math.sin on complex, imaginary part

Percentage Accurate: 54.2% → 99.5%

Time: 11.0s

Alternatives: 9

Speedup: 2.8×

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

Specification

Math

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

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: 54.2% 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: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im\_m} - e^{im\_m}\\ t_1 := 0.5 \cdot \cos re\\ im\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_0 \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \left(im\_m \cdot -2 + \left(-0.3333333333333333 \cdot {im\_m}^{3} + \left(-0.016666666666666666 \cdot {im\_m}^{5} + -0.0003968253968253968 \cdot {im\_m}^{7}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

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 (cos re))))
   (*
    im_s
    (if (<= t_0 (- INFINITY))
      (* t_0 t_1)
      (*
       t_1
       (+
        (* im_m -2.0)
        (+
         (* -0.3333333333333333 (pow im_m 3.0))
         (+
          (* -0.016666666666666666 (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 * cos(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)) + ((-0.016666666666666666 * pow(im_m, 5.0)) + (-0.0003968253968253968 * pow(im_m, 7.0)))));
	}
	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.cos(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)) + ((-0.016666666666666666 * Math.pow(im_m, 5.0)) + (-0.0003968253968253968 * 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):
	t_0 = math.exp(-im_m) - math.exp(im_m)
	t_1 = 0.5 * math.cos(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)) + ((-0.016666666666666666 * math.pow(im_m, 5.0)) + (-0.0003968253968253968 * 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)
	t_0 = Float64(exp(Float64(-im_m)) - exp(im_m))
	t_1 = Float64(0.5 * cos(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(-0.016666666666666666 * (im_m ^ 5.0)) + Float64(-0.0003968253968253968 * (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)
	t_0 = exp(-im_m) - exp(im_m);
	t_1 = 0.5 * cos(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)) + ((-0.016666666666666666 * (im_m ^ 5.0)) + (-0.0003968253968253968 * (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_] := 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[Cos[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[(-0.016666666666666666 * N[Power[im$95$m, 5.0], $MachinePrecision]), $MachinePrecision] + N[(-0.0003968253968253968 * N[Power[im$95$m, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)) < -inf.0

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   if -inf.0 < (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

   1. Initial program 35.5%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 35.5%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 35.5%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 94.3%

      \[\leadsto \color{blue}{\left(-2 \cdot im + \left(-0.3333333333333333 \cdot {im}^{3} + \left(-0.016666666666666666 \cdot {im}^{5} + -0.0003968253968253968 \cdot {im}^{7}\right)\right)\right)} \cdot \left(0.5 \cdot \cos re\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{-im} - e^{im} \leq -\infty:\\ \;\;\;\;\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.5 \cdot \cos re\right) \cdot \left(im \cdot -2 + \left(-0.3333333333333333 \cdot {im}^{3} + \left(-0.016666666666666666 \cdot {im}^{5} + -0.0003968253968253968 \cdot {im}^{7}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ \begin{array}{l} t_0 := e^{-im\_m} - e^{im\_m}\\ im\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 \leq -0.05:\\ \;\;\;\;t\_0 \cdot \left(0.5 \cdot \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im\_m}^{3} \cdot -0.16666666666666666 - im\_m\right)\\ \end{array} \end{array} \end{array} \]

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)) (exp im_m))))
   (*
    im_s
    (if (<= t_0 -0.05)
      (* t_0 (* 0.5 (cos re)))
      (* (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) - exp(im_m);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_0 * (0.5 * cos(re));
	} 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) - exp(im_m)
    if (t_0 <= (-0.05d0)) then
        tmp = t_0 * (0.5d0 * cos(re))
    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) - Math.exp(im_m);
	double tmp;
	if (t_0 <= -0.05) {
		tmp = t_0 * (0.5 * Math.cos(re));
	} 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) - math.exp(im_m)
	tmp = 0
	if t_0 <= -0.05:
		tmp = t_0 * (0.5 * math.cos(re))
	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 = Float64(exp(Float64(-im_m)) - exp(im_m))
	tmp = 0.0
	if (t_0 <= -0.05)
		tmp = Float64(t_0 * Float64(0.5 * cos(re)));
	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) - exp(im_m);
	tmp = 0.0;
	if (t_0 <= -0.05)
		tmp = t_0 * (0.5 * cos(re));
	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[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision]}, N[(im$95$s * If[LessEqual[t$95$0, -0.05], N[(t$95$0 * N[(0.5 * N[Cos[re], $MachinePrecision]), $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

1. Split input into 2 regimes

2. if (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)) < -0.050000000000000003

   1. Initial program 99.9%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 99.9%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   if -0.050000000000000003 < (-.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

   1. Initial program 35.1%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 35.1%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 88.7%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right) + -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. +-commutative 88.7%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + -1 \cdot \left(im \cdot \cos re\right)} \]

      2. mul-1-neg 88.7%

         \[\leadsto -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + \color{blue}{\left(-im \cdot \cos re\right)} \]

      3. unsub-neg 88.7%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) - im \cdot \cos re} \]

      4. associate-*r* 88.7%

         \[\leadsto \color{blue}{\left(-0.16666666666666666 \cdot {im}^{3}\right) \cdot \cos re} - im \cdot \cos re \]

      5. distribute-rgt-out-- 88.7%

         \[\leadsto \color{blue}{\cos re \cdot \left(-0.16666666666666666 \cdot {im}^{3} - im\right)} \]

      6. *-commutative 88.7%

         \[\leadsto \cos re \cdot \left(\color{blue}{{im}^{3} \cdot -0.16666666666666666} - im\right) \]

   7. Simplified 88.7%

      \[\leadsto \color{blue}{\cos re \cdot \left({im}^{3} \cdot -0.16666666666666666 - im\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{-im} - e^{im} \leq -0.05:\\ \;\;\;\;\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im}^{3} \cdot -0.16666666666666666 - im\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im\_s \cdot \begin{array}{l} \mathbf{if}\;im\_m \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;im\_m \cdot \left(-\cos re\right)\\ \mathbf{elif}\;im\_m \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(e^{-im\_m} - e^{im\_m}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im\_m}^{7} \cdot -0.0001984126984126984\right)\\ \end{array} \end{array} \]

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-5)
    (* im_m (- (cos re)))
    (if (<= im_m 1.1e+44)
      (* (- (exp (- im_m)) (exp im_m)) 0.5)
      (* (cos re) (* (pow im_m 7.0) -0.0001984126984126984))))))

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-5) {
		tmp = im_m * -cos(re);
	} else if (im_m <= 1.1e+44) {
		tmp = (exp(-im_m) - exp(im_m)) * 0.5;
	} else {
		tmp = cos(re) * (pow(im_m, 7.0) * -0.0001984126984126984);
	}
	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-5) then
        tmp = im_m * -cos(re)
    else if (im_m <= 1.1d+44) then
        tmp = (exp(-im_m) - exp(im_m)) * 0.5d0
    else
        tmp = cos(re) * ((im_m ** 7.0d0) * (-0.0001984126984126984d0))
    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-5) {
		tmp = im_m * -Math.cos(re);
	} else if (im_m <= 1.1e+44) {
		tmp = (Math.exp(-im_m) - Math.exp(im_m)) * 0.5;
	} else {
		tmp = Math.cos(re) * (Math.pow(im_m, 7.0) * -0.0001984126984126984);
	}
	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-5:
		tmp = im_m * -math.cos(re)
	elif im_m <= 1.1e+44:
		tmp = (math.exp(-im_m) - math.exp(im_m)) * 0.5
	else:
		tmp = math.cos(re) * (math.pow(im_m, 7.0) * -0.0001984126984126984)
	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-5)
		tmp = Float64(im_m * Float64(-cos(re)));
	elseif (im_m <= 1.1e+44)
		tmp = Float64(Float64(exp(Float64(-im_m)) - exp(im_m)) * 0.5);
	else
		tmp = Float64(cos(re) * Float64((im_m ^ 7.0) * -0.0001984126984126984));
	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-5)
		tmp = im_m * -cos(re);
	elseif (im_m <= 1.1e+44)
		tmp = (exp(-im_m) - exp(im_m)) * 0.5;
	else
		tmp = cos(re) * ((im_m ^ 7.0) * -0.0001984126984126984);
	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-5], N[(im$95$m * (-N[Cos[re], $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] * 0.5), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[Power[im$95$m, 7.0], $MachinePrecision] * -0.0001984126984126984), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if im < 6.49999999999999943e-5

   1. Initial program 34.9%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 34.9%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 71.6%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.6%

         \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

      2. neg-mul-1 71.6%

         \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

   7. Simplified 71.6%

      \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

   if 6.49999999999999943e-5 < im < 1.09999999999999998e44

   1. Initial program 98.2%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 98.2%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in re around 0 89.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{-im} - e^{im}\right)} \]

   if 1.09999999999999998e44 < im

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 100.0%

      \[\leadsto \color{blue}{\left(-2 \cdot im + \left(-0.3333333333333333 \cdot {im}^{3} + \left(-0.016666666666666666 \cdot {im}^{5} + -0.0003968253968253968 \cdot {im}^{7}\right)\right)\right)} \cdot \left(0.5 \cdot \cos re\right) \]

   6. Taylor expanded in im around inf 100.0%

      \[\leadsto \color{blue}{-0.0001984126984126984 \cdot \left({im}^{7} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-0.0001984126984126984 \cdot {im}^{7}\right) \cdot \cos re} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\cos re \cdot \left(-0.0001984126984126984 \cdot {im}^{7}\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\cos re \cdot \left(-0.0001984126984126984 \cdot {im}^{7}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 6.5 \cdot 10^{-5}:\\ \;\;\;\;im \cdot \left(-\cos re\right)\\ \mathbf{elif}\;im \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(e^{-im} - e^{im}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im}^{7} \cdot -0.0001984126984126984\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im\_s \cdot \begin{array}{l} \mathbf{if}\;im\_m \leq 0.023:\\ \;\;\;\;\cos re \cdot \left({im\_m}^{3} \cdot -0.16666666666666666 - im\_m\right)\\ \mathbf{elif}\;im\_m \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(e^{-im\_m} - e^{im\_m}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im\_m}^{7} \cdot -0.0001984126984126984\right)\\ \end{array} \end{array} \]

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 0.023)
    (* (cos re) (- (* (pow im_m 3.0) -0.16666666666666666) im_m))
    (if (<= im_m 1.1e+44)
      (* (- (exp (- im_m)) (exp im_m)) 0.5)
      (* (cos re) (* (pow im_m 7.0) -0.0001984126984126984))))))

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 <= 0.023) {
		tmp = cos(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;
	} else {
		tmp = cos(re) * (pow(im_m, 7.0) * -0.0001984126984126984);
	}
	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 <= 0.023d0) then
        tmp = cos(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
    else
        tmp = cos(re) * ((im_m ** 7.0d0) * (-0.0001984126984126984d0))
    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 <= 0.023) {
		tmp = Math.cos(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;
	} else {
		tmp = Math.cos(re) * (Math.pow(im_m, 7.0) * -0.0001984126984126984);
	}
	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 <= 0.023:
		tmp = math.cos(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
	else:
		tmp = math.cos(re) * (math.pow(im_m, 7.0) * -0.0001984126984126984)
	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 <= 0.023)
		tmp = Float64(cos(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)) * 0.5);
	else
		tmp = Float64(cos(re) * Float64((im_m ^ 7.0) * -0.0001984126984126984));
	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 <= 0.023)
		tmp = cos(re) * (((im_m ^ 3.0) * -0.16666666666666666) - im_m);
	elseif (im_m <= 1.1e+44)
		tmp = (exp(-im_m) - exp(im_m)) * 0.5;
	else
		tmp = cos(re) * ((im_m ^ 7.0) * -0.0001984126984126984);
	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, 0.023], 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, 1.1e+44], N[(N[(N[Exp[(-im$95$m)], $MachinePrecision] - N[Exp[im$95$m], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision], N[(N[Cos[re], $MachinePrecision] * N[(N[Power[im$95$m, 7.0], $MachinePrecision] * -0.0001984126984126984), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if im < 0.023

   1. Initial program 35.1%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 35.1%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 35.1%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 88.7%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right) + -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. +-commutative 88.7%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + -1 \cdot \left(im \cdot \cos re\right)} \]

      2. mul-1-neg 88.7%

         \[\leadsto -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + \color{blue}{\left(-im \cdot \cos re\right)} \]

      3. unsub-neg 88.7%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) - im \cdot \cos re} \]

      4. associate-*r* 88.7%

         \[\leadsto \color{blue}{\left(-0.16666666666666666 \cdot {im}^{3}\right) \cdot \cos re} - im \cdot \cos re \]

      5. distribute-rgt-out-- 88.7%

         \[\leadsto \color{blue}{\cos re \cdot \left(-0.16666666666666666 \cdot {im}^{3} - im\right)} \]

      6. *-commutative 88.7%

         \[\leadsto \cos re \cdot \left(\color{blue}{{im}^{3} \cdot -0.16666666666666666} - im\right) \]

   7. Simplified 88.7%

      \[\leadsto \color{blue}{\cos re \cdot \left({im}^{3} \cdot -0.16666666666666666 - im\right)} \]

   if 0.023 < im < 1.09999999999999998e44

   1. Initial program 99.5%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 99.5%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in re around 0 90.4%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{-im} - e^{im}\right)} \]

   if 1.09999999999999998e44 < im

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 100.0%

      \[\leadsto \color{blue}{\left(-2 \cdot im + \left(-0.3333333333333333 \cdot {im}^{3} + \left(-0.016666666666666666 \cdot {im}^{5} + -0.0003968253968253968 \cdot {im}^{7}\right)\right)\right)} \cdot \left(0.5 \cdot \cos re\right) \]

   6. Taylor expanded in im around inf 100.0%

      \[\leadsto \color{blue}{-0.0001984126984126984 \cdot \left({im}^{7} \cdot \cos re\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-0.0001984126984126984 \cdot {im}^{7}\right) \cdot \cos re} \]

      2. *-commutative 100.0%

         \[\leadsto \color{blue}{\cos re \cdot \left(-0.0001984126984126984 \cdot {im}^{7}\right)} \]

   8. Simplified 100.0%

      \[\leadsto \color{blue}{\cos re \cdot \left(-0.0001984126984126984 \cdot {im}^{7}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 0.023:\\ \;\;\;\;\cos re \cdot \left({im}^{3} \cdot -0.16666666666666666 - im\right)\\ \mathbf{elif}\;im \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\left(e^{-im} - e^{im}\right) \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\cos re \cdot \left({im}^{7} \cdot -0.0001984126984126984\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im\_s \cdot \begin{array}{l} \mathbf{if}\;im\_m \leq 0.000106:\\ \;\;\;\;im\_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-im\_m} - e^{im\_m}\right) \cdot 0.5\\ \end{array} \end{array} \]

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 0.000106)
    (* 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 <= 0.000106) {
		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 <= 0.000106d0) 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 <= 0.000106) {
		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 <= 0.000106:
		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 <= 0.000106)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = Float64(Float64(exp(Float64(-im_m)) - exp(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 <= 0.000106)
		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, 0.000106], 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

1. Split input into 2 regimes

2. if im < 1.06e-4

   1. Initial program 34.9%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 34.9%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 34.9%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 71.6%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.6%

         \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

      2. neg-mul-1 71.6%

         \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

   7. Simplified 71.6%

      \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

   if 1.06e-4 < im

   1. Initial program 99.7%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 99.7%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in re around 0 85.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(e^{-im} - e^{im}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 0.000106:\\ \;\;\;\;im \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;\left(e^{-im} - e^{im}\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im\_s \cdot \begin{array}{l} \mathbf{if}\;im\_m \leq 460:\\ \;\;\;\;im\_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;im\_m \cdot \frac{\cos \left(re \cdot 2\right) + 1}{0}\\ \end{array} \end{array} \]

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 460.0)
    (* im_m (- (cos re)))
    (* im_m (/ (+ (cos (* re 2.0)) 1.0) 0.0)))))

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 <= 460.0) {
		tmp = im_m * -cos(re);
	} else {
		tmp = im_m * ((cos((re * 2.0)) + 1.0) / 0.0);
	}
	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 <= 460.0d0) then
        tmp = im_m * -cos(re)
    else
        tmp = im_m * ((cos((re * 2.0d0)) + 1.0d0) / 0.0d0)
    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 <= 460.0) {
		tmp = im_m * -Math.cos(re);
	} else {
		tmp = im_m * ((Math.cos((re * 2.0)) + 1.0) / 0.0);
	}
	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 <= 460.0:
		tmp = im_m * -math.cos(re)
	else:
		tmp = im_m * ((math.cos((re * 2.0)) + 1.0) / 0.0)
	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 <= 460.0)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = Float64(im_m * Float64(Float64(cos(Float64(re * 2.0)) + 1.0) / 0.0));
	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 <= 460.0)
		tmp = im_m * -cos(re);
	else
		tmp = im_m * ((cos((re * 2.0)) + 1.0) / 0.0);
	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, 460.0], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], N[(im$95$m * N[(N[(N[Cos[N[(re * 2.0), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision] / 0.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if im < 460

   1. Initial program 35.5%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 35.5%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 35.5%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 35.5%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 71.4%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.4%

         \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

      2. neg-mul-1 71.4%

         \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

   7. Simplified 71.4%

      \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

   if 460 < im

   1. Initial program 100.0%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 100.0%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 5.3%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 5.3%

         \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

      2. neg-mul-1 5.3%

         \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

   7. Simplified 5.3%

      \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

   9. Applied egg-rr 85.5%

      \[\leadsto \left(-im\right) \cdot \color{blue}{\frac{\cos \left(re + re\right) + \cos \left(re - re\right)}{0}} \]
   10. Step-by-step derivation

       1. +-commutative 85.5%

          \[\leadsto \left(-im\right) \cdot \frac{\color{blue}{\cos \left(re - re\right) + \cos \left(re + re\right)}}{0} \]

       2. +-inverses 85.5%

          \[\leadsto \left(-im\right) \cdot \frac{\cos \color{blue}{0} + \cos \left(re + re\right)}{0} \]

       3. cos-0 85.5%

          \[\leadsto \left(-im\right) \cdot \frac{\color{blue}{1} + \cos \left(re + re\right)}{0} \]

       4. count-2 85.5%

          \[\leadsto \left(-im\right) \cdot \frac{1 + \cos \color{blue}{\left(2 \cdot re\right)}}{0} \]

       5. *-commutative 85.5%

          \[\leadsto \left(-im\right) \cdot \frac{1 + \cos \color{blue}{\left(re \cdot 2\right)}}{0} \]

   11. Simplified 85.5%

       \[\leadsto \left(-im\right) \cdot \color{blue}{\frac{1 + \cos \left(re \cdot 2\right)}{0}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 460:\\ \;\;\;\;im \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;im \cdot \frac{\cos \left(re \cdot 2\right) + 1}{0}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} im_m = \left|im\right| \\ im_s = \mathsf{copysign}\left(1, im\right) \\ im\_s \cdot \begin{array}{l} \mathbf{if}\;im\_m \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;im\_m \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;{im\_m}^{3} \cdot -0.16666666666666666 - im\_m\\ \end{array} \end{array} \]

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 5.6e-8)
    (* im_m (- (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 tmp;
	if (im_m <= 5.6e-8) {
		tmp = im_m * -cos(re);
	} else {
		tmp = (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 <= 5.6d-8) then
        tmp = im_m * -cos(re)
    else
        tmp = ((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 <= 5.6e-8) {
		tmp = im_m * -Math.cos(re);
	} else {
		tmp = (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 <= 5.6e-8:
		tmp = im_m * -math.cos(re)
	else:
		tmp = (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 <= 5.6e-8)
		tmp = Float64(im_m * Float64(-cos(re)));
	else
		tmp = 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 <= 5.6e-8)
		tmp = im_m * -cos(re);
	else
		tmp = ((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, 5.6e-8], N[(im$95$m * (-N[Cos[re], $MachinePrecision])), $MachinePrecision], N[(N[(N[Power[im$95$m, 3.0], $MachinePrecision] * -0.16666666666666666), $MachinePrecision] - im$95$m), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if im < 5.5999999999999999e-8

   1. Initial program 34.5%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 34.5%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 34.5%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 34.5%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 71.3%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 71.3%

         \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

      2. neg-mul-1 71.3%

         \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

   7. Simplified 71.3%

      \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

   if 5.5999999999999999e-8 < im

   1. Initial program 98.8%

      \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
   2. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

      2. neg-sub0 98.8%

         \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in im around 0 67.3%

      \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right) + -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right)} \]
   6. Step-by-step derivation

      1. +-commutative 67.3%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + -1 \cdot \left(im \cdot \cos re\right)} \]

      2. mul-1-neg 67.3%

         \[\leadsto -0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) + \color{blue}{\left(-im \cdot \cos re\right)} \]

      3. unsub-neg 67.3%

         \[\leadsto \color{blue}{-0.16666666666666666 \cdot \left({im}^{3} \cdot \cos re\right) - im \cdot \cos re} \]

      4. associate-*r* 67.3%

         \[\leadsto \color{blue}{\left(-0.16666666666666666 \cdot {im}^{3}\right) \cdot \cos re} - im \cdot \cos re \]

      5. distribute-rgt-out-- 67.3%

         \[\leadsto \color{blue}{\cos re \cdot \left(-0.16666666666666666 \cdot {im}^{3} - im\right)} \]

      6. *-commutative 67.3%

         \[\leadsto \cos re \cdot \left(\color{blue}{{im}^{3} \cdot -0.16666666666666666} - im\right) \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\cos re \cdot \left({im}^{3} \cdot -0.16666666666666666 - im\right)} \]

   8. Taylor expanded in re around 0 56.2%

      \[\leadsto \color{blue}{-0.16666666666666666 \cdot {im}^{3} - im} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;im \leq 5.6 \cdot 10^{-8}:\\ \;\;\;\;im \cdot \left(-\cos re\right)\\ \mathbf{else}:\\ \;\;\;\;{im}^{3} \cdot -0.16666666666666666 - im\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.1% 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

1. Initial program 52.9%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
2. Step-by-step derivation

   1. *-commutative 52.9%

      \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

   2. neg-sub0 52.9%

      \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

3. Simplified 52.9%

   \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
4. Add Preprocessing

5. Taylor expanded in im around 0 53.6%

   \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
6. Step-by-step derivation

   1. associate-*r* 53.6%

      \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

   2. neg-mul-1 53.6%

      \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

7. Simplified 53.6%

   \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

8. Final simplification 53.6%

   \[\leadsto im \cdot \left(-\cos re\right) \]
9. Add Preprocessing

Alternative 9: 29.4% accurate, 154.5× speedup

Math

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

FPCore

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

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;
}

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
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;
}

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

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))
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;
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 * (-im$95$m)), $MachinePrecision]

Derivation

1. Initial program 52.9%

   \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{0 - im} - e^{im}\right) \]
2. Step-by-step derivation

   1. *-commutative 52.9%

      \[\leadsto \color{blue}{\left(e^{0 - im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]

   2. neg-sub0 52.9%

      \[\leadsto \left(e^{\color{blue}{-im}} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right) \]

3. Simplified 52.9%

   \[\leadsto \color{blue}{\left(e^{-im} - e^{im}\right) \cdot \left(0.5 \cdot \cos re\right)} \]
4. Add Preprocessing

5. Taylor expanded in im around 0 53.6%

   \[\leadsto \color{blue}{-1 \cdot \left(im \cdot \cos re\right)} \]
6. Step-by-step derivation

   1. associate-*r* 53.6%

      \[\leadsto \color{blue}{\left(-1 \cdot im\right) \cdot \cos re} \]

   2. neg-mul-1 53.6%

      \[\leadsto \color{blue}{\left(-im\right)} \cdot \cos re \]

7. Simplified 53.6%

   \[\leadsto \color{blue}{\left(-im\right) \cdot \cos re} \]

9. Applied egg-rr 53.4%

   \[\leadsto \left(-im\right) \cdot \color{blue}{\log \left(e^{\cos re}\right)} \]

10. Taylor expanded in re around 0 28.3%

    \[\leadsto \color{blue}{-1 \cdot im} \]
11. Step-by-step derivation

    1. mul-1-neg 28.3%

       \[\leadsto \color{blue}{-im} \]

12. Simplified 28.3%

    \[\leadsto \color{blue}{-im} \]

13. Final simplification 28.3%

    \[\leadsto -im \]
14. 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 2024046 
(FPCore (re im)
  :name "math.sin on complex, imaginary part"
  :precision binary64

  :alt
  (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))))