math.cos on complex, imaginary part

Percentage Accurate: 66.0% → 99.4%

Time: 8.8s

Alternatives: 12

Speedup: 2.9×

• 49.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double re, double im) {
	return (0.5 * sin(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 * sin(re)) * (exp(-im) - exp(im))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double re, double im) {
	return (0.5 * sin(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 * sin(re)) * (exp(-im) - exp(im))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ t_1 := 0.5 \cdot \sin re\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_0 \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, im_m \cdot -2, t_1 \cdot \mathsf{fma}\left(-0.3333333333333333, {im_m}^{3}, \mathsf{fma}\left(-0.016666666666666666, {im_m}^{5}, -0.0003968253968253968 \cdot {im_m}^{7}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

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))) (t_1 (* 0.5 (sin re))))
   (*
    im_s
    (if (<= t_0 (- INFINITY))
      (* t_0 t_1)
      (fma
       t_1
       (* im_m -2.0)
       (*
        t_1
        (fma
         -0.3333333333333333
         (pow im_m 3.0)
         (fma
          -0.016666666666666666
          (pow im_m 5.0)
          (* -0.0003968253968253968 (pow im_m 7.0))))))))))

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 t_1 = 0.5 * sin(re);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_0 * t_1;
	} else {
		tmp = fma(t_1, (im_m * -2.0), (t_1 * fma(-0.3333333333333333, pow(im_m, 3.0), fma(-0.016666666666666666, pow(im_m, 5.0), (-0.0003968253968253968 * pow(im_m, 7.0))))));
	}
	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))
	t_1 = Float64(0.5 * sin(re))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(t_0 * t_1);
	else
		tmp = fma(t_1, Float64(im_m * -2.0), Float64(t_1 * fma(-0.3333333333333333, (im_m ^ 3.0), fma(-0.016666666666666666, (im_m ^ 5.0), Float64(-0.0003968253968253968 * (im_m ^ 7.0))))));
	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_] := Block[{t$95$0 = N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, (-Infinity)], N[(t$95$0 * t$95$1), $MachinePrecision], N[(t$95$1 * N[(im$95$m * -2.0), $MachinePrecision] + N[(t$95$1 * N[(-0.3333333333333333 * N[Power[im$95$m, 3.0], $MachinePrecision] + N[(-0.016666666666666666 * N[Power[im$95$m, 5.0], $MachinePrecision] + N[(-0.0003968253968253968 * N[Power[im$95$m, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ t_1 := 0.5 \cdot \sin re\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_0 \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(im_m \cdot -2 + \left(-0.3333333333333333 \cdot {im_m}^{3} + \left(-0.0003968253968253968 \cdot {im_m}^{7} + -0.016666666666666666 \cdot {im_m}^{5}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

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))) (t_1 (* 0.5 (sin re))))
   (*
    im_s
    (if (<= t_0 (- INFINITY))
      (* t_0 t_1)
      (*
       t_1
       (+
        (* im_m -2.0)
        (+
         (* -0.3333333333333333 (pow im_m 3.0))
         (+
          (* -0.0003968253968253968 (pow im_m 7.0))
          (* -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 t_1 = 0.5 * sin(re);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_0 * t_1;
	} else {
		tmp = t_1 * ((im_m * -2.0) + ((-0.3333333333333333 * pow(im_m, 3.0)) + ((-0.0003968253968253968 * pow(im_m, 7.0)) + (-0.016666666666666666 * pow(im_m, 5.0)))));
	}
	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 t_0 = Math.exp(-im_m) - Math.exp(im_m);
	double t_1 = 0.5 * Math.sin(re);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_0 * t_1;
	} else {
		tmp = t_1 * ((im_m * -2.0) + ((-0.3333333333333333 * Math.pow(im_m, 3.0)) + ((-0.0003968253968253968 * Math.pow(im_m, 7.0)) + (-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)
	t_1 = 0.5 * math.sin(re)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_0 * t_1
	else:
		tmp = t_1 * ((im_m * -2.0) + ((-0.3333333333333333 * math.pow(im_m, 3.0)) + ((-0.0003968253968253968 * math.pow(im_m, 7.0)) + (-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))
	t_1 = Float64(0.5 * sin(re))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(t_0 * t_1);
	else
		tmp = Float64(t_1 * Float64(Float64(im_m * -2.0) + Float64(Float64(-0.3333333333333333 * (im_m ^ 3.0)) + Float64(Float64(-0.0003968253968253968 * (im_m ^ 7.0)) + 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);
	t_1 = 0.5 * sin(re);
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_0 * t_1;
	else
		tmp = t_1 * ((im_m * -2.0) + ((-0.3333333333333333 * (im_m ^ 3.0)) + ((-0.0003968253968253968 * (im_m ^ 7.0)) + (-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]}, Block[{t$95$1 = N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, (-Infinity)], N[(t$95$0 * t$95$1), $MachinePrecision], N[(t$95$1 * N[(N[(im$95$m * -2.0), $MachinePrecision] + N[(N[(-0.3333333333333333 * N[Power[im$95$m, 3.0], $MachinePrecision]), $MachinePrecision] + N[(N[(-0.0003968253968253968 * N[Power[im$95$m, 7.0], $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 3: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ t_1 := 0.5 \cdot \sin re\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -0.02:\\ \;\;\;\;t_0 \cdot t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(im_m \cdot -2 + \left(-0.3333333333333333 \cdot {im_m}^{3} + -0.016666666666666666 \cdot {im_m}^{5}\right)\right)\\ \end{array} \end{array} \end{array} \]

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))) (t_1 (* 0.5 (sin re))))
   (*
    im_s
    (if (<= t_0 -0.02)
      (* t_0 t_1)
      (*
       t_1
       (+
        (* 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 t_1 = 0.5 * sin(re);
	double tmp;
	if (t_0 <= -0.02) {
		tmp = t_0 * t_1;
	} else {
		tmp = t_1 * ((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) :: t_1
    real(8) :: tmp
    t_0 = exp(-im_m) - exp(im_m)
    t_1 = 0.5d0 * sin(re)
    if (t_0 <= (-0.02d0)) then
        tmp = t_0 * t_1
    else
        tmp = t_1 * ((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 t_1 = 0.5 * Math.sin(re);
	double tmp;
	if (t_0 <= -0.02) {
		tmp = t_0 * t_1;
	} else {
		tmp = t_1 * ((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)
	t_1 = 0.5 * math.sin(re)
	tmp = 0
	if t_0 <= -0.02:
		tmp = t_0 * t_1
	else:
		tmp = t_1 * ((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))
	t_1 = Float64(0.5 * sin(re))
	tmp = 0.0
	if (t_0 <= -0.02)
		tmp = Float64(t_0 * t_1);
	else
		tmp = Float64(t_1 * 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);
	t_1 = 0.5 * sin(re);
	tmp = 0.0;
	if (t_0 <= -0.02)
		tmp = t_0 * t_1;
	else
		tmp = t_1 * ((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]}, Block[{t$95$1 = N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, -0.02], N[(t$95$0 * t$95$1), $MachinePrecision], N[(t$95$1 * 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]]]

Derivation

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

Alternative 4: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im_m} - e^{im_m}\\ im_s \cdot \begin{array}{l} \mathbf{if}\;t_0 \leq -0.02:\\ \;\;\;\;t_0 \cdot \left(0.5 \cdot \sin re\right)\\ \mathbf{else}:\\ \;\;\;\;\sin re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \end{array} \end{array} \end{array} \]

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)) (exp im_m))))
   (*
    im_s
    (if (<= t_0 -0.02)
      (* t_0 (* 0.5 (sin re)))
      (* (sin 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) - exp(im_m);
	double tmp;
	if (t_0 <= -0.02) {
		tmp = t_0 * (0.5 * sin(re));
	} else {
		tmp = sin(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) - exp(im_m)
    if (t_0 <= (-0.02d0)) then
        tmp = t_0 * (0.5d0 * sin(re))
    else
        tmp = sin(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) - Math.exp(im_m);
	double tmp;
	if (t_0 <= -0.02) {
		tmp = t_0 * (0.5 * Math.sin(re));
	} else {
		tmp = Math.sin(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) - math.exp(im_m)
	tmp = 0
	if t_0 <= -0.02:
		tmp = t_0 * (0.5 * math.sin(re))
	else:
		tmp = math.sin(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 = Float64(exp(Float64(-im_m)) - exp(im_m))
	tmp = 0.0
	if (t_0 <= -0.02)
		tmp = Float64(t_0 * Float64(0.5 * sin(re)));
	else
		tmp = Float64(sin(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) - exp(im_m);
	tmp = 0.0;
	if (t_0 <= -0.02)
		tmp = t_0 * (0.5 * sin(re));
	else
		tmp = sin(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[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, -0.02], N[(t$95$0 * N[(0.5 * N[Sin[re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sin[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 5: 97.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.0145:\\ \;\;\;\;\sin re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \mathbf{elif}\;im_m \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(e^{-im_m} - e^{im_m}\right) \cdot \left(0.5 \cdot re\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0001984126984126984 \cdot \left(\sin re \cdot {im_m}^{7}\right)\\ \end{array} \end{array} \]

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 0.0145)
    (* (sin re) (- (* (pow im_m 3.0) -0.16666666666666666) im_m))
    (if (<= im_m 1.1e+44)
      (* (- (exp (- im_m)) (exp im_m)) (* 0.5 re))
      (* -0.0001984126984126984 (* (sin re) (pow im_m 7.0)))))))

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 <= 0.0145) {
		tmp = sin(re) * ((pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else if (im_m <= 1.1e+44) {
		tmp = (exp(-im_m) - exp(im_m)) * (0.5 * re);
	} else {
		tmp = -0.0001984126984126984 * (sin(re) * pow(im_m, 7.0));
	}
	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 <= 0.0145d0) then
        tmp = sin(re) * (((im_m ** 3.0d0) * (-0.16666666666666666d0)) - im_m)
    else if (im_m <= 1.1d+44) then
        tmp = (exp(-im_m) - exp(im_m)) * (0.5d0 * re)
    else
        tmp = (-0.0001984126984126984d0) * (sin(re) * (im_m ** 7.0d0))
    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 <= 0.0145) {
		tmp = Math.sin(re) * ((Math.pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else if (im_m <= 1.1e+44) {
		tmp = (Math.exp(-im_m) - Math.exp(im_m)) * (0.5 * re);
	} else {
		tmp = -0.0001984126984126984 * (Math.sin(re) * Math.pow(im_m, 7.0));
	}
	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 <= 0.0145:
		tmp = math.sin(re) * ((math.pow(im_m, 3.0) * -0.16666666666666666) - im_m)
	elif im_m <= 1.1e+44:
		tmp = (math.exp(-im_m) - math.exp(im_m)) * (0.5 * re)
	else:
		tmp = -0.0001984126984126984 * (math.sin(re) * math.pow(im_m, 7.0))
	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 <= 0.0145)
		tmp = Float64(sin(re) * Float64(Float64((im_m ^ 3.0) * -0.16666666666666666) - im_m));
	elseif (im_m <= 1.1e+44)
		tmp = Float64(Float64(exp(Float64(-im_m)) - exp(im_m)) * Float64(0.5 * re));
	else
		tmp = Float64(-0.0001984126984126984 * Float64(sin(re) * (im_m ^ 7.0)));
	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 <= 0.0145)
		tmp = sin(re) * (((im_m ^ 3.0) * -0.16666666666666666) - im_m);
	elseif (im_m <= 1.1e+44)
		tmp = (exp(-im_m) - exp(im_m)) * (0.5 * re);
	else
		tmp = -0.0001984126984126984 * (sin(re) * (im_m ^ 7.0));
	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, 0.0145], N[(N[Sin[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, 1.1e+44], N[(N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision] * N[(0.5 * re), $MachinePrecision]), $MachinePrecision], N[(-0.0001984126984126984 * N[(N[Sin[re], $MachinePrecision] * N[Power[im$95$m, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

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

Alternative 6: 93.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 5.6:\\ \;\;\;\;\sin re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \mathbf{else}:\\ \;\;\;\;-0.0001984126984126984 \cdot \left(\sin re \cdot {im_m}^{7}\right)\\ \end{array} \end{array} \]

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 5.6)
    (* (sin re) (- (* (pow im_m 3.0) -0.16666666666666666) im_m))
    (* -0.0001984126984126984 (* (sin re) (pow im_m 7.0))))))

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 <= 5.6) {
		tmp = sin(re) * ((pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else {
		tmp = -0.0001984126984126984 * (sin(re) * pow(im_m, 7.0));
	}
	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 <= 5.6d0) then
        tmp = sin(re) * (((im_m ** 3.0d0) * (-0.16666666666666666d0)) - im_m)
    else
        tmp = (-0.0001984126984126984d0) * (sin(re) * (im_m ** 7.0d0))
    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 <= 5.6) {
		tmp = Math.sin(re) * ((Math.pow(im_m, 3.0) * -0.16666666666666666) - im_m);
	} else {
		tmp = -0.0001984126984126984 * (Math.sin(re) * Math.pow(im_m, 7.0));
	}
	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 <= 5.6:
		tmp = math.sin(re) * ((math.pow(im_m, 3.0) * -0.16666666666666666) - im_m)
	else:
		tmp = -0.0001984126984126984 * (math.sin(re) * math.pow(im_m, 7.0))
	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 <= 5.6)
		tmp = Float64(sin(re) * Float64(Float64((im_m ^ 3.0) * -0.16666666666666666) - im_m));
	else
		tmp = Float64(-0.0001984126984126984 * Float64(sin(re) * (im_m ^ 7.0)));
	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 <= 5.6)
		tmp = sin(re) * (((im_m ^ 3.0) * -0.16666666666666666) - im_m);
	else
		tmp = -0.0001984126984126984 * (sin(re) * (im_m ^ 7.0));
	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, 5.6], N[(N[Sin[re], $MachinePrecision] * N[(N[(N[Power[im$95$m, 3.0], $MachinePrecision] * -0.16666666666666666), $MachinePrecision] - im$95$m), $MachinePrecision]), $MachinePrecision], N[(-0.0001984126984126984 * N[(N[Sin[re], $MachinePrecision] * N[Power[im$95$m, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 7: 92.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 4:\\ \;\;\;\;\left(-im_m\right) \cdot \sin re\\ \mathbf{else}:\\ \;\;\;\;-0.0001984126984126984 \cdot \left(\sin re \cdot {im_m}^{7}\right)\\ \end{array} \end{array} \]

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 4.0)
    (* (- im_m) (sin re))
    (* -0.0001984126984126984 (* (sin re) (pow im_m 7.0))))))

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 <= 4.0) {
		tmp = -im_m * sin(re);
	} else {
		tmp = -0.0001984126984126984 * (sin(re) * pow(im_m, 7.0));
	}
	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 <= 4.0d0) then
        tmp = -im_m * sin(re)
    else
        tmp = (-0.0001984126984126984d0) * (sin(re) * (im_m ** 7.0d0))
    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 <= 4.0) {
		tmp = -im_m * Math.sin(re);
	} else {
		tmp = -0.0001984126984126984 * (Math.sin(re) * Math.pow(im_m, 7.0));
	}
	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 <= 4.0:
		tmp = -im_m * math.sin(re)
	else:
		tmp = -0.0001984126984126984 * (math.sin(re) * math.pow(im_m, 7.0))
	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 <= 4.0)
		tmp = Float64(Float64(-im_m) * sin(re));
	else
		tmp = Float64(-0.0001984126984126984 * Float64(sin(re) * (im_m ^ 7.0)));
	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 <= 4.0)
		tmp = -im_m * sin(re);
	else
		tmp = -0.0001984126984126984 * (sin(re) * (im_m ^ 7.0));
	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, 4.0], N[((-im$95$m) * N[Sin[re], $MachinePrecision]), $MachinePrecision], N[(-0.0001984126984126984 * N[(N[Sin[re], $MachinePrecision] * N[Power[im$95$m, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 8: 76.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 0.0064:\\ \;\;\;\;\left(-im_m\right) \cdot \sin re\\ \mathbf{else}:\\ \;\;\;\;re \cdot \left({im_m}^{3} \cdot -0.16666666666666666 - im_m\right)\\ \end{array} \end{array} \]

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 0.0064)
    (* (- im_m) (sin re))
    (* 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 tmp;
	if (im_m <= 0.0064) {
		tmp = -im_m * sin(re);
	} else {
		tmp = 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) :: tmp
    if (im_m <= 0.0064d0) then
        tmp = -im_m * sin(re)
    else
        tmp = 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 tmp;
	if (im_m <= 0.0064) {
		tmp = -im_m * Math.sin(re);
	} else {
		tmp = 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):
	tmp = 0
	if im_m <= 0.0064:
		tmp = -im_m * math.sin(re)
	else:
		tmp = 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)
	tmp = 0.0
	if (im_m <= 0.0064)
		tmp = Float64(Float64(-im_m) * sin(re));
	else
		tmp = Float64(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)
	tmp = 0.0;
	if (im_m <= 0.0064)
		tmp = -im_m * sin(re);
	else
		tmp = 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_] := N[(im$95$s * If[LessEqual[im$95$m, 0.0064], N[((-im$95$m) * N[Sin[re], $MachinePrecision]), $MachinePrecision], N[(re * 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 9: 76.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;\left(-im_m\right) \cdot \sin re\\ \mathbf{else}:\\ \;\;\;\;-0.16666666666666666 \cdot \left(re \cdot {im_m}^{3}\right)\\ \end{array} \end{array} \]

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 6.5e+32)
    (* (- im_m) (sin re))
    (* -0.16666666666666666 (* re (pow im_m 3.0))))))

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 <= 6.5e+32) {
		tmp = -im_m * sin(re);
	} else {
		tmp = -0.16666666666666666 * (re * pow(im_m, 3.0));
	}
	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 <= 6.5d+32) then
        tmp = -im_m * sin(re)
    else
        tmp = (-0.16666666666666666d0) * (re * (im_m ** 3.0d0))
    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 <= 6.5e+32) {
		tmp = -im_m * Math.sin(re);
	} else {
		tmp = -0.16666666666666666 * (re * Math.pow(im_m, 3.0));
	}
	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 <= 6.5e+32:
		tmp = -im_m * math.sin(re)
	else:
		tmp = -0.16666666666666666 * (re * math.pow(im_m, 3.0))
	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 <= 6.5e+32)
		tmp = Float64(Float64(-im_m) * sin(re));
	else
		tmp = Float64(-0.16666666666666666 * Float64(re * (im_m ^ 3.0)));
	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 <= 6.5e+32)
		tmp = -im_m * sin(re);
	else
		tmp = -0.16666666666666666 * (re * (im_m ^ 3.0));
	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, 6.5e+32], N[((-im$95$m) * N[Sin[re], $MachinePrecision]), $MachinePrecision], N[(-0.16666666666666666 * N[(re * N[Power[im$95$m, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 10: 56.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im_s \cdot \begin{array}{l} \mathbf{if}\;im_m \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;\left(-im_m\right) \cdot \sin re\\ \mathbf{else}:\\ \;\;\;\;im_m \cdot \left(-re\right)\\ \end{array} \end{array} \]

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 6.2e+34) (* (- im_m) (sin re)) (* im_m (- re)))))

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 <= 6.2e+34) {
		tmp = -im_m * sin(re);
	} else {
		tmp = im_m * -re;
	}
	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 <= 6.2d+34) then
        tmp = -im_m * sin(re)
    else
        tmp = im_m * -re
    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 <= 6.2e+34) {
		tmp = -im_m * Math.sin(re);
	} else {
		tmp = im_m * -re;
	}
	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 <= 6.2e+34:
		tmp = -im_m * math.sin(re)
	else:
		tmp = im_m * -re
	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 <= 6.2e+34)
		tmp = Float64(Float64(-im_m) * sin(re));
	else
		tmp = Float64(im_m * Float64(-re));
	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 <= 6.2e+34)
		tmp = -im_m * sin(re);
	else
		tmp = im_m * -re;
	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, 6.2e+34], N[((-im$95$m) * N[Sin[re], $MachinePrecision]), $MachinePrecision], N[(im$95$m * (-re)), $MachinePrecision]]), $MachinePrecision]

Derivation

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

Alternative 11: 33.9% accurate, 77.0× speedup

Math

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

FPCore

im_m = (fabs.f64 im)
im_s = (copysign.f64 1 im)
(FPCore (im_s re im_m) :precision binary64 (* im_s (* im_m (- 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 * -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 * -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 * -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 * -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(-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 * -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 * (-re)), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 12: 15.0% accurate, 308.0× 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, 0.8× speedup

Math

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

FPCore

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

C

double code(double re, double im) {
	double tmp;
	if (fabs(im) < 1.0) {
		tmp = -(sin(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)));
	} else {
		tmp = (0.5 * sin(re)) * (exp(-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 = -(sin(re) * ((im + (((0.16666666666666666d0 * im) * im) * im)) + (((((0.008333333333333333d0 * im) * im) * im) * im) * im)))
    else
        tmp = (0.5d0 * sin(re)) * (exp(-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.sin(re) * ((im + (((0.16666666666666666 * im) * im) * im)) + (((((0.008333333333333333 * im) * im) * im) * im) * im)));
	} else {
		tmp = (0.5 * Math.sin(re)) * (Math.exp(-im) - Math.exp(im));
	}
	return tmp;
}

Python

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

Julia

function code(re, im)
	tmp = 0.0
	if (abs(im) < 1.0)
		tmp = Float64(-Float64(sin(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 * sin(re)) * Float64(exp(Float64(-im)) - exp(im)));
	end
	return tmp
end

MATLAB

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

Wolfram

code[re_, im_] := If[Less[N[Abs[im], $MachinePrecision], 1.0], (-N[(N[Sin[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[Sin[re], $MachinePrecision]), $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] - N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023343 
(FPCore (re im)
  :name "math.cos on complex, imaginary part"
  :precision binary64

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

  (* (* 0.5 (sin re)) (- (exp (- im)) (exp im))))