math.sin on complex, real part

Percentage Accurate: 100.0% → 100.0%

Time: 8.0s

Alternatives: 15

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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(0.5 * Float64(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[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(N[Exp[(-im)], $MachinePrecision] + N[Exp[im], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 2: 85.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 6500000000000:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \mathbf{elif}\;im \leq 8.8 \cdot 10^{+47}:\\ \;\;\;\;0.5 \cdot \frac{re \cdot \left(4 - {im}^{12} \cdot 7.71604938271605 \cdot 10^{-6}\right)}{2 + -0.002777777777777778 \cdot {im}^{6}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 6500000000000.0)
   (* 0.5 (* (sin re) (fma im im 2.0)))
   (if (<= im 8.8e+47)
     (*
      0.5
      (/
       (* re (- 4.0 (* (pow im 12.0) 7.71604938271605e-6)))
       (+ 2.0 (* -0.002777777777777778 (pow im 6.0)))))
     (* 0.5 (* (sin re) (+ 2.0 (* (pow im 6.0) 0.002777777777777778)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 6500000000000.0) {
		tmp = 0.5 * (sin(re) * fma(im, im, 2.0));
	} else if (im <= 8.8e+47) {
		tmp = 0.5 * ((re * (4.0 - (pow(im, 12.0) * 7.71604938271605e-6))) / (2.0 + (-0.002777777777777778 * pow(im, 6.0))));
	} else {
		tmp = 0.5 * (sin(re) * (2.0 + (pow(im, 6.0) * 0.002777777777777778)));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 6500000000000.0)
		tmp = Float64(0.5 * Float64(sin(re) * fma(im, im, 2.0)));
	elseif (im <= 8.8e+47)
		tmp = Float64(0.5 * Float64(Float64(re * Float64(4.0 - Float64((im ^ 12.0) * 7.71604938271605e-6))) / Float64(2.0 + Float64(-0.002777777777777778 * (im ^ 6.0)))));
	else
		tmp = Float64(0.5 * Float64(sin(re) * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 6500000000000.0], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 8.8e+47], N[(0.5 * N[(N[(re * N[(4.0 - N[(N[Power[im, 12.0], $MachinePrecision] * 7.71604938271605e-6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(2.0 + N[(-0.002777777777777778 * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 3: 84.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 5300000000000:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \mathbf{elif}\;im \leq 8.8 \cdot 10^{+47}:\\ \;\;\;\;0.5 \cdot \left(re \cdot \left(2 + \sqrt{{im}^{12} \cdot 7.71604938271605 \cdot 10^{-6}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(\sin re \cdot {im}^{6}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 5300000000000.0)
   (* 0.5 (* (sin re) (fma im im 2.0)))
   (if (<= im 8.8e+47)
     (* 0.5 (* re (+ 2.0 (sqrt (* (pow im 12.0) 7.71604938271605e-6)))))
     (* 0.5 (* 0.002777777777777778 (* (sin re) (pow im 6.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 5300000000000.0) {
		tmp = 0.5 * (sin(re) * fma(im, im, 2.0));
	} else if (im <= 8.8e+47) {
		tmp = 0.5 * (re * (2.0 + sqrt((pow(im, 12.0) * 7.71604938271605e-6))));
	} else {
		tmp = 0.5 * (0.002777777777777778 * (sin(re) * pow(im, 6.0)));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 5300000000000.0)
		tmp = Float64(0.5 * Float64(sin(re) * fma(im, im, 2.0)));
	elseif (im <= 8.8e+47)
		tmp = Float64(0.5 * Float64(re * Float64(2.0 + sqrt(Float64((im ^ 12.0) * 7.71604938271605e-6)))));
	else
		tmp = Float64(0.5 * Float64(0.002777777777777778 * Float64(sin(re) * (im ^ 6.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 5300000000000.0], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 8.8e+47], N[(0.5 * N[(re * N[(2.0 + N[Sqrt[N[(N[Power[im, 12.0], $MachinePrecision] * 7.71604938271605e-6), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(0.002777777777777778 * N[(N[Sin[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 4: 84.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 115000000:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \mathbf{elif}\;im \leq 2.35 \cdot 10^{+51}:\\ \;\;\;\;0.5 \cdot \left(\left({im}^{6} \cdot {re}^{3}\right) \cdot -0.000462962962962963\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(\sin re \cdot {im}^{6}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 115000000.0)
   (* 0.5 (* (sin re) (fma im im 2.0)))
   (if (<= im 2.35e+51)
     (* 0.5 (* (* (pow im 6.0) (pow re 3.0)) -0.000462962962962963))
     (* 0.5 (* 0.002777777777777778 (* (sin re) (pow im 6.0)))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 115000000.0) {
		tmp = 0.5 * (sin(re) * fma(im, im, 2.0));
	} else if (im <= 2.35e+51) {
		tmp = 0.5 * ((pow(im, 6.0) * pow(re, 3.0)) * -0.000462962962962963);
	} else {
		tmp = 0.5 * (0.002777777777777778 * (sin(re) * pow(im, 6.0)));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 115000000.0)
		tmp = Float64(0.5 * Float64(sin(re) * fma(im, im, 2.0)));
	elseif (im <= 2.35e+51)
		tmp = Float64(0.5 * Float64(Float64((im ^ 6.0) * (re ^ 3.0)) * -0.000462962962962963));
	else
		tmp = Float64(0.5 * Float64(0.002777777777777778 * Float64(sin(re) * (im ^ 6.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 115000000.0], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 2.35e+51], N[(0.5 * N[(N[(N[Power[im, 6.0], $MachinePrecision] * N[Power[re, 3.0], $MachinePrecision]), $MachinePrecision] * -0.000462962962962963), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(0.002777777777777778 * N[(N[Sin[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 5: 68.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{elif}\;im \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(re \cdot {im}^{6}\right) + re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 3.1e-7)
   (* 0.5 (* (sin re) 2.0))
   (if (<= im 1.35e+154)
     (* 0.5 (+ (* 0.002777777777777778 (* re (pow im 6.0))) (* re 2.0)))
     (* 0.5 (* (sin re) (pow im 2.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else if (im <= 1.35e+154) {
		tmp = 0.5 * ((0.002777777777777778 * (re * pow(im, 6.0))) + (re * 2.0));
	} else {
		tmp = 0.5 * (sin(re) * pow(im, 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 <= 3.1d-7) then
        tmp = 0.5d0 * (sin(re) * 2.0d0)
    else if (im <= 1.35d+154) then
        tmp = 0.5d0 * ((0.002777777777777778d0 * (re * (im ** 6.0d0))) + (re * 2.0d0))
    else
        tmp = 0.5d0 * (sin(re) * (im ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (Math.sin(re) * 2.0);
	} else if (im <= 1.35e+154) {
		tmp = 0.5 * ((0.002777777777777778 * (re * Math.pow(im, 6.0))) + (re * 2.0));
	} else {
		tmp = 0.5 * (Math.sin(re) * Math.pow(im, 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 3.1e-7:
		tmp = 0.5 * (math.sin(re) * 2.0)
	elif im <= 1.35e+154:
		tmp = 0.5 * ((0.002777777777777778 * (re * math.pow(im, 6.0))) + (re * 2.0))
	else:
		tmp = 0.5 * (math.sin(re) * math.pow(im, 2.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 3.1e-7)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	elseif (im <= 1.35e+154)
		tmp = Float64(0.5 * Float64(Float64(0.002777777777777778 * Float64(re * (im ^ 6.0))) + Float64(re * 2.0)));
	else
		tmp = Float64(0.5 * Float64(sin(re) * (im ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 3.1e-7)
		tmp = 0.5 * (sin(re) * 2.0);
	elseif (im <= 1.35e+154)
		tmp = 0.5 * ((0.002777777777777778 * (re * (im ^ 6.0))) + (re * 2.0));
	else
		tmp = 0.5 * (sin(re) * (im ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 3.1e-7], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.35e+154], N[(0.5 * N[(N[(0.002777777777777778 * N[(re * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(re * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 6: 82.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 7500000000000:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \mathbf{elif}\;im \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;0.5 \cdot \left(re \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 7500000000000.0)
   (* 0.5 (* (sin re) (fma im im 2.0)))
   (if (<= im 1.35e+154)
     (* 0.5 (* re (+ 2.0 (* (pow im 6.0) 0.002777777777777778))))
     (* 0.5 (* (sin re) (pow im 2.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 7500000000000.0) {
		tmp = 0.5 * (sin(re) * fma(im, im, 2.0));
	} else if (im <= 1.35e+154) {
		tmp = 0.5 * (re * (2.0 + (pow(im, 6.0) * 0.002777777777777778)));
	} else {
		tmp = 0.5 * (sin(re) * pow(im, 2.0));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 7500000000000.0)
		tmp = Float64(0.5 * Float64(sin(re) * fma(im, im, 2.0)));
	elseif (im <= 1.35e+154)
		tmp = Float64(0.5 * Float64(re * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778))));
	else
		tmp = Float64(0.5 * Float64(sin(re) * (im ^ 2.0)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 7500000000000.0], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[im, 1.35e+154], N[(0.5 * N[(re * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

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1. Add Preprocessing

Alternative 7: 83.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 4.5:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(\sin re \cdot {im}^{6}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 4.5)
   (* 0.5 (* (sin re) (fma im im 2.0)))
   (* 0.5 (* 0.002777777777777778 (* (sin re) (pow im 6.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 4.5) {
		tmp = 0.5 * (sin(re) * fma(im, im, 2.0));
	} else {
		tmp = 0.5 * (0.002777777777777778 * (sin(re) * pow(im, 6.0)));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 4.5)
		tmp = Float64(0.5 * Float64(sin(re) * fma(im, im, 2.0)));
	else
		tmp = Float64(0.5 * Float64(0.002777777777777778 * Float64(sin(re) * (im ^ 6.0))));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 4.5], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(0.002777777777777778 * N[(N[Sin[re], $MachinePrecision] * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 8: 91.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(\sin re \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right)\right) \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (* 0.5 (* (sin re) (+ 2.0 (* (pow im 6.0) 0.002777777777777778)))))

C

double code(double re, double im) {
	return 0.5 * (sin(re) * (2.0 + (pow(im, 6.0) * 0.002777777777777778)));
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    code = 0.5d0 * (sin(re) * (2.0d0 + ((im ** 6.0d0) * 0.002777777777777778d0)))
end function

Java

public static double code(double re, double im) {
	return 0.5 * (Math.sin(re) * (2.0 + (Math.pow(im, 6.0) * 0.002777777777777778)));
}

Python

def code(re, im):
	return 0.5 * (math.sin(re) * (2.0 + (math.pow(im, 6.0) * 0.002777777777777778)))

Julia

function code(re, im)
	return Float64(0.5 * Float64(sin(re) * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778))))
end

MATLAB

function tmp = code(re, im)
	tmp = 0.5 * (sin(re) * (2.0 + ((im ^ 6.0) * 0.002777777777777778)));
end

Wolfram

code[re_, im_] := N[(0.5 * N[(N[Sin[re], $MachinePrecision] * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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1. Add Preprocessing

Alternative 9: 65.5% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(re \cdot {im}^{6}\right) + re \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 3.1e-7)
   (* 0.5 (* (sin re) 2.0))
   (* 0.5 (+ (* 0.002777777777777778 (* re (pow im 6.0))) (* re 2.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else {
		tmp = 0.5 * ((0.002777777777777778 * (re * pow(im, 6.0))) + (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 <= 3.1d-7) then
        tmp = 0.5d0 * (sin(re) * 2.0d0)
    else
        tmp = 0.5d0 * ((0.002777777777777778d0 * (re * (im ** 6.0d0))) + (re * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (Math.sin(re) * 2.0);
	} else {
		tmp = 0.5 * ((0.002777777777777778 * (re * Math.pow(im, 6.0))) + (re * 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 3.1e-7:
		tmp = 0.5 * (math.sin(re) * 2.0)
	else:
		tmp = 0.5 * ((0.002777777777777778 * (re * math.pow(im, 6.0))) + (re * 2.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 3.1e-7)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	else
		tmp = Float64(0.5 * Float64(Float64(0.002777777777777778 * Float64(re * (im ^ 6.0))) + Float64(re * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 3.1e-7)
		tmp = 0.5 * (sin(re) * 2.0);
	else
		tmp = 0.5 * ((0.002777777777777778 * (re * (im ^ 6.0))) + (re * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 3.1e-7], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(0.002777777777777778 * N[(re * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(re * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 10: 65.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(re \cdot \left(2 + {im}^{6} \cdot 0.002777777777777778\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 3.1e-7)
   (* 0.5 (* (sin re) 2.0))
   (* 0.5 (* re (+ 2.0 (* (pow im 6.0) 0.002777777777777778))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else {
		tmp = 0.5 * (re * (2.0 + (pow(im, 6.0) * 0.002777777777777778)));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 3.1d-7) then
        tmp = 0.5d0 * (sin(re) * 2.0d0)
    else
        tmp = 0.5d0 * (re * (2.0d0 + ((im ** 6.0d0) * 0.002777777777777778d0)))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (Math.sin(re) * 2.0);
	} else {
		tmp = 0.5 * (re * (2.0 + (Math.pow(im, 6.0) * 0.002777777777777778)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 3.1e-7:
		tmp = 0.5 * (math.sin(re) * 2.0)
	else:
		tmp = 0.5 * (re * (2.0 + (math.pow(im, 6.0) * 0.002777777777777778)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 3.1e-7)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	else
		tmp = Float64(0.5 * Float64(re * Float64(2.0 + Float64((im ^ 6.0) * 0.002777777777777778))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 3.1e-7)
		tmp = 0.5 * (sin(re) * 2.0);
	else
		tmp = 0.5 * (re * (2.0 + ((im ^ 6.0) * 0.002777777777777778)));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 3.1e-7], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(re * N[(2.0 + N[(N[Power[im, 6.0], $MachinePrecision] * 0.002777777777777778), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 11: 65.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 20:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(0.002777777777777778 \cdot \left(re \cdot {im}^{6}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 20.0)
   (* 0.5 (* (sin re) 2.0))
   (* 0.5 (* 0.002777777777777778 (* re (pow im 6.0))))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 20.0) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else {
		tmp = 0.5 * (0.002777777777777778 * (re * pow(im, 6.0)));
	}
	return tmp;
}

Fortran

real(8) function code(re, im)
    real(8), intent (in) :: re
    real(8), intent (in) :: im
    real(8) :: tmp
    if (im <= 20.0d0) then
        tmp = 0.5d0 * (sin(re) * 2.0d0)
    else
        tmp = 0.5d0 * (0.002777777777777778d0 * (re * (im ** 6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 20.0) {
		tmp = 0.5 * (Math.sin(re) * 2.0);
	} else {
		tmp = 0.5 * (0.002777777777777778 * (re * Math.pow(im, 6.0)));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 20.0:
		tmp = 0.5 * (math.sin(re) * 2.0)
	else:
		tmp = 0.5 * (0.002777777777777778 * (re * math.pow(im, 6.0)))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 20.0)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	else
		tmp = Float64(0.5 * Float64(0.002777777777777778 * Float64(re * (im ^ 6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 20.0)
		tmp = 0.5 * (sin(re) * 2.0);
	else
		tmp = 0.5 * (0.002777777777777778 * (re * (im ^ 6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 20.0], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(0.002777777777777778 * N[(re * N[Power[im, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 12: 60.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 3.1 \cdot 10^{-7}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(re \cdot \mathsf{fma}\left(im, im, 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 3.1e-7) (* 0.5 (* (sin re) 2.0)) (* 0.5 (* re (fma im im 2.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 3.1e-7) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else {
		tmp = 0.5 * (re * fma(im, im, 2.0));
	}
	return tmp;
}

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 3.1e-7)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	else
		tmp = Float64(0.5 * Float64(re * fma(im, im, 2.0)));
	end
	return tmp
end

Wolfram

code[re_, im_] := If[LessEqual[im, 3.1e-7], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(re * N[(im * im + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 13: 60.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;im \leq 10^{+21}:\\ \;\;\;\;0.5 \cdot \left(\sin re \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(re \cdot {im}^{2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (re im)
 :precision binary64
 (if (<= im 1e+21) (* 0.5 (* (sin re) 2.0)) (* 0.5 (* re (pow im 2.0)))))

C

double code(double re, double im) {
	double tmp;
	if (im <= 1e+21) {
		tmp = 0.5 * (sin(re) * 2.0);
	} else {
		tmp = 0.5 * (re * pow(im, 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 <= 1d+21) then
        tmp = 0.5d0 * (sin(re) * 2.0d0)
    else
        tmp = 0.5d0 * (re * (im ** 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double re, double im) {
	double tmp;
	if (im <= 1e+21) {
		tmp = 0.5 * (Math.sin(re) * 2.0);
	} else {
		tmp = 0.5 * (re * Math.pow(im, 2.0));
	}
	return tmp;
}

Python

def code(re, im):
	tmp = 0
	if im <= 1e+21:
		tmp = 0.5 * (math.sin(re) * 2.0)
	else:
		tmp = 0.5 * (re * math.pow(im, 2.0))
	return tmp

Julia

function code(re, im)
	tmp = 0.0
	if (im <= 1e+21)
		tmp = Float64(0.5 * Float64(sin(re) * 2.0));
	else
		tmp = Float64(0.5 * Float64(re * (im ^ 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(re, im)
	tmp = 0.0;
	if (im <= 1e+21)
		tmp = 0.5 * (sin(re) * 2.0);
	else
		tmp = 0.5 * (re * (im ^ 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[re_, im_] := If[LessEqual[im, 1e+21], N[(0.5 * N[(N[Sin[re], $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(re * N[Power[im, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 14: 50.4% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(re, im):
	return 0.5 * (math.sin(re) * 2.0)

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 15: 26.1% accurate, 61.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Reproduce

herbie shell --seed 2024006 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))