmp = ((im_m ** 5.0d0) * (-0.008333333333333333d0)) - im_m
    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 <= 3.85e+55) {
		tmp = im_m * -Math.cos(re);
	} else {
		tmp = (Math.pow(im_m, 5.0) * -0.008333333333333333) - im_m;
	}
	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 <= 3.85e+55:
		tmp = im_m * -math.cos(re)
	else:
		tmp = (math.pow(im_m, 5.0) * -0.008333333333333333) - im_m
	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 <= 3.85e+55)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = Float64(Float64((im_m ^ 5.0) * -0.008333333333333333) - im_m);
	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 <= 3.85e+55)
		tmp = im_m * -cos(re);
	else
		tmp = ((im_m ^ 5.0) * -0.008333333333333333) - im_m;
	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, 3.85e+55], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], N[(N[(N[Power[im$95$m, 5.0], $MachinePrecision] * -0.008333333333333333), $MachinePrecision] - im$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 9: 51.6% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

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 * (im_m * -cos(re))
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 * (im_m * -Math.cos(re));
}

Python

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

Julia

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

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp = code(im_s, re, im_m)
	tmp = im_s * (im_m * -cos(re));
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[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 29.3% 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: 2.2% 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

Alternative 12: 3.4% accurate, 309.0× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot 0 \end{array} \]

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m) :precision binary64 (* im_s 0.0))

C

im_m = fabs(im);
im_s = copysign(1.0, im);
double code(double im_s, double re, double im_m) {
	return im_s * 0.0;
}

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 * 0.0d0
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 * 0.0;
}

Python

im_m = math.fabs(im)
im_s = math.copysign(1.0, im)
def code(im_s, re, im_m):
	return im_s * 0.0

Julia

im_m = abs(im)
im_s = copysign(1.0, im)
function code(im_s, re, im_m)
	return Float64(im_s * 0.0)
end

MATLAB

im_m = abs(im);
im_s = sign(im) * abs(1.0);
function tmp = code(im_s, re, im_m)
	tmp = im_s * 0.0;
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 * 0.0), $MachinePrecision]

Derivation

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

Developer target: 99.8% accurate, 0.7× 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 2024006 
(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))))