math.sin on complex, imaginary part

Percentage Accurate: 54.4% → 99.0%

Time: 8.0s

Alternatives: 8

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: 54.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = (0.5d0 * cos(re)) * (exp((0.0d0 - im)) - exp(im))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(-2 \cdot \left(im \cdot \cos re\right)\right)\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* 0.5 (log1p (expm1 (* -2.0 (* im (cos re)))))))

C

double code(double re, double im) {
	return 0.5 * log1p(expm1((-2.0 * (im * cos(re)))));
}

Java

public static double code(double re, double im) {
	return 0.5 * Math.log1p(Math.expm1((-2.0 * (im * Math.cos(re)))));
}

Python

def code(re, im):
	return 0.5 * math.log1p(math.expm1((-2.0 * (im * math.cos(re)))))

Julia

function code(re, im)
	return Float64(0.5 * log1p(expm1(Float64(-2.0 * Float64(im * cos(re))))))
end

Wolfram

code[re_, im_] := N[(0.5 * N[Log[1 + N[(Exp[N[(-2.0 * N[(im * N[Cos[re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 90.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 420:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(-2 \cdot im + -0.3333333333333333 \cdot {im}^{3}\right)\right)\\ \mathbf{elif}\;im \leq 4.6 \cdot 10^{+39}:\\ \;\;\;\;0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(-2 \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-0.0003968253968253968 \cdot \left(\cos re \cdot {im}^{7}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 420.0)
   (* 0.5 (* (cos re) (+ (* -2.0 im) (* -0.3333333333333333 (pow im 3.0)))))
   (if (<= im 4.6e+39)
     (* 0.5 (log1p (expm1 (* -2.0 im))))
     (* 0.5 (* -0.0003968253968253968 (* (cos re) (pow im 7.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 420.0) {
		tmp = 0.5 * (cos(re) * ((-2.0 * im) + (-0.3333333333333333 * pow(im, 3.0))));
	} else if (im <= 4.6e+39) {
		tmp = 0.5 * log1p(expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * (cos(re) * pow(im, 7.0)));
	}
	return tmp;
}

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 420.0) {
		tmp = 0.5 * (Math.cos(re) * ((-2.0 * im) + (-0.3333333333333333 * Math.pow(im, 3.0))));
	} else if (im <= 4.6e+39) {
		tmp = 0.5 * Math.log1p(Math.expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * (Math.cos(re) * Math.pow(im, 7.0)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 420.0:
		tmp = 0.5 * (math.cos(re) * ((-2.0 * im) + (-0.3333333333333333 * math.pow(im, 3.0))))
	elif im <= 4.6e+39:
		tmp = 0.5 * math.log1p(math.expm1((-2.0 * im)))
	else:
		tmp = 0.5 * (-0.0003968253968253968 * (math.cos(re) * math.pow(im, 7.0)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 420.0)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(Float64(-2.0 * im) + Float64(-0.3333333333333333 * (im ^ 3.0)))));
	elseif (im <= 4.6e+39)
		tmp = Float64(0.5 * log1p(expm1(Float64(-2.0 * im))));
	else
		tmp = Float64(0.5 * Float64(-0.0003968253968253968 * Float64(cos(re) * (im ^ 7.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 420.0], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(N[(-2.0 * im), $MachinePrecision] + N[(-0.3333333333333333 * N[Power[im, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 4.6e+39], N[(0.5 * N[Log[1 + N[(Exp[N[(-2.0 * im), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(-0.0003968253968253968 * N[(N[Cos[re], $MachinePrecision] * N[Power[im, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 74.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.015:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(-2 \cdot im\right)\right)\\ \mathbf{elif}\;im \leq 4.6 \cdot 10^{+39}:\\ \;\;\;\;0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(-2 \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-0.0003968253968253968 \cdot \left(\cos re \cdot {im}^{7}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.015)
   (* 0.5 (* (cos re) (* -2.0 im)))
   (if (<= im 4.6e+39)
     (* 0.5 (log1p (expm1 (* -2.0 im))))
     (* 0.5 (* -0.0003968253968253968 (* (cos re) (pow im 7.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.015) {
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	} else if (im <= 4.6e+39) {
		tmp = 0.5 * log1p(expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * (cos(re) * pow(im, 7.0)));
	}
	return tmp;
}

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 0.015) {
		tmp = 0.5 * (Math.cos(re) * (-2.0 * im));
	} else if (im <= 4.6e+39) {
		tmp = 0.5 * Math.log1p(Math.expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * (Math.cos(re) * Math.pow(im, 7.0)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 0.015:
		tmp = 0.5 * (math.cos(re) * (-2.0 * im))
	elif im <= 4.6e+39:
		tmp = 0.5 * math.log1p(math.expm1((-2.0 * im)))
	else:
		tmp = 0.5 * (-0.0003968253968253968 * (math.cos(re) * math.pow(im, 7.0)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.015)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(-2.0 * im)));
	elseif (im <= 4.6e+39)
		tmp = Float64(0.5 * log1p(expm1(Float64(-2.0 * im))));
	else
		tmp = Float64(0.5 * Float64(-0.0003968253968253968 * Float64(cos(re) * (im ^ 7.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.015], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 4.6e+39], N[(0.5 * N[Log[1 + N[(Exp[N[(-2.0 * im), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(-0.0003968253968253968 * N[(N[Cos[re], $MachinePrecision] * N[Power[im, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 68.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 0.015:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(-2 \cdot im\right)\right)\\ \mathbf{elif}\;im \leq 4.2 \cdot 10^{+64} \lor \neg \left(im \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;0.5 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(-2 \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(im \cdot \left(-2 + {re}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 0.015)
   (* 0.5 (* (cos re) (* -2.0 im)))
   (if (or (<= im 4.2e+64) (not (<= im 2.7e+76)))
     (* 0.5 (log1p (expm1 (* -2.0 im))))
     (* 0.5 (* im (+ -2.0 (pow re 2.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 0.015) {
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	} else if ((im <= 4.2e+64) || !(im <= 2.7e+76)) {
		tmp = 0.5 * log1p(expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (im * (-2.0 + pow(re, 2.0)));
	}
	return tmp;
}

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 0.015) {
		tmp = 0.5 * (Math.cos(re) * (-2.0 * im));
	} else if ((im <= 4.2e+64) || !(im <= 2.7e+76)) {
		tmp = 0.5 * Math.log1p(Math.expm1((-2.0 * im)));
	} else {
		tmp = 0.5 * (im * (-2.0 + Math.pow(re, 2.0)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 0.015:
		tmp = 0.5 * (math.cos(re) * (-2.0 * im))
	elif (im <= 4.2e+64) or not (im <= 2.7e+76):
		tmp = 0.5 * math.log1p(math.expm1((-2.0 * im)))
	else:
		tmp = 0.5 * (im * (-2.0 + math.pow(re, 2.0)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 0.015)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(-2.0 * im)));
	elseif ((im <= 4.2e+64) || !(im <= 2.7e+76))
		tmp = Float64(0.5 * log1p(expm1(Float64(-2.0 * im))));
	else
		tmp = Float64(0.5 * Float64(im * Float64(-2.0 + (re ^ 2.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 0.015], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[im, 4.2e+64], N[Not[LessEqual[im, 2.7e+76]], $MachinePrecision]], N[(0.5 * N[Log[1 + N[(Exp[N[(-2.0 * im), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(im * N[(-2.0 + N[Power[re, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 5: 66.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 8200000:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(-2 \cdot im\right)\right)\\ \mathbf{elif}\;im \leq 4.2 \cdot 10^{+64} \lor \neg \left(im \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;0.5 \cdot \left(-0.0003968253968253968 \cdot {im}^{7}\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(im \cdot \left(-2 + {re}^{2}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 8200000.0)
   (* 0.5 (* (cos re) (* -2.0 im)))
   (if (or (<= im 4.2e+64) (not (<= im 2.7e+76)))
     (* 0.5 (* -0.0003968253968253968 (pow im 7.0)))
     (* 0.5 (* im (+ -2.0 (pow re 2.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 8200000.0) {
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	} else if ((im <= 4.2e+64) || !(im <= 2.7e+76)) {
		tmp = 0.5 * (-0.0003968253968253968 * pow(im, 7.0));
	} else {
		tmp = 0.5 * (im * (-2.0 + pow(re, 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 8200000.0d0) then
        tmp = 0.5d0 * (cos(re) * ((-2.0d0) * im))
    else if ((im <= 4.2d+64) .or. (.not. (im <= 2.7d+76))) then
        tmp = 0.5d0 * ((-0.0003968253968253968d0) * (im ** 7.0d0))
    else
        tmp = 0.5d0 * (im * ((-2.0d0) + (re ** 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 8200000.0) {
		tmp = 0.5 * (Math.cos(re) * (-2.0 * im));
	} else if ((im <= 4.2e+64) || !(im <= 2.7e+76)) {
		tmp = 0.5 * (-0.0003968253968253968 * Math.pow(im, 7.0));
	} else {
		tmp = 0.5 * (im * (-2.0 + Math.pow(re, 2.0)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 8200000.0:
		tmp = 0.5 * (math.cos(re) * (-2.0 * im))
	elif (im <= 4.2e+64) or not (im <= 2.7e+76):
		tmp = 0.5 * (-0.0003968253968253968 * math.pow(im, 7.0))
	else:
		tmp = 0.5 * (im * (-2.0 + math.pow(re, 2.0)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 8200000.0)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(-2.0 * im)));
	elseif ((im <= 4.2e+64) || !(im <= 2.7e+76))
		tmp = Float64(0.5 * Float64(-0.0003968253968253968 * (im ^ 7.0)));
	else
		tmp = Float64(0.5 * Float64(im * Float64(-2.0 + (re ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 8200000.0)
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	elseif ((im <= 4.2e+64) || ~((im <= 2.7e+76)))
		tmp = 0.5 * (-0.0003968253968253968 * (im ^ 7.0));
	else
		tmp = 0.5 * (im * (-2.0 + (re ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 8200000.0], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[im, 4.2e+64], N[Not[LessEqual[im, 2.7e+76]], $MachinePrecision]], N[(0.5 * N[(-0.0003968253968253968 * N[Power[im, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(im * N[(-2.0 + N[Power[re, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 67.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 7200000:\\ \;\;\;\;0.5 \cdot \left(\cos re \cdot \left(-2 \cdot im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-0.0003968253968253968 \cdot {im}^{7}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 7200000.0)
   (* 0.5 (* (cos re) (* -2.0 im)))
   (* 0.5 (* -0.0003968253968253968 (pow im 7.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 7200000.0) {
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * pow(im, 7.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 7200000.0d0) then
        tmp = 0.5d0 * (cos(re) * ((-2.0d0) * im))
    else
        tmp = 0.5d0 * ((-0.0003968253968253968d0) * (im ** 7.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 7200000.0) {
		tmp = 0.5 * (Math.cos(re) * (-2.0 * im));
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * Math.pow(im, 7.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 7200000.0:
		tmp = 0.5 * (math.cos(re) * (-2.0 * im))
	else:
		tmp = 0.5 * (-0.0003968253968253968 * math.pow(im, 7.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 7200000.0)
		tmp = Float64(0.5 * Float64(cos(re) * Float64(-2.0 * im)));
	else
		tmp = Float64(0.5 * Float64(-0.0003968253968253968 * (im ^ 7.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 7200000.0)
		tmp = 0.5 * (cos(re) * (-2.0 * im));
	else
		tmp = 0.5 * (-0.0003968253968253968 * (im ^ 7.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 7200000.0], N[(0.5 * N[(N[Cos[re], $MachinePrecision] * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(-0.0003968253968253968 * N[Power[im, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 7: 45.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 4:\\ \;\;\;\;0.5 \cdot \left(-2 \cdot im\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(-0.0003968253968253968 \cdot {im}^{7}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 4.0)
   (* 0.5 (* -2.0 im))
   (* 0.5 (* -0.0003968253968253968 (pow im 7.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 4.0) {
		tmp = 0.5 * (-2.0 * im);
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * pow(im, 7.0));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 4.0d0) then
        tmp = 0.5d0 * ((-2.0d0) * im)
    else
        tmp = 0.5d0 * ((-0.0003968253968253968d0) * (im ** 7.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 4.0) {
		tmp = 0.5 * (-2.0 * im);
	} else {
		tmp = 0.5 * (-0.0003968253968253968 * Math.pow(im, 7.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 4.0:
		tmp = 0.5 * (-2.0 * im)
	else:
		tmp = 0.5 * (-0.0003968253968253968 * math.pow(im, 7.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 4.0)
		tmp = Float64(0.5 * Float64(-2.0 * im));
	else
		tmp = Float64(0.5 * Float64(-0.0003968253968253968 * (im ^ 7.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 4.0)
		tmp = 0.5 * (-2.0 * im);
	else
		tmp = 0.5 * (-0.0003968253968253968 * (im ^ 7.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 4.0], N[(0.5 * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(-0.0003968253968253968 * N[Power[im, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 8: 30.6% accurate, 61.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(-2 \cdot im\right) \end{array} \]

FPCore

(FPCore (re im) :precision binary64 (* 0.5 (* -2.0 im)))

C

double code(double re, double im) {
	return 0.5 * (-2.0 * im);
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 0.5d0 * ((-2.0d0) * im)
end function

Java

public static double code(double re, double im) {
	return 0.5 * (-2.0 * im);
}

Python

def code(re, im):
	return 0.5 * (-2.0 * im)

Julia

function code(re, im)
	return Float64(0.5 * Float64(-2.0 * im))
end

MATLAB

function tmp = code(re, im)
	tmp = 0.5 * (-2.0 * im);
end

Wolfram

code[re_, im_] := N[(0.5 * N[(-2.0 * im), $MachinePrecision]), $MachinePrecision]

Derivation

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

Developer target: 99.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (abs(im) < 1.0d0) then
        tmp = -(cos(re) * ((im + (((0.16666666666666666d0 * im) * im) * im)) + (((((0.008333333333333333d0 * im) * im) * im) * im) * im)))
    else
        tmp = (0.5d0 * cos(re)) * (exp((0.0d0 - im)) - exp(im))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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