powComplex, imaginary part

Percentage Accurate: 40.4% → 76.1%

Time: 34.5s

Alternatives: 21

Speedup: 1.9×

• 35.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ e^{t_0 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \sin \left(t_0 \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (sqrt (+ (* x.re x.re) (* x.im x.im))))))
   (*
    (exp (- (* t_0 y.re) (* (atan2 x.im x.re) y.im)))
    (sin (+ (* t_0 y.im) (* (atan2 x.im x.re) y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * sin(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    t_0 = log(sqrt(((x_46re * x_46re) + (x_46im * x_46im))))
    code = exp(((t_0 * y_46re) - (atan2(x_46im, x_46re) * y_46im))) * sin(((t_0 * y_46im) + (atan2(x_46im, x_46re) * y_46re)))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return Math.exp(((t_0 * y_46_re) - (Math.atan2(x_46_im, x_46_re) * y_46_im))) * Math.sin(((t_0 * y_46_im) + (Math.atan2(x_46_im, x_46_re) * y_46_re)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))))
	return math.exp(((t_0 * y_46_re) - (math.atan2(x_46_im, x_46_re) * y_46_im))) * math.sin(((t_0 * y_46_im) + (math.atan2(x_46_im, x_46_re) * y_46_re)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	return Float64(exp(Float64(Float64(t_0 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * sin(Float64(Float64(t_0 * y_46_im) + Float64(atan(x_46_im, x_46_re) * y_46_re))))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	tmp = exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * sin(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, N[(N[Exp[N[(N[(t$95$0 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(N[(t$95$0 * y$46$im), $MachinePrecision] + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Initial Program: 40.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ e^{t_0 \cdot y.re - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \sin \left(t_0 \cdot y.im + \tan^{-1}_* \frac{x.im}{x.re} \cdot y.re\right) \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (sqrt (+ (* x.re x.re) (* x.im x.im))))))
   (*
    (exp (- (* t_0 y.re) (* (atan2 x.im x.re) y.im)))
    (sin (+ (* t_0 y.im) (* (atan2 x.im x.re) y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * sin(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    t_0 = log(sqrt(((x_46re * x_46re) + (x_46im * x_46im))))
    code = exp(((t_0 * y_46re) - (atan2(x_46im, x_46re) * y_46im))) * sin(((t_0 * y_46im) + (atan2(x_46im, x_46re) * y_46re)))
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.log(Math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	return Math.exp(((t_0 * y_46_re) - (Math.atan2(x_46_im, x_46_re) * y_46_im))) * Math.sin(((t_0 * y_46_im) + (Math.atan2(x_46_im, x_46_re) * y_46_re)));
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.log(math.sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))))
	return math.exp(((t_0 * y_46_re) - (math.atan2(x_46_im, x_46_re) * y_46_im))) * math.sin(((t_0 * y_46_im) + (math.atan2(x_46_im, x_46_re) * y_46_re)))

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	return Float64(exp(Float64(Float64(t_0 * y_46_re) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * sin(Float64(Float64(t_0 * y_46_im) + Float64(atan(x_46_im, x_46_re) * y_46_re))))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	tmp = exp(((t_0 * y_46_re) - (atan2(x_46_im, x_46_re) * y_46_im))) * sin(((t_0 * y_46_im) + (atan2(x_46_im, x_46_re) * y_46_re)));
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, N[(N[Exp[N[(N[(t$95$0 * y$46$re), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(N[(t$95$0 * y$46$im), $MachinePrecision] + N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$re), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_1 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_2 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_3 := e^{y.re \cdot t_2 - t_0}\\ t_4 := y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\\ \mathbf{if}\;y.re \leq -9.6 \cdot 10^{+152}:\\ \;\;\;\;\sin \left({\left(\sqrt[3]{t_1}\right)}^{3}\right) \cdot {\left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq -3.7 \cdot 10^{-23}:\\ \;\;\;\;t_3 \cdot \sin t_1\\ \mathbf{elif}\;y.re \leq 1.22 \cdot 10^{-62}:\\ \;\;\;\;e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)} \cdot \sin \left(\mathsf{fma}\left(y.re, \tan^{-1}_* \frac{x.im}{x.re}, y.im \cdot t_2\right)\right)\\ \mathbf{elif}\;y.re \leq 1.55 \cdot 10^{+134}:\\ \;\;\;\;e^{\log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right) \cdot y.re - t_0} \cdot \sin \left(t_1 - t_4\right)\\ \mathbf{else}:\\ \;\;\;\;t_3 \cdot \sin t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (atan2 x.im x.re) y.im))
        (t_1 (* y.re (atan2 x.im x.re)))
        (t_2 (log (hypot x.re x.im)))
        (t_3 (exp (- (* y.re t_2) t_0)))
        (t_4 (* y.im (log (hypot x.im x.re)))))
   (if (<= y.re -9.6e+152)
     (*
      (sin (pow (cbrt t_1) 3.0))
      (pow (sqrt (+ (pow x.re 2.0) (pow x.im 2.0))) y.re))
     (if (<= y.re -3.7e-23)
       (* t_3 (sin t_1))
       (if (<= y.re 1.22e-62)
         (*
          (exp (* y.im (- (atan2 x.im x.re))))
          (sin (fma y.re (atan2 x.im x.re) (* y.im t_2))))
         (if (<= y.re 1.55e+134)
           (*
            (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) t_0))
            (sin (- t_1 t_4)))
           (* t_3 (sin t_4))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = y_46_re * atan2(x_46_im, x_46_re);
	double t_2 = log(hypot(x_46_re, x_46_im));
	double t_3 = exp(((y_46_re * t_2) - t_0));
	double t_4 = y_46_im * log(hypot(x_46_im, x_46_re));
	double tmp;
	if (y_46_re <= -9.6e+152) {
		tmp = sin(pow(cbrt(t_1), 3.0)) * pow(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0))), y_46_re);
	} else if (y_46_re <= -3.7e-23) {
		tmp = t_3 * sin(t_1);
	} else if (y_46_re <= 1.22e-62) {
		tmp = exp((y_46_im * -atan2(x_46_im, x_46_re))) * sin(fma(y_46_re, atan2(x_46_im, x_46_re), (y_46_im * t_2)));
	} else if (y_46_re <= 1.55e+134) {
		tmp = exp(((log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im)))) * y_46_re) - t_0)) * sin((t_1 - t_4));
	} else {
		tmp = t_3 * sin(t_4);
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_1 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_2 = log(hypot(x_46_re, x_46_im))
	t_3 = exp(Float64(Float64(y_46_re * t_2) - t_0))
	t_4 = Float64(y_46_im * log(hypot(x_46_im, x_46_re)))
	tmp = 0.0
	if (y_46_re <= -9.6e+152)
		tmp = Float64(sin((cbrt(t_1) ^ 3.0)) * (sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re));
	elseif (y_46_re <= -3.7e-23)
		tmp = Float64(t_3 * sin(t_1));
	elseif (y_46_re <= 1.22e-62)
		tmp = Float64(exp(Float64(y_46_im * Float64(-atan(x_46_im, x_46_re)))) * sin(fma(y_46_re, atan(x_46_im, x_46_re), Float64(y_46_im * t_2))));
	elseif (y_46_re <= 1.55e+134)
		tmp = Float64(exp(Float64(Float64(log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im)))) * y_46_re) - t_0)) * sin(Float64(t_1 - t_4)));
	else
		tmp = Float64(t_3 * sin(t_4));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$1 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Exp[N[(N[(y$46$re * t$95$2), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -9.6e+152], N[(N[Sin[N[Power[N[Power[t$95$1, 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[Power[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -3.7e-23], N[(t$95$3 * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.22e-62], N[(N[Exp[N[(y$46$im * (-N[ArcTan[x$46$im / x$46$re], $MachinePrecision])), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision] + N[(y$46$im * t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.55e+134], N[(N[Exp[N[(N[(N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] * y$46$re), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(t$95$1 - t$95$4), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$3 * N[Sin[t$95$4], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

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

Alternative 2: 79.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_1 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_2 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_3 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_4 := e^{t_3 \cdot y.re - t_1}\\ t_5 := t_4 \cdot \sin \left(t_3 \cdot y.im + t_2\right)\\ t_6 := y.im \cdot t_0\\ \mathbf{if}\;t_5 \leq 0.1:\\ \;\;\;\;t_4 \cdot \sin \left({\left(\sqrt[3]{t_6}\right)}^{3} + t_2\right)\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_4 \cdot \sin \left(t_2 - y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot t_0 - t_1} \cdot \mathsf{fma}\left(\sin t_6, \cos t_2, \sin t_2 \cdot \cos t_6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (hypot x.re x.im)))
        (t_1 (* (atan2 x.im x.re) y.im))
        (t_2 (* y.re (atan2 x.im x.re)))
        (t_3 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_4 (exp (- (* t_3 y.re) t_1)))
        (t_5 (* t_4 (sin (+ (* t_3 y.im) t_2))))
        (t_6 (* y.im t_0)))
   (if (<= t_5 0.1)
     (* t_4 (sin (+ (pow (cbrt t_6) 3.0) t_2)))
     (if (<= t_5 INFINITY)
       (* t_4 (sin (- t_2 (* y.im (log (hypot x.im x.re))))))
       (*
        (exp (- (* y.re t_0) t_1))
        (fma (sin t_6) (cos t_2) (* (sin t_2) (cos t_6))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(hypot(x_46_re, x_46_im));
	double t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = y_46_re * atan2(x_46_im, x_46_re);
	double t_3 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_4 = exp(((t_3 * y_46_re) - t_1));
	double t_5 = t_4 * sin(((t_3 * y_46_im) + t_2));
	double t_6 = y_46_im * t_0;
	double tmp;
	if (t_5 <= 0.1) {
		tmp = t_4 * sin((pow(cbrt(t_6), 3.0) + t_2));
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_4 * sin((t_2 - (y_46_im * log(hypot(x_46_im, x_46_re)))));
	} else {
		tmp = exp(((y_46_re * t_0) - t_1)) * fma(sin(t_6), cos(t_2), (sin(t_2) * cos(t_6)));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(hypot(x_46_re, x_46_im))
	t_1 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_2 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_3 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_4 = exp(Float64(Float64(t_3 * y_46_re) - t_1))
	t_5 = Float64(t_4 * sin(Float64(Float64(t_3 * y_46_im) + t_2)))
	t_6 = Float64(y_46_im * t_0)
	tmp = 0.0
	if (t_5 <= 0.1)
		tmp = Float64(t_4 * sin(Float64((cbrt(t_6) ^ 3.0) + t_2)));
	elseif (t_5 <= Inf)
		tmp = Float64(t_4 * sin(Float64(t_2 - Float64(y_46_im * log(hypot(x_46_im, x_46_re))))));
	else
		tmp = Float64(exp(Float64(Float64(y_46_re * t_0) - t_1)) * fma(sin(t_6), cos(t_2), Float64(sin(t_2) * cos(t_6))));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$2 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Exp[N[(N[(t$95$3 * y$46$re), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[Sin[N[(N[(t$95$3 * y$46$im), $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(y$46$im * t$95$0), $MachinePrecision]}, If[LessEqual[t$95$5, 0.1], N[(t$95$4 * N[Sin[N[(N[Power[N[Power[t$95$6, 1/3], $MachinePrecision], 3.0], $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(t$95$4 * N[Sin[N[(t$95$2 - N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(N[(y$46$re * t$95$0), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision] * N[(N[Sin[t$95$6], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision] + N[(N[Sin[t$95$2], $MachinePrecision] * N[Cos[t$95$6], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

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

Alternative 3: 79.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_1 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_2 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_3 := \log \left(\sqrt{x.re \cdot x.re + x.im \cdot x.im}\right)\\ t_4 := e^{t_3 \cdot y.re - t_1}\\ t_5 := t_4 \cdot \sin \left(t_3 \cdot y.im + t_2\right)\\ \mathbf{if}\;t_5 \leq 0.1:\\ \;\;\;\;t_4 \cdot \sin \left({\left(\sqrt[3]{y.im \cdot t_0}\right)}^{3} + t_2\right)\\ \mathbf{elif}\;t_5 \leq \infty:\\ \;\;\;\;t_4 \cdot \sin \left(t_2 - y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;e^{y.re \cdot t_0 - t_1} \cdot \sin \left(\mathsf{fma}\left(t_0, y.im, t_2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (hypot x.re x.im)))
        (t_1 (* (atan2 x.im x.re) y.im))
        (t_2 (* y.re (atan2 x.im x.re)))
        (t_3 (log (sqrt (+ (* x.re x.re) (* x.im x.im)))))
        (t_4 (exp (- (* t_3 y.re) t_1)))
        (t_5 (* t_4 (sin (+ (* t_3 y.im) t_2)))))
   (if (<= t_5 0.1)
     (* t_4 (sin (+ (pow (cbrt (* y.im t_0)) 3.0) t_2)))
     (if (<= t_5 INFINITY)
       (* t_4 (sin (- t_2 (* y.im (log (hypot x.im x.re))))))
       (* (exp (- (* y.re t_0) t_1)) (sin (fma t_0 y.im t_2)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(hypot(x_46_re, x_46_im));
	double t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = y_46_re * atan2(x_46_im, x_46_re);
	double t_3 = log(sqrt(((x_46_re * x_46_re) + (x_46_im * x_46_im))));
	double t_4 = exp(((t_3 * y_46_re) - t_1));
	double t_5 = t_4 * sin(((t_3 * y_46_im) + t_2));
	double tmp;
	if (t_5 <= 0.1) {
		tmp = t_4 * sin((pow(cbrt((y_46_im * t_0)), 3.0) + t_2));
	} else if (t_5 <= ((double) INFINITY)) {
		tmp = t_4 * sin((t_2 - (y_46_im * log(hypot(x_46_im, x_46_re)))));
	} else {
		tmp = exp(((y_46_re * t_0) - t_1)) * sin(fma(t_0, y_46_im, t_2));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(hypot(x_46_re, x_46_im))
	t_1 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_2 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_3 = log(sqrt(Float64(Float64(x_46_re * x_46_re) + Float64(x_46_im * x_46_im))))
	t_4 = exp(Float64(Float64(t_3 * y_46_re) - t_1))
	t_5 = Float64(t_4 * sin(Float64(Float64(t_3 * y_46_im) + t_2)))
	tmp = 0.0
	if (t_5 <= 0.1)
		tmp = Float64(t_4 * sin(Float64((cbrt(Float64(y_46_im * t_0)) ^ 3.0) + t_2)));
	elseif (t_5 <= Inf)
		tmp = Float64(t_4 * sin(Float64(t_2 - Float64(y_46_im * log(hypot(x_46_im, x_46_re))))));
	else
		tmp = Float64(exp(Float64(Float64(y_46_re * t_0) - t_1)) * sin(fma(t_0, y_46_im, t_2)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$2 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Log[N[Sqrt[N[(N[(x$46$re * x$46$re), $MachinePrecision] + N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Exp[N[(N[(t$95$3 * y$46$re), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 * N[Sin[N[(N[(t$95$3 * y$46$im), $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$5, 0.1], N[(t$95$4 * N[Sin[N[(N[Power[N[Power[N[(y$46$im * t$95$0), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$5, Infinity], N[(t$95$4 * N[Sin[N[(t$95$2 - N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Exp[N[(N[(y$46$re * t$95$0), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(t$95$0 * y$46$im + t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 4: 80.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ e^{y.re \cdot t_0 - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot \sin \left(\mathsf{fma}\left(t_0, y.im, y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\right) \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (hypot x.re x.im))))
   (*
    (exp (- (* y.re t_0) (* (atan2 x.im x.re) y.im)))
    (sin (fma t_0 y.im (* y.re (atan2 x.im x.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(hypot(x_46_re, x_46_im));
	return exp(((y_46_re * t_0) - (atan2(x_46_im, x_46_re) * y_46_im))) * sin(fma(t_0, y_46_im, (y_46_re * atan2(x_46_im, x_46_re))));
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(hypot(x_46_re, x_46_im))
	return Float64(exp(Float64(Float64(y_46_re * t_0) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * sin(fma(t_0, y_46_im, Float64(y_46_re * atan(x_46_im, x_46_re)))))
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, N[(N[Exp[N[(N[(y$46$re * t$95$0), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(t$95$0 * y$46$im + N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 5: 78.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_2 := e^{y.re \cdot t_1 - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ t_3 := t_2 \cdot \sin t_0\\ \mathbf{if}\;y.re \leq -2.5 \cdot 10^{+150}:\\ \;\;\;\;\sin \left({\left(\sqrt[3]{t_0}\right)}^{3}\right) \cdot {\left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq -1.65 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y.re \leq 1.2 \cdot 10^{-71}:\\ \;\;\;\;e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)} \cdot \sin \left(\mathsf{fma}\left(y.re, \tan^{-1}_* \frac{x.im}{x.re}, y.im \cdot t_1\right)\right)\\ \mathbf{elif}\;y.re \leq 8.5 \cdot 10^{+134}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \sin \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (log (hypot x.re x.im)))
        (t_2 (exp (- (* y.re t_1) (* (atan2 x.im x.re) y.im))))
        (t_3 (* t_2 (sin t_0))))
   (if (<= y.re -2.5e+150)
     (*
      (sin (pow (cbrt t_0) 3.0))
      (pow (sqrt (+ (pow x.re 2.0) (pow x.im 2.0))) y.re))
     (if (<= y.re -1.65e-25)
       t_3
       (if (<= y.re 1.2e-71)
         (*
          (exp (* y.im (- (atan2 x.im x.re))))
          (sin (fma y.re (atan2 x.im x.re) (* y.im t_1))))
         (if (<= y.re 8.5e+134)
           t_3
           (* t_2 (sin (* y.im (log (hypot x.im x.re)))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = log(hypot(x_46_re, x_46_im));
	double t_2 = exp(((y_46_re * t_1) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double t_3 = t_2 * sin(t_0);
	double tmp;
	if (y_46_re <= -2.5e+150) {
		tmp = sin(pow(cbrt(t_0), 3.0)) * pow(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0))), y_46_re);
	} else if (y_46_re <= -1.65e-25) {
		tmp = t_3;
	} else if (y_46_re <= 1.2e-71) {
		tmp = exp((y_46_im * -atan2(x_46_im, x_46_re))) * sin(fma(y_46_re, atan2(x_46_im, x_46_re), (y_46_im * t_1)));
	} else if (y_46_re <= 8.5e+134) {
		tmp = t_3;
	} else {
		tmp = t_2 * sin((y_46_im * log(hypot(x_46_im, x_46_re))));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = log(hypot(x_46_re, x_46_im))
	t_2 = exp(Float64(Float64(y_46_re * t_1) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	t_3 = Float64(t_2 * sin(t_0))
	tmp = 0.0
	if (y_46_re <= -2.5e+150)
		tmp = Float64(sin((cbrt(t_0) ^ 3.0)) * (sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re));
	elseif (y_46_re <= -1.65e-25)
		tmp = t_3;
	elseif (y_46_re <= 1.2e-71)
		tmp = Float64(exp(Float64(y_46_im * Float64(-atan(x_46_im, x_46_re)))) * sin(fma(y_46_re, atan(x_46_im, x_46_re), Float64(y_46_im * t_1))));
	elseif (y_46_re <= 8.5e+134)
		tmp = t_3;
	else
		tmp = Float64(t_2 * sin(Float64(y_46_im * log(hypot(x_46_im, x_46_re)))));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(y$46$re * t$95$1), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -2.5e+150], N[(N[Sin[N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[Power[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, -1.65e-25], t$95$3, If[LessEqual[y$46$re, 1.2e-71], N[(N[Exp[N[(y$46$im * (-N[ArcTan[x$46$im / x$46$re], $MachinePrecision])), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision] + N[(y$46$im * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 8.5e+134], t$95$3, N[(t$95$2 * N[Sin[N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 6: 78.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_1 := e^{y.re \cdot t_0 - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}\\ t_2 := t_1 \cdot \sin \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{if}\;y.re \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y.re \leq 9.5 \cdot 10^{-71}:\\ \;\;\;\;e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)} \cdot \sin \left(\mathsf{fma}\left(y.re, \tan^{-1}_* \frac{x.im}{x.re}, y.im \cdot t_0\right)\right)\\ \mathbf{elif}\;y.re \leq 1.75 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sin \left(y.im \cdot \log \left(\mathsf{hypot}\left(x.im, x.re\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (log (hypot x.re x.im)))
        (t_1 (exp (- (* y.re t_0) (* (atan2 x.im x.re) y.im))))
        (t_2 (* t_1 (sin (* y.re (atan2 x.im x.re))))))
   (if (<= y.re -1.45e-23)
     t_2
     (if (<= y.re 9.5e-71)
       (*
        (exp (* y.im (- (atan2 x.im x.re))))
        (sin (fma y.re (atan2 x.im x.re) (* y.im t_0))))
       (if (<= y.re 1.75e+135)
         t_2
         (* t_1 (sin (* y.im (log (hypot x.im x.re))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = log(hypot(x_46_re, x_46_im));
	double t_1 = exp(((y_46_re * t_0) - (atan2(x_46_im, x_46_re) * y_46_im)));
	double t_2 = t_1 * sin((y_46_re * atan2(x_46_im, x_46_re)));
	double tmp;
	if (y_46_re <= -1.45e-23) {
		tmp = t_2;
	} else if (y_46_re <= 9.5e-71) {
		tmp = exp((y_46_im * -atan2(x_46_im, x_46_re))) * sin(fma(y_46_re, atan2(x_46_im, x_46_re), (y_46_im * t_0)));
	} else if (y_46_re <= 1.75e+135) {
		tmp = t_2;
	} else {
		tmp = t_1 * sin((y_46_im * log(hypot(x_46_im, x_46_re))));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = log(hypot(x_46_re, x_46_im))
	t_1 = exp(Float64(Float64(y_46_re * t_0) - Float64(atan(x_46_im, x_46_re) * y_46_im)))
	t_2 = Float64(t_1 * sin(Float64(y_46_re * atan(x_46_im, x_46_re))))
	tmp = 0.0
	if (y_46_re <= -1.45e-23)
		tmp = t_2;
	elseif (y_46_re <= 9.5e-71)
		tmp = Float64(exp(Float64(y_46_im * Float64(-atan(x_46_im, x_46_re)))) * sin(fma(y_46_re, atan(x_46_im, x_46_re), Float64(y_46_im * t_0))));
	elseif (y_46_re <= 1.75e+135)
		tmp = t_2;
	else
		tmp = Float64(t_1 * sin(Float64(y_46_im * log(hypot(x_46_im, x_46_re)))));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(y$46$re * t$95$0), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -1.45e-23], t$95$2, If[LessEqual[y$46$re, 9.5e-71], N[(N[Exp[N[(y$46$im * (-N[ArcTan[x$46$im / x$46$re], $MachinePrecision])), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision] + N[(y$46$im * t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.75e+135], t$95$2, N[(t$95$1 * N[Sin[N[(y$46$im * N[Log[N[Sqrt[x$46$im ^ 2 + x$46$re ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 7: 69.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_2 := e^{y.re \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right) - t_1} \cdot \sin t_0\\ t_3 := \log \left(-x.re\right)\\ t_4 := e^{t_1}\\ \mathbf{if}\;x.re \leq -4.4 \cdot 10^{-50}:\\ \;\;\;\;e^{y.re \cdot t_3 - t_1} \cdot \sin \left(t_0 + y.im \cdot t_3\right)\\ \mathbf{elif}\;x.re \leq 9.2 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x.re \leq 1.02 \cdot 10^{-79}:\\ \;\;\;\;\frac{\sin \left(y.im \cdot \log \left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)\right)}{t_4}\\ \mathbf{elif}\;x.re \leq 21000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot \sin \left(t_0 + y.im \cdot \log x.re\right)}{t_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (* (atan2 x.im x.re) y.im))
        (t_2 (* (exp (- (* y.re (log (hypot x.re x.im))) t_1)) (sin t_0)))
        (t_3 (log (- x.re)))
        (t_4 (exp t_1)))
   (if (<= x.re -4.4e-50)
     (* (exp (- (* y.re t_3) t_1)) (sin (+ t_0 (* y.im t_3))))
     (if (<= x.re 9.2e-106)
       t_2
       (if (<= x.re 1.02e-79)
         (/ (sin (* y.im (log (sqrt (+ (pow x.re 2.0) (pow x.im 2.0)))))) t_4)
         (if (<= x.re 21000000000.0)
           t_2
           (/ (* (pow x.re y.re) (sin (+ t_0 (* y.im (log x.re))))) t_4)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_1)) * sin(t_0);
	double t_3 = log(-x_46_re);
	double t_4 = exp(t_1);
	double tmp;
	if (x_46_re <= -4.4e-50) {
		tmp = exp(((y_46_re * t_3) - t_1)) * sin((t_0 + (y_46_im * t_3)));
	} else if (x_46_re <= 9.2e-106) {
		tmp = t_2;
	} else if (x_46_re <= 1.02e-79) {
		tmp = sin((y_46_im * log(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0)))))) / t_4;
	} else if (x_46_re <= 21000000000.0) {
		tmp = t_2;
	} else {
		tmp = (pow(x_46_re, y_46_re) * sin((t_0 + (y_46_im * log(x_46_re))))) / t_4;
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_2 = Math.exp(((y_46_re * Math.log(Math.hypot(x_46_re, x_46_im))) - t_1)) * Math.sin(t_0);
	double t_3 = Math.log(-x_46_re);
	double t_4 = Math.exp(t_1);
	double tmp;
	if (x_46_re <= -4.4e-50) {
		tmp = Math.exp(((y_46_re * t_3) - t_1)) * Math.sin((t_0 + (y_46_im * t_3)));
	} else if (x_46_re <= 9.2e-106) {
		tmp = t_2;
	} else if (x_46_re <= 1.02e-79) {
		tmp = Math.sin((y_46_im * Math.log(Math.sqrt((Math.pow(x_46_re, 2.0) + Math.pow(x_46_im, 2.0)))))) / t_4;
	} else if (x_46_re <= 21000000000.0) {
		tmp = t_2;
	} else {
		tmp = (Math.pow(x_46_re, y_46_re) * Math.sin((t_0 + (y_46_im * Math.log(x_46_re))))) / t_4;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_2 = math.exp(((y_46_re * math.log(math.hypot(x_46_re, x_46_im))) - t_1)) * math.sin(t_0)
	t_3 = math.log(-x_46_re)
	t_4 = math.exp(t_1)
	tmp = 0
	if x_46_re <= -4.4e-50:
		tmp = math.exp(((y_46_re * t_3) - t_1)) * math.sin((t_0 + (y_46_im * t_3)))
	elif x_46_re <= 9.2e-106:
		tmp = t_2
	elif x_46_re <= 1.02e-79:
		tmp = math.sin((y_46_im * math.log(math.sqrt((math.pow(x_46_re, 2.0) + math.pow(x_46_im, 2.0)))))) / t_4
	elif x_46_re <= 21000000000.0:
		tmp = t_2
	else:
		tmp = (math.pow(x_46_re, y_46_re) * math.sin((t_0 + (y_46_im * math.log(x_46_re))))) / t_4
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_2 = Float64(exp(Float64(Float64(y_46_re * log(hypot(x_46_re, x_46_im))) - t_1)) * sin(t_0))
	t_3 = log(Float64(-x_46_re))
	t_4 = exp(t_1)
	tmp = 0.0
	if (x_46_re <= -4.4e-50)
		tmp = Float64(exp(Float64(Float64(y_46_re * t_3) - t_1)) * sin(Float64(t_0 + Float64(y_46_im * t_3))));
	elseif (x_46_re <= 9.2e-106)
		tmp = t_2;
	elseif (x_46_re <= 1.02e-79)
		tmp = Float64(sin(Float64(y_46_im * log(sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0)))))) / t_4);
	elseif (x_46_re <= 21000000000.0)
		tmp = t_2;
	else
		tmp = Float64(Float64((x_46_re ^ y_46_re) * sin(Float64(t_0 + Float64(y_46_im * log(x_46_re))))) / t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = atan2(x_46_im, x_46_re) * y_46_im;
	t_2 = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_1)) * sin(t_0);
	t_3 = log(-x_46_re);
	t_4 = exp(t_1);
	tmp = 0.0;
	if (x_46_re <= -4.4e-50)
		tmp = exp(((y_46_re * t_3) - t_1)) * sin((t_0 + (y_46_im * t_3)));
	elseif (x_46_re <= 9.2e-106)
		tmp = t_2;
	elseif (x_46_re <= 1.02e-79)
		tmp = sin((y_46_im * log(sqrt(((x_46_re ^ 2.0) + (x_46_im ^ 2.0)))))) / t_4;
	elseif (x_46_re <= 21000000000.0)
		tmp = t_2;
	else
		tmp = ((x_46_re ^ y_46_re) * sin((t_0 + (y_46_im * log(x_46_re))))) / t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$2 = N[(N[Exp[N[(N[(y$46$re * N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Log[(-x$46$re)], $MachinePrecision]}, Block[{t$95$4 = N[Exp[t$95$1], $MachinePrecision]}, If[LessEqual[x$46$re, -4.4e-50], N[(N[Exp[N[(N[(y$46$re * t$95$3), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(t$95$0 + N[(y$46$im * t$95$3), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, 9.2e-106], t$95$2, If[LessEqual[x$46$re, 1.02e-79], N[(N[Sin[N[(y$46$im * N[Log[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[x$46$re, 21000000000.0], t$95$2, N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * N[Sin[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]]]]]]]]]]

Derivation

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

Alternative 8: 76.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \sin t_0\\ t_2 := \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right)\\ t_3 := e^{y.re \cdot t_2 - \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im} \cdot t_1\\ \mathbf{if}\;y.re \leq -9.6 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y.re \leq 8 \cdot 10^{-71}:\\ \;\;\;\;e^{y.im \cdot \left(-\tan^{-1}_* \frac{x.im}{x.re}\right)} \cdot \sin \left(\mathsf{fma}\left(y.re, \tan^{-1}_* \frac{x.im}{x.re}, y.im \cdot t_2\right)\right)\\ \mathbf{elif}\;y.re \leq 2.4 \cdot 10^{+216}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y.re \leq 2.2 \cdot 10^{+278}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot {\left(x.im + \frac{{x.re}^{2} \cdot 0.5}{x.im}\right)}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (sin t_0))
        (t_2 (log (hypot x.re x.im)))
        (t_3 (* (exp (- (* y.re t_2) (* (atan2 x.im x.re) y.im))) t_1)))
   (if (<= y.re -9.6e-23)
     t_3
     (if (<= y.re 8e-71)
       (*
        (exp (* y.im (- (atan2 x.im x.re))))
        (sin (fma y.re (atan2 x.im x.re) (* y.im t_2))))
       (if (<= y.re 2.4e+216)
         t_3
         (if (<= y.re 2.2e+278)
           (* t_0 (pow x.re y.re))
           (* t_1 (pow (+ x.im (/ (* (pow x.re 2.0) 0.5) x.im)) y.re))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = sin(t_0);
	double t_2 = log(hypot(x_46_re, x_46_im));
	double t_3 = exp(((y_46_re * t_2) - (atan2(x_46_im, x_46_re) * y_46_im))) * t_1;
	double tmp;
	if (y_46_re <= -9.6e-23) {
		tmp = t_3;
	} else if (y_46_re <= 8e-71) {
		tmp = exp((y_46_im * -atan2(x_46_im, x_46_re))) * sin(fma(y_46_re, atan2(x_46_im, x_46_re), (y_46_im * t_2)));
	} else if (y_46_re <= 2.4e+216) {
		tmp = t_3;
	} else if (y_46_re <= 2.2e+278) {
		tmp = t_0 * pow(x_46_re, y_46_re);
	} else {
		tmp = t_1 * pow((x_46_im + ((pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re);
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = sin(t_0)
	t_2 = log(hypot(x_46_re, x_46_im))
	t_3 = Float64(exp(Float64(Float64(y_46_re * t_2) - Float64(atan(x_46_im, x_46_re) * y_46_im))) * t_1)
	tmp = 0.0
	if (y_46_re <= -9.6e-23)
		tmp = t_3;
	elseif (y_46_re <= 8e-71)
		tmp = Float64(exp(Float64(y_46_im * Float64(-atan(x_46_im, x_46_re)))) * sin(fma(y_46_re, atan(x_46_im, x_46_re), Float64(y_46_im * t_2))));
	elseif (y_46_re <= 2.4e+216)
		tmp = t_3;
	elseif (y_46_re <= 2.2e+278)
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	else
		tmp = Float64(t_1 * (Float64(x_46_im + Float64(Float64((x_46_re ^ 2.0) * 0.5) / x_46_im)) ^ y_46_re));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[Exp[N[(N[(y$46$re * t$95$2), $MachinePrecision] - N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]}, If[LessEqual[y$46$re, -9.6e-23], t$95$3, If[LessEqual[y$46$re, 8e-71], N[(N[Exp[N[(y$46$im * (-N[ArcTan[x$46$im / x$46$re], $MachinePrecision])), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision] + N[(y$46$im * t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.4e+216], t$95$3, If[LessEqual[y$46$re, 2.2e+278], N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[Power[N[(x$46$im + N[(N[(N[Power[x$46$re, 2.0], $MachinePrecision] * 0.5), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 9: 46.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(y.im \cdot \log x.re\right)\\ t_1 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_2 := \sin t_1\\ t_3 := {\left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)}^{y.re}\\ \mathbf{if}\;x.re \leq 1.6 \cdot 10^{-291}:\\ \;\;\;\;t_1 \cdot t_3\\ \mathbf{elif}\;x.re \leq 2.4 \cdot 10^{-248}:\\ \;\;\;\;\sin \left({\left(\sqrt[3]{t_1}\right)}^{3}\right) \cdot {x.re}^{y.re}\\ \mathbf{elif}\;x.re \leq 7.8 \cdot 10^{-203}:\\ \;\;\;\;t_2 \cdot t_3\\ \mathbf{elif}\;x.re \leq 4.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{t_0}{{\left(e^{y.im}\right)}^{\tan^{-1}_* \frac{x.im}{x.re}}}\\ \mathbf{elif}\;x.re \leq 0.039:\\ \;\;\;\;t_2 \cdot {x.im}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot t_0}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (sin (* y.im (log x.re))))
        (t_1 (* y.re (atan2 x.im x.re)))
        (t_2 (sin t_1))
        (t_3 (pow (sqrt (+ (pow x.re 2.0) (pow x.im 2.0))) y.re)))
   (if (<= x.re 1.6e-291)
     (* t_1 t_3)
     (if (<= x.re 2.4e-248)
       (* (sin (pow (cbrt t_1) 3.0)) (pow x.re y.re))
       (if (<= x.re 7.8e-203)
         (* t_2 t_3)
         (if (<= x.re 4.8e-74)
           (/ t_0 (pow (exp y.im) (atan2 x.im x.re)))
           (if (<= x.re 0.039)
             (* t_2 (pow x.im y.re))
             (/
              (* (pow x.re y.re) t_0)
              (exp (* (atan2 x.im x.re) y.im))))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = sin((y_46_im * log(x_46_re)));
	double t_1 = y_46_re * atan2(x_46_im, x_46_re);
	double t_2 = sin(t_1);
	double t_3 = pow(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0))), y_46_re);
	double tmp;
	if (x_46_re <= 1.6e-291) {
		tmp = t_1 * t_3;
	} else if (x_46_re <= 2.4e-248) {
		tmp = sin(pow(cbrt(t_1), 3.0)) * pow(x_46_re, y_46_re);
	} else if (x_46_re <= 7.8e-203) {
		tmp = t_2 * t_3;
	} else if (x_46_re <= 4.8e-74) {
		tmp = t_0 / pow(exp(y_46_im), atan2(x_46_im, x_46_re));
	} else if (x_46_re <= 0.039) {
		tmp = t_2 * pow(x_46_im, y_46_re);
	} else {
		tmp = (pow(x_46_re, y_46_re) * t_0) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.sin((y_46_im * Math.log(x_46_re)));
	double t_1 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_2 = Math.sin(t_1);
	double t_3 = Math.pow(Math.sqrt((Math.pow(x_46_re, 2.0) + Math.pow(x_46_im, 2.0))), y_46_re);
	double tmp;
	if (x_46_re <= 1.6e-291) {
		tmp = t_1 * t_3;
	} else if (x_46_re <= 2.4e-248) {
		tmp = Math.sin(Math.pow(Math.cbrt(t_1), 3.0)) * Math.pow(x_46_re, y_46_re);
	} else if (x_46_re <= 7.8e-203) {
		tmp = t_2 * t_3;
	} else if (x_46_re <= 4.8e-74) {
		tmp = t_0 / Math.pow(Math.exp(y_46_im), Math.atan2(x_46_im, x_46_re));
	} else if (x_46_re <= 0.039) {
		tmp = t_2 * Math.pow(x_46_im, y_46_re);
	} else {
		tmp = (Math.pow(x_46_re, y_46_re) * t_0) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	}
	return tmp;
}

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = sin(Float64(y_46_im * log(x_46_re)))
	t_1 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_2 = sin(t_1)
	t_3 = sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re
	tmp = 0.0
	if (x_46_re <= 1.6e-291)
		tmp = Float64(t_1 * t_3);
	elseif (x_46_re <= 2.4e-248)
		tmp = Float64(sin((cbrt(t_1) ^ 3.0)) * (x_46_re ^ y_46_re));
	elseif (x_46_re <= 7.8e-203)
		tmp = Float64(t_2 * t_3);
	elseif (x_46_re <= 4.8e-74)
		tmp = Float64(t_0 / (exp(y_46_im) ^ atan(x_46_im, x_46_re)));
	elseif (x_46_re <= 0.039)
		tmp = Float64(t_2 * (x_46_im ^ y_46_re));
	else
		tmp = Float64(Float64((x_46_re ^ y_46_re) * t_0) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	end
	return tmp
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sin[t$95$1], $MachinePrecision]}, Block[{t$95$3 = N[Power[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], y$46$re], $MachinePrecision]}, If[LessEqual[x$46$re, 1.6e-291], N[(t$95$1 * t$95$3), $MachinePrecision], If[LessEqual[x$46$re, 2.4e-248], N[(N[Sin[N[Power[N[Power[t$95$1, 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, 7.8e-203], N[(t$95$2 * t$95$3), $MachinePrecision], If[LessEqual[x$46$re, 4.8e-74], N[(t$95$0 / N[Power[N[Exp[y$46$im], $MachinePrecision], N[ArcTan[x$46$im / x$46$re], $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, 0.039], N[(t$95$2 * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * t$95$0), $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

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

Alternative 10: 70.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \log \left(-x.re\right)\\ t_2 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ \mathbf{if}\;x.re \leq -2.9 \cdot 10^{-49}:\\ \;\;\;\;e^{y.re \cdot t_1 - t_2} \cdot \sin \left(t_0 + y.im \cdot t_1\right)\\ \mathbf{elif}\;x.re \leq 15200000000:\\ \;\;\;\;e^{y.re \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right) - t_2} \cdot \sin t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot \sin \left(t_0 + y.im \cdot \log x.re\right)}{e^{t_2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (log (- x.re)))
        (t_2 (* (atan2 x.im x.re) y.im)))
   (if (<= x.re -2.9e-49)
     (* (exp (- (* y.re t_1) t_2)) (sin (+ t_0 (* y.im t_1))))
     (if (<= x.re 15200000000.0)
       (* (exp (- (* y.re (log (hypot x.re x.im))) t_2)) (sin t_0))
       (/ (* (pow x.re y.re) (sin (+ t_0 (* y.im (log x.re))))) (exp t_2))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = log(-x_46_re);
	double t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	double tmp;
	if (x_46_re <= -2.9e-49) {
		tmp = exp(((y_46_re * t_1) - t_2)) * sin((t_0 + (y_46_im * t_1)));
	} else if (x_46_re <= 15200000000.0) {
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_2)) * sin(t_0);
	} else {
		tmp = (pow(x_46_re, y_46_re) * sin((t_0 + (y_46_im * log(x_46_re))))) / exp(t_2);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.log(-x_46_re);
	double t_2 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double tmp;
	if (x_46_re <= -2.9e-49) {
		tmp = Math.exp(((y_46_re * t_1) - t_2)) * Math.sin((t_0 + (y_46_im * t_1)));
	} else if (x_46_re <= 15200000000.0) {
		tmp = Math.exp(((y_46_re * Math.log(Math.hypot(x_46_re, x_46_im))) - t_2)) * Math.sin(t_0);
	} else {
		tmp = (Math.pow(x_46_re, y_46_re) * Math.sin((t_0 + (y_46_im * Math.log(x_46_re))))) / Math.exp(t_2);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.log(-x_46_re)
	t_2 = math.atan2(x_46_im, x_46_re) * y_46_im
	tmp = 0
	if x_46_re <= -2.9e-49:
		tmp = math.exp(((y_46_re * t_1) - t_2)) * math.sin((t_0 + (y_46_im * t_1)))
	elif x_46_re <= 15200000000.0:
		tmp = math.exp(((y_46_re * math.log(math.hypot(x_46_re, x_46_im))) - t_2)) * math.sin(t_0)
	else:
		tmp = (math.pow(x_46_re, y_46_re) * math.sin((t_0 + (y_46_im * math.log(x_46_re))))) / math.exp(t_2)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = log(Float64(-x_46_re))
	t_2 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	tmp = 0.0
	if (x_46_re <= -2.9e-49)
		tmp = Float64(exp(Float64(Float64(y_46_re * t_1) - t_2)) * sin(Float64(t_0 + Float64(y_46_im * t_1))));
	elseif (x_46_re <= 15200000000.0)
		tmp = Float64(exp(Float64(Float64(y_46_re * log(hypot(x_46_re, x_46_im))) - t_2)) * sin(t_0));
	else
		tmp = Float64(Float64((x_46_re ^ y_46_re) * sin(Float64(t_0 + Float64(y_46_im * log(x_46_re))))) / exp(t_2));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = log(-x_46_re);
	t_2 = atan2(x_46_im, x_46_re) * y_46_im;
	tmp = 0.0;
	if (x_46_re <= -2.9e-49)
		tmp = exp(((y_46_re * t_1) - t_2)) * sin((t_0 + (y_46_im * t_1)));
	elseif (x_46_re <= 15200000000.0)
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_2)) * sin(t_0);
	else
		tmp = ((x_46_re ^ y_46_re) * sin((t_0 + (y_46_im * log(x_46_re))))) / exp(t_2);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Log[(-x$46$re)], $MachinePrecision]}, Block[{t$95$2 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, If[LessEqual[x$46$re, -2.9e-49], N[(N[Exp[N[(N[(y$46$re * t$95$1), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(t$95$0 + N[(y$46$im * t$95$1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re, 15200000000.0], N[(N[Exp[N[(N[(y$46$re * N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]], $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * N[Sin[N[(t$95$0 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[t$95$2], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 11: 68.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ t_1 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ \mathbf{if}\;x.re \leq 13500000000:\\ \;\;\;\;e^{y.re \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right) - t_0} \cdot \sin t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot \sin \left(t_1 + y.im \cdot \log x.re\right)}{e^{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (atan2 x.im x.re) y.im)) (t_1 (* y.re (atan2 x.im x.re))))
   (if (<= x.re 13500000000.0)
     (* (exp (- (* y.re (log (hypot x.re x.im))) t_0)) (sin t_1))
     (/ (* (pow x.re y.re) (sin (+ t_1 (* y.im (log x.re))))) (exp t_0)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = y_46_re * atan2(x_46_im, x_46_re);
	double tmp;
	if (x_46_re <= 13500000000.0) {
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin(t_1);
	} else {
		tmp = (pow(x_46_re, y_46_re) * sin((t_1 + (y_46_im * log(x_46_re))))) / exp(t_0);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double t_1 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double tmp;
	if (x_46_re <= 13500000000.0) {
		tmp = Math.exp(((y_46_re * Math.log(Math.hypot(x_46_re, x_46_im))) - t_0)) * Math.sin(t_1);
	} else {
		tmp = (Math.pow(x_46_re, y_46_re) * Math.sin((t_1 + (y_46_im * Math.log(x_46_re))))) / Math.exp(t_0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.atan2(x_46_im, x_46_re) * y_46_im
	t_1 = y_46_re * math.atan2(x_46_im, x_46_re)
	tmp = 0
	if x_46_re <= 13500000000.0:
		tmp = math.exp(((y_46_re * math.log(math.hypot(x_46_re, x_46_im))) - t_0)) * math.sin(t_1)
	else:
		tmp = (math.pow(x_46_re, y_46_re) * math.sin((t_1 + (y_46_im * math.log(x_46_re))))) / math.exp(t_0)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	t_1 = Float64(y_46_re * atan(x_46_im, x_46_re))
	tmp = 0.0
	if (x_46_re <= 13500000000.0)
		tmp = Float64(exp(Float64(Float64(y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin(t_1));
	else
		tmp = Float64(Float64((x_46_re ^ y_46_re) * sin(Float64(t_1 + Float64(y_46_im * log(x_46_re))))) / exp(t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	t_1 = y_46_re * atan2(x_46_im, x_46_re);
	tmp = 0.0;
	if (x_46_re <= 13500000000.0)
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin(t_1);
	else
		tmp = ((x_46_re ^ y_46_re) * sin((t_1 + (y_46_im * log(x_46_re))))) / exp(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, Block[{t$95$1 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$46$re, 13500000000.0], N[(N[Exp[N[(N[(y$46$re * N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * N[Sin[N[(t$95$1 + N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[t$95$0], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 12: 66.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \tan^{-1}_* \frac{x.im}{x.re} \cdot y.im\\ \mathbf{if}\;x.re \leq 18000000000:\\ \;\;\;\;e^{y.re \cdot \log \left(\mathsf{hypot}\left(x.re, x.im\right)\right) - t_0} \cdot \sin \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot \sin \left(y.im \cdot \log x.re\right)}{e^{t_0}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* (atan2 x.im x.re) y.im)))
   (if (<= x.re 18000000000.0)
     (*
      (exp (- (* y.re (log (hypot x.re x.im))) t_0))
      (sin (* y.re (atan2 x.im x.re))))
     (/ (* (pow x.re y.re) (sin (* y.im (log x.re)))) (exp t_0)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	double tmp;
	if (x_46_re <= 18000000000.0) {
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin((y_46_re * atan2(x_46_im, x_46_re)));
	} else {
		tmp = (pow(x_46_re, y_46_re) * sin((y_46_im * log(x_46_re)))) / exp(t_0);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.atan2(x_46_im, x_46_re) * y_46_im;
	double tmp;
	if (x_46_re <= 18000000000.0) {
		tmp = Math.exp(((y_46_re * Math.log(Math.hypot(x_46_re, x_46_im))) - t_0)) * Math.sin((y_46_re * Math.atan2(x_46_im, x_46_re)));
	} else {
		tmp = (Math.pow(x_46_re, y_46_re) * Math.sin((y_46_im * Math.log(x_46_re)))) / Math.exp(t_0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.atan2(x_46_im, x_46_re) * y_46_im
	tmp = 0
	if x_46_re <= 18000000000.0:
		tmp = math.exp(((y_46_re * math.log(math.hypot(x_46_re, x_46_im))) - t_0)) * math.sin((y_46_re * math.atan2(x_46_im, x_46_re)))
	else:
		tmp = (math.pow(x_46_re, y_46_re) * math.sin((y_46_im * math.log(x_46_re)))) / math.exp(t_0)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(atan(x_46_im, x_46_re) * y_46_im)
	tmp = 0.0
	if (x_46_re <= 18000000000.0)
		tmp = Float64(exp(Float64(Float64(y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin(Float64(y_46_re * atan(x_46_im, x_46_re))));
	else
		tmp = Float64(Float64((x_46_re ^ y_46_re) * sin(Float64(y_46_im * log(x_46_re)))) / exp(t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = atan2(x_46_im, x_46_re) * y_46_im;
	tmp = 0.0;
	if (x_46_re <= 18000000000.0)
		tmp = exp(((y_46_re * log(hypot(x_46_re, x_46_im))) - t_0)) * sin((y_46_re * atan2(x_46_im, x_46_re)));
	else
		tmp = ((x_46_re ^ y_46_re) * sin((y_46_im * log(x_46_re)))) / exp(t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]}, If[LessEqual[x$46$re, 18000000000.0], N[(N[Exp[N[(N[(y$46$re * N[Log[N[Sqrt[x$46$re ^ 2 + x$46$im ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]], $MachinePrecision] * N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[t$95$0], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 13: 47.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ \mathbf{if}\;x.re \leq 2.05 \cdot 10^{-290}:\\ \;\;\;\;t_0 \cdot {\left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)}^{y.re}\\ \mathbf{elif}\;x.re \leq 3.5 \cdot 10^{-76} \lor \neg \left(x.re \leq 0.0058\right):\\ \;\;\;\;\frac{{x.re}^{y.re} \cdot \sin \left(y.im \cdot \log x.re\right)}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \mathbf{else}:\\ \;\;\;\;\sin t_0 \cdot {x.im}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re))))
   (if (<= x.re 2.05e-290)
     (* t_0 (pow (sqrt (+ (pow x.re 2.0) (pow x.im 2.0))) y.re))
     (if (or (<= x.re 3.5e-76) (not (<= x.re 0.0058)))
       (/
        (* (pow x.re y.re) (sin (* y.im (log x.re))))
        (exp (* (atan2 x.im x.re) y.im)))
       (* (sin t_0) (pow x.im y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double tmp;
	if (x_46_re <= 2.05e-290) {
		tmp = t_0 * pow(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0))), y_46_re);
	} else if ((x_46_re <= 3.5e-76) || !(x_46_re <= 0.0058)) {
		tmp = (pow(x_46_re, y_46_re) * sin((y_46_im * log(x_46_re)))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	} else {
		tmp = sin(t_0) * pow(x_46_im, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    if (x_46re <= 2.05d-290) then
        tmp = t_0 * (sqrt(((x_46re ** 2.0d0) + (x_46im ** 2.0d0))) ** y_46re)
    else if ((x_46re <= 3.5d-76) .or. (.not. (x_46re <= 0.0058d0))) then
        tmp = ((x_46re ** y_46re) * sin((y_46im * log(x_46re)))) / exp((atan2(x_46im, x_46re) * y_46im))
    else
        tmp = sin(t_0) * (x_46im ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double tmp;
	if (x_46_re <= 2.05e-290) {
		tmp = t_0 * Math.pow(Math.sqrt((Math.pow(x_46_re, 2.0) + Math.pow(x_46_im, 2.0))), y_46_re);
	} else if ((x_46_re <= 3.5e-76) || !(x_46_re <= 0.0058)) {
		tmp = (Math.pow(x_46_re, y_46_re) * Math.sin((y_46_im * Math.log(x_46_re)))) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	} else {
		tmp = Math.sin(t_0) * Math.pow(x_46_im, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	tmp = 0
	if x_46_re <= 2.05e-290:
		tmp = t_0 * math.pow(math.sqrt((math.pow(x_46_re, 2.0) + math.pow(x_46_im, 2.0))), y_46_re)
	elif (x_46_re <= 3.5e-76) or not (x_46_re <= 0.0058):
		tmp = (math.pow(x_46_re, y_46_re) * math.sin((y_46_im * math.log(x_46_re)))) / math.exp((math.atan2(x_46_im, x_46_re) * y_46_im))
	else:
		tmp = math.sin(t_0) * math.pow(x_46_im, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	tmp = 0.0
	if (x_46_re <= 2.05e-290)
		tmp = Float64(t_0 * (sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re));
	elseif ((x_46_re <= 3.5e-76) || !(x_46_re <= 0.0058))
		tmp = Float64(Float64((x_46_re ^ y_46_re) * sin(Float64(y_46_im * log(x_46_re)))) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	else
		tmp = Float64(sin(t_0) * (x_46_im ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	tmp = 0.0;
	if (x_46_re <= 2.05e-290)
		tmp = t_0 * (sqrt(((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re);
	elseif ((x_46_re <= 3.5e-76) || ~((x_46_re <= 0.0058)))
		tmp = ((x_46_re ^ y_46_re) * sin((y_46_im * log(x_46_re)))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	else
		tmp = sin(t_0) * (x_46_im ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x$46$re, 2.05e-290], N[(t$95$0 * N[Power[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x$46$re, 3.5e-76], N[Not[LessEqual[x$46$re, 0.0058]], $MachinePrecision]], N[(N[(N[Power[x$46$re, y$46$re], $MachinePrecision] * N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sin[t$95$0], $MachinePrecision] * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 14: 43.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \sin t_0\\ \mathbf{if}\;y.re \leq -5.8 \cdot 10^{-81}:\\ \;\;\;\;t_0 \cdot {\left(\sqrt{{x.re}^{2} + {x.im}^{2}}\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq 1.18 \cdot 10^{-68}:\\ \;\;\;\;\frac{\sin \left(y.im \cdot \log x.re\right)}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \mathbf{elif}\;y.re \leq 7.8 \cdot 10^{+103}:\\ \;\;\;\;t_1 \cdot {x.im}^{y.re}\\ \mathbf{elif}\;y.re \leq 1.15 \cdot 10^{+193}:\\ \;\;\;\;t_1 \cdot {\left(x.re + 0.5 \cdot \frac{{x.im}^{2}}{x.re}\right)}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re))) (t_1 (sin t_0)))
   (if (<= y.re -5.8e-81)
     (* t_0 (pow (sqrt (+ (pow x.re 2.0) (pow x.im 2.0))) y.re))
     (if (<= y.re 1.18e-68)
       (/ (sin (* y.im (log x.re))) (exp (* (atan2 x.im x.re) y.im)))
       (if (<= y.re 7.8e+103)
         (* t_1 (pow x.im y.re))
         (if (<= y.re 1.15e+193)
           (* t_1 (pow (+ x.re (* 0.5 (/ (pow x.im 2.0) x.re))) y.re))
           (* t_0 (pow x.re y.re))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = sin(t_0);
	double tmp;
	if (y_46_re <= -5.8e-81) {
		tmp = t_0 * pow(sqrt((pow(x_46_re, 2.0) + pow(x_46_im, 2.0))), y_46_re);
	} else if (y_46_re <= 1.18e-68) {
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 7.8e+103) {
		tmp = t_1 * pow(x_46_im, y_46_re);
	} else if (y_46_re <= 1.15e+193) {
		tmp = t_1 * pow((x_46_re + (0.5 * (pow(x_46_im, 2.0) / x_46_re))), y_46_re);
	} else {
		tmp = t_0 * pow(x_46_re, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = sin(t_0)
    if (y_46re <= (-5.8d-81)) then
        tmp = t_0 * (sqrt(((x_46re ** 2.0d0) + (x_46im ** 2.0d0))) ** y_46re)
    else if (y_46re <= 1.18d-68) then
        tmp = sin((y_46im * log(x_46re))) / exp((atan2(x_46im, x_46re) * y_46im))
    else if (y_46re <= 7.8d+103) then
        tmp = t_1 * (x_46im ** y_46re)
    else if (y_46re <= 1.15d+193) then
        tmp = t_1 * ((x_46re + (0.5d0 * ((x_46im ** 2.0d0) / x_46re))) ** y_46re)
    else
        tmp = t_0 * (x_46re ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.sin(t_0);
	double tmp;
	if (y_46_re <= -5.8e-81) {
		tmp = t_0 * Math.pow(Math.sqrt((Math.pow(x_46_re, 2.0) + Math.pow(x_46_im, 2.0))), y_46_re);
	} else if (y_46_re <= 1.18e-68) {
		tmp = Math.sin((y_46_im * Math.log(x_46_re))) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 7.8e+103) {
		tmp = t_1 * Math.pow(x_46_im, y_46_re);
	} else if (y_46_re <= 1.15e+193) {
		tmp = t_1 * Math.pow((x_46_re + (0.5 * (Math.pow(x_46_im, 2.0) / x_46_re))), y_46_re);
	} else {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.sin(t_0)
	tmp = 0
	if y_46_re <= -5.8e-81:
		tmp = t_0 * math.pow(math.sqrt((math.pow(x_46_re, 2.0) + math.pow(x_46_im, 2.0))), y_46_re)
	elif y_46_re <= 1.18e-68:
		tmp = math.sin((y_46_im * math.log(x_46_re))) / math.exp((math.atan2(x_46_im, x_46_re) * y_46_im))
	elif y_46_re <= 7.8e+103:
		tmp = t_1 * math.pow(x_46_im, y_46_re)
	elif y_46_re <= 1.15e+193:
		tmp = t_1 * math.pow((x_46_re + (0.5 * (math.pow(x_46_im, 2.0) / x_46_re))), y_46_re)
	else:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = sin(t_0)
	tmp = 0.0
	if (y_46_re <= -5.8e-81)
		tmp = Float64(t_0 * (sqrt(Float64((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re));
	elseif (y_46_re <= 1.18e-68)
		tmp = Float64(sin(Float64(y_46_im * log(x_46_re))) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	elseif (y_46_re <= 7.8e+103)
		tmp = Float64(t_1 * (x_46_im ^ y_46_re));
	elseif (y_46_re <= 1.15e+193)
		tmp = Float64(t_1 * (Float64(x_46_re + Float64(0.5 * Float64((x_46_im ^ 2.0) / x_46_re))) ^ y_46_re));
	else
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = sin(t_0);
	tmp = 0.0;
	if (y_46_re <= -5.8e-81)
		tmp = t_0 * (sqrt(((x_46_re ^ 2.0) + (x_46_im ^ 2.0))) ^ y_46_re);
	elseif (y_46_re <= 1.18e-68)
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	elseif (y_46_re <= 7.8e+103)
		tmp = t_1 * (x_46_im ^ y_46_re);
	elseif (y_46_re <= 1.15e+193)
		tmp = t_1 * ((x_46_re + (0.5 * ((x_46_im ^ 2.0) / x_46_re))) ^ y_46_re);
	else
		tmp = t_0 * (x_46_re ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[LessEqual[y$46$re, -5.8e-81], N[(t$95$0 * N[Power[N[Sqrt[N[(N[Power[x$46$re, 2.0], $MachinePrecision] + N[Power[x$46$im, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.18e-68], N[(N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 7.8e+103], N[(t$95$1 * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.15e+193], N[(t$95$1 * N[Power[N[(x$46$re + N[(0.5 * N[(N[Power[x$46$im, 2.0], $MachinePrecision] / x$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

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

Alternative 15: 42.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \sin t_0\\ t_2 := t_1 \cdot {\left(x.im + \frac{{x.re}^{2} \cdot 0.5}{x.im}\right)}^{y.re}\\ \mathbf{if}\;y.re \leq -5.1 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y.re \leq 3 \cdot 10^{-69}:\\ \;\;\;\;\frac{\sin \left(y.im \cdot \log x.re\right)}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \mathbf{elif}\;y.re \leq 9 \cdot 10^{+103}:\\ \;\;\;\;t_1 \cdot {x.im}^{y.re}\\ \mathbf{elif}\;y.re \leq 4 \cdot 10^{+194}:\\ \;\;\;\;t_1 \cdot {\left(x.re + 0.5 \cdot \frac{{x.im}^{2}}{x.re}\right)}^{y.re}\\ \mathbf{elif}\;y.re \leq 1.25 \cdot 10^{+217}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1 (sin t_0))
        (t_2 (* t_1 (pow (+ x.im (/ (* (pow x.re 2.0) 0.5) x.im)) y.re))))
   (if (<= y.re -5.1e-39)
     t_2
     (if (<= y.re 3e-69)
       (/ (sin (* y.im (log x.re))) (exp (* (atan2 x.im x.re) y.im)))
       (if (<= y.re 9e+103)
         (* t_1 (pow x.im y.re))
         (if (<= y.re 4e+194)
           (* t_1 (pow (+ x.re (* 0.5 (/ (pow x.im 2.0) x.re))) y.re))
           (if (<= y.re 1.25e+217) t_2 (* t_0 (pow x.re y.re)))))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = sin(t_0);
	double t_2 = t_1 * pow((x_46_im + ((pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re);
	double tmp;
	if (y_46_re <= -5.1e-39) {
		tmp = t_2;
	} else if (y_46_re <= 3e-69) {
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 9e+103) {
		tmp = t_1 * pow(x_46_im, y_46_re);
	} else if (y_46_re <= 4e+194) {
		tmp = t_1 * pow((x_46_re + (0.5 * (pow(x_46_im, 2.0) / x_46_re))), y_46_re);
	} else if (y_46_re <= 1.25e+217) {
		tmp = t_2;
	} else {
		tmp = t_0 * pow(x_46_re, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = sin(t_0)
    t_2 = t_1 * ((x_46im + (((x_46re ** 2.0d0) * 0.5d0) / x_46im)) ** y_46re)
    if (y_46re <= (-5.1d-39)) then
        tmp = t_2
    else if (y_46re <= 3d-69) then
        tmp = sin((y_46im * log(x_46re))) / exp((atan2(x_46im, x_46re) * y_46im))
    else if (y_46re <= 9d+103) then
        tmp = t_1 * (x_46im ** y_46re)
    else if (y_46re <= 4d+194) then
        tmp = t_1 * ((x_46re + (0.5d0 * ((x_46im ** 2.0d0) / x_46re))) ** y_46re)
    else if (y_46re <= 1.25d+217) then
        tmp = t_2
    else
        tmp = t_0 * (x_46re ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.sin(t_0);
	double t_2 = t_1 * Math.pow((x_46_im + ((Math.pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re);
	double tmp;
	if (y_46_re <= -5.1e-39) {
		tmp = t_2;
	} else if (y_46_re <= 3e-69) {
		tmp = Math.sin((y_46_im * Math.log(x_46_re))) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 9e+103) {
		tmp = t_1 * Math.pow(x_46_im, y_46_re);
	} else if (y_46_re <= 4e+194) {
		tmp = t_1 * Math.pow((x_46_re + (0.5 * (Math.pow(x_46_im, 2.0) / x_46_re))), y_46_re);
	} else if (y_46_re <= 1.25e+217) {
		tmp = t_2;
	} else {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.sin(t_0)
	t_2 = t_1 * math.pow((x_46_im + ((math.pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re)
	tmp = 0
	if y_46_re <= -5.1e-39:
		tmp = t_2
	elif y_46_re <= 3e-69:
		tmp = math.sin((y_46_im * math.log(x_46_re))) / math.exp((math.atan2(x_46_im, x_46_re) * y_46_im))
	elif y_46_re <= 9e+103:
		tmp = t_1 * math.pow(x_46_im, y_46_re)
	elif y_46_re <= 4e+194:
		tmp = t_1 * math.pow((x_46_re + (0.5 * (math.pow(x_46_im, 2.0) / x_46_re))), y_46_re)
	elif y_46_re <= 1.25e+217:
		tmp = t_2
	else:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = sin(t_0)
	t_2 = Float64(t_1 * (Float64(x_46_im + Float64(Float64((x_46_re ^ 2.0) * 0.5) / x_46_im)) ^ y_46_re))
	tmp = 0.0
	if (y_46_re <= -5.1e-39)
		tmp = t_2;
	elseif (y_46_re <= 3e-69)
		tmp = Float64(sin(Float64(y_46_im * log(x_46_re))) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	elseif (y_46_re <= 9e+103)
		tmp = Float64(t_1 * (x_46_im ^ y_46_re));
	elseif (y_46_re <= 4e+194)
		tmp = Float64(t_1 * (Float64(x_46_re + Float64(0.5 * Float64((x_46_im ^ 2.0) / x_46_re))) ^ y_46_re));
	elseif (y_46_re <= 1.25e+217)
		tmp = t_2;
	else
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = sin(t_0);
	t_2 = t_1 * ((x_46_im + (((x_46_re ^ 2.0) * 0.5) / x_46_im)) ^ y_46_re);
	tmp = 0.0;
	if (y_46_re <= -5.1e-39)
		tmp = t_2;
	elseif (y_46_re <= 3e-69)
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	elseif (y_46_re <= 9e+103)
		tmp = t_1 * (x_46_im ^ y_46_re);
	elseif (y_46_re <= 4e+194)
		tmp = t_1 * ((x_46_re + (0.5 * ((x_46_im ^ 2.0) / x_46_re))) ^ y_46_re);
	elseif (y_46_re <= 1.25e+217)
		tmp = t_2;
	else
		tmp = t_0 * (x_46_re ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Power[N[(x$46$im + N[(N[(N[Power[x$46$re, 2.0], $MachinePrecision] * 0.5), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -5.1e-39], t$95$2, If[LessEqual[y$46$re, 3e-69], N[(N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 9e+103], N[(t$95$1 * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 4e+194], N[(t$95$1 * N[Power[N[(x$46$re + N[(0.5 * N[(N[Power[x$46$im, 2.0], $MachinePrecision] / x$46$re), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.25e+217], t$95$2, N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

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

Alternative 16: 42.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \sin t_0 \cdot {\left(x.im + \frac{{x.re}^{2} \cdot 0.5}{x.im}\right)}^{y.re}\\ \mathbf{if}\;y.re \leq -4 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.re \leq 3.5 \cdot 10^{-69}:\\ \;\;\;\;\frac{\sin \left(y.im \cdot \log x.re\right)}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \mathbf{elif}\;y.re \leq 2.9 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re)))
        (t_1
         (* (sin t_0) (pow (+ x.im (/ (* (pow x.re 2.0) 0.5) x.im)) y.re))))
   (if (<= y.re -4e-30)
     t_1
     (if (<= y.re 3.5e-69)
       (/ (sin (* y.im (log x.re))) (exp (* (atan2 x.im x.re) y.im)))
       (if (<= y.re 2.9e+192) t_1 (* t_0 (pow x.re y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = sin(t_0) * pow((x_46_im + ((pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re);
	double tmp;
	if (y_46_re <= -4e-30) {
		tmp = t_1;
	} else if (y_46_re <= 3.5e-69) {
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 2.9e+192) {
		tmp = t_1;
	} else {
		tmp = t_0 * pow(x_46_re, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = sin(t_0) * ((x_46im + (((x_46re ** 2.0d0) * 0.5d0) / x_46im)) ** y_46re)
    if (y_46re <= (-4d-30)) then
        tmp = t_1
    else if (y_46re <= 3.5d-69) then
        tmp = sin((y_46im * log(x_46re))) / exp((atan2(x_46im, x_46re) * y_46im))
    else if (y_46re <= 2.9d+192) then
        tmp = t_1
    else
        tmp = t_0 * (x_46re ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.sin(t_0) * Math.pow((x_46_im + ((Math.pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re);
	double tmp;
	if (y_46_re <= -4e-30) {
		tmp = t_1;
	} else if (y_46_re <= 3.5e-69) {
		tmp = Math.sin((y_46_im * Math.log(x_46_re))) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 2.9e+192) {
		tmp = t_1;
	} else {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.sin(t_0) * math.pow((x_46_im + ((math.pow(x_46_re, 2.0) * 0.5) / x_46_im)), y_46_re)
	tmp = 0
	if y_46_re <= -4e-30:
		tmp = t_1
	elif y_46_re <= 3.5e-69:
		tmp = math.sin((y_46_im * math.log(x_46_re))) / math.exp((math.atan2(x_46_im, x_46_re) * y_46_im))
	elif y_46_re <= 2.9e+192:
		tmp = t_1
	else:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = Float64(sin(t_0) * (Float64(x_46_im + Float64(Float64((x_46_re ^ 2.0) * 0.5) / x_46_im)) ^ y_46_re))
	tmp = 0.0
	if (y_46_re <= -4e-30)
		tmp = t_1;
	elseif (y_46_re <= 3.5e-69)
		tmp = Float64(sin(Float64(y_46_im * log(x_46_re))) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	elseif (y_46_re <= 2.9e+192)
		tmp = t_1;
	else
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = sin(t_0) * ((x_46_im + (((x_46_re ^ 2.0) * 0.5) / x_46_im)) ^ y_46_re);
	tmp = 0.0;
	if (y_46_re <= -4e-30)
		tmp = t_1;
	elseif (y_46_re <= 3.5e-69)
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	elseif (y_46_re <= 2.9e+192)
		tmp = t_1;
	else
		tmp = t_0 * (x_46_re ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[t$95$0], $MachinePrecision] * N[Power[N[(x$46$im + N[(N[(N[Power[x$46$re, 2.0], $MachinePrecision] * 0.5), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision], y$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -4e-30], t$95$1, If[LessEqual[y$46$re, 3.5e-69], N[(N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 2.9e+192], t$95$1, N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 17: 37.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ t_1 := \sin t_0 \cdot {x.im}^{y.re}\\ \mathbf{if}\;y.re \leq -7.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y.re \leq 5.6 \cdot 10^{-68}:\\ \;\;\;\;\frac{\sin \left(y.im \cdot \log x.re\right)}{e^{\tan^{-1}_* \frac{x.im}{x.re} \cdot y.im}}\\ \mathbf{elif}\;y.re \leq 1.22 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re))) (t_1 (* (sin t_0) (pow x.im y.re))))
   (if (<= y.re -7.8e-32)
     t_1
     (if (<= y.re 5.6e-68)
       (/ (sin (* y.im (log x.re))) (exp (* (atan2 x.im x.re) y.im)))
       (if (<= y.re 1.22e+161) t_1 (* t_0 (pow x.re y.re)))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double t_1 = sin(t_0) * pow(x_46_im, y_46_re);
	double tmp;
	if (y_46_re <= -7.8e-32) {
		tmp = t_1;
	} else if (y_46_re <= 5.6e-68) {
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 1.22e+161) {
		tmp = t_1;
	} else {
		tmp = t_0 * pow(x_46_re, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    t_1 = sin(t_0) * (x_46im ** y_46re)
    if (y_46re <= (-7.8d-32)) then
        tmp = t_1
    else if (y_46re <= 5.6d-68) then
        tmp = sin((y_46im * log(x_46re))) / exp((atan2(x_46im, x_46re) * y_46im))
    else if (y_46re <= 1.22d+161) then
        tmp = t_1
    else
        tmp = t_0 * (x_46re ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double t_1 = Math.sin(t_0) * Math.pow(x_46_im, y_46_re);
	double tmp;
	if (y_46_re <= -7.8e-32) {
		tmp = t_1;
	} else if (y_46_re <= 5.6e-68) {
		tmp = Math.sin((y_46_im * Math.log(x_46_re))) / Math.exp((Math.atan2(x_46_im, x_46_re) * y_46_im));
	} else if (y_46_re <= 1.22e+161) {
		tmp = t_1;
	} else {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	t_1 = math.sin(t_0) * math.pow(x_46_im, y_46_re)
	tmp = 0
	if y_46_re <= -7.8e-32:
		tmp = t_1
	elif y_46_re <= 5.6e-68:
		tmp = math.sin((y_46_im * math.log(x_46_re))) / math.exp((math.atan2(x_46_im, x_46_re) * y_46_im))
	elif y_46_re <= 1.22e+161:
		tmp = t_1
	else:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	t_1 = Float64(sin(t_0) * (x_46_im ^ y_46_re))
	tmp = 0.0
	if (y_46_re <= -7.8e-32)
		tmp = t_1;
	elseif (y_46_re <= 5.6e-68)
		tmp = Float64(sin(Float64(y_46_im * log(x_46_re))) / exp(Float64(atan(x_46_im, x_46_re) * y_46_im)));
	elseif (y_46_re <= 1.22e+161)
		tmp = t_1;
	else
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	t_1 = sin(t_0) * (x_46_im ^ y_46_re);
	tmp = 0.0;
	if (y_46_re <= -7.8e-32)
		tmp = t_1;
	elseif (y_46_re <= 5.6e-68)
		tmp = sin((y_46_im * log(x_46_re))) / exp((atan2(x_46_im, x_46_re) * y_46_im));
	elseif (y_46_re <= 1.22e+161)
		tmp = t_1;
	else
		tmp = t_0 * (x_46_re ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[t$95$0], $MachinePrecision] * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$re, -7.8e-32], t$95$1, If[LessEqual[y$46$re, 5.6e-68], N[(N[Sin[N[(y$46$im * N[Log[x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[Exp[N[(N[ArcTan[x$46$im / x$46$re], $MachinePrecision] * y$46$im), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y$46$re, 1.22e+161], t$95$1, N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 18: 39.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sin \left(y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\right)\\ \mathbf{if}\;x.im \leq -7 \cdot 10^{-83}:\\ \;\;\;\;t_0 \cdot {\left(-x.im\right)}^{y.re}\\ \mathbf{elif}\;x.im \leq 1.6 \cdot 10^{-269}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.im}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (sin (* y.re (atan2 x.im x.re)))))
   (if (<= x.im -7e-83)
     (* t_0 (pow (- x.im) y.re))
     (if (<= x.im 1.6e-269) (* t_0 (pow x.re y.re)) (* t_0 (pow x.im y.re))))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = sin((y_46_re * atan2(x_46_im, x_46_re)));
	double tmp;
	if (x_46_im <= -7e-83) {
		tmp = t_0 * pow(-x_46_im, y_46_re);
	} else if (x_46_im <= 1.6e-269) {
		tmp = t_0 * pow(x_46_re, y_46_re);
	} else {
		tmp = t_0 * pow(x_46_im, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sin((y_46re * atan2(x_46im, x_46re)))
    if (x_46im <= (-7d-83)) then
        tmp = t_0 * (-x_46im ** y_46re)
    else if (x_46im <= 1.6d-269) then
        tmp = t_0 * (x_46re ** y_46re)
    else
        tmp = t_0 * (x_46im ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = Math.sin((y_46_re * Math.atan2(x_46_im, x_46_re)));
	double tmp;
	if (x_46_im <= -7e-83) {
		tmp = t_0 * Math.pow(-x_46_im, y_46_re);
	} else if (x_46_im <= 1.6e-269) {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	} else {
		tmp = t_0 * Math.pow(x_46_im, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = math.sin((y_46_re * math.atan2(x_46_im, x_46_re)))
	tmp = 0
	if x_46_im <= -7e-83:
		tmp = t_0 * math.pow(-x_46_im, y_46_re)
	elif x_46_im <= 1.6e-269:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	else:
		tmp = t_0 * math.pow(x_46_im, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = sin(Float64(y_46_re * atan(x_46_im, x_46_re)))
	tmp = 0.0
	if (x_46_im <= -7e-83)
		tmp = Float64(t_0 * (Float64(-x_46_im) ^ y_46_re));
	elseif (x_46_im <= 1.6e-269)
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	else
		tmp = Float64(t_0 * (x_46_im ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = sin((y_46_re * atan2(x_46_im, x_46_re)));
	tmp = 0.0;
	if (x_46_im <= -7e-83)
		tmp = t_0 * (-x_46_im ^ y_46_re);
	elseif (x_46_im <= 1.6e-269)
		tmp = t_0 * (x_46_re ^ y_46_re);
	else
		tmp = t_0 * (x_46_im ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[Sin[N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x$46$im, -7e-83], N[(t$95$0 * N[Power[(-x$46$im), y$46$re], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$im, 1.6e-269], N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 19: 31.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ \mathbf{if}\;y.im \leq 4.9 \cdot 10^{-23}:\\ \;\;\;\;\sin t_0 \cdot {x.im}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re))))
   (if (<= y.im 4.9e-23)
     (* (sin t_0) (pow x.im y.re))
     (* t_0 (pow x.re y.re)))))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double tmp;
	if (y_46_im <= 4.9e-23) {
		tmp = sin(t_0) * pow(x_46_im, y_46_re);
	} else {
		tmp = t_0 * pow(x_46_re, y_46_re);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    if (y_46im <= 4.9d-23) then
        tmp = sin(t_0) * (x_46im ** y_46re)
    else
        tmp = t_0 * (x_46re ** y_46re)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double tmp;
	if (y_46_im <= 4.9e-23) {
		tmp = Math.sin(t_0) * Math.pow(x_46_im, y_46_re);
	} else {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	tmp = 0
	if y_46_im <= 4.9e-23:
		tmp = math.sin(t_0) * math.pow(x_46_im, y_46_re)
	else:
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	tmp = 0.0
	if (y_46_im <= 4.9e-23)
		tmp = Float64(sin(t_0) * (x_46_im ^ y_46_re));
	else
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	tmp = 0.0;
	if (y_46_im <= 4.9e-23)
		tmp = sin(t_0) * (x_46_im ^ y_46_re);
	else
		tmp = t_0 * (x_46_re ^ y_46_re);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y$46$im, 4.9e-23], N[(N[Sin[t$95$0], $MachinePrecision] * N[Power[x$46$im, y$46$re], $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 20: 36.4% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y.re \cdot \tan^{-1}_* \frac{x.im}{x.re}\\ \mathbf{if}\;y.re \leq -195000000 \lor \neg \left(y.re \leq 1620000\right):\\ \;\;\;\;t_0 \cdot {x.re}^{y.re}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im)
 :precision binary64
 (let* ((t_0 (* y.re (atan2 x.im x.re))))
   (if (or (<= y.re -195000000.0) (not (<= y.re 1620000.0)))
     (* t_0 (pow x.re y.re))
     t_0)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * atan2(x_46_im, x_46_re);
	double tmp;
	if ((y_46_re <= -195000000.0) || !(y_46_re <= 1620000.0)) {
		tmp = t_0 * pow(x_46_re, y_46_re);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y_46re * atan2(x_46im, x_46re)
    if ((y_46re <= (-195000000.0d0)) .or. (.not. (y_46re <= 1620000.0d0))) then
        tmp = t_0 * (x_46re ** y_46re)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	double t_0 = y_46_re * Math.atan2(x_46_im, x_46_re);
	double tmp;
	if ((y_46_re <= -195000000.0) || !(y_46_re <= 1620000.0)) {
		tmp = t_0 * Math.pow(x_46_re, y_46_re);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	t_0 = y_46_re * math.atan2(x_46_im, x_46_re)
	tmp = 0
	if (y_46_re <= -195000000.0) or not (y_46_re <= 1620000.0):
		tmp = t_0 * math.pow(x_46_re, y_46_re)
	else:
		tmp = t_0
	return tmp

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = Float64(y_46_re * atan(x_46_im, x_46_re))
	tmp = 0.0
	if ((y_46_re <= -195000000.0) || !(y_46_re <= 1620000.0))
		tmp = Float64(t_0 * (x_46_re ^ y_46_re));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im, y_46_re, y_46_im)
	t_0 = y_46_re * atan2(x_46_im, x_46_re);
	tmp = 0.0;
	if ((y_46_re <= -195000000.0) || ~((y_46_re <= 1620000.0)))
		tmp = t_0 * (x_46_re ^ y_46_re);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := Block[{t$95$0 = N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[y$46$re, -195000000.0], N[Not[LessEqual[y$46$re, 1620000.0]], $MachinePrecision]], N[(t$95$0 * N[Power[x$46$re, y$46$re], $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

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

Alternative 21: 13.4% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ y.re \cdot \tan^{-1}_* \frac{x.im}{x.re} \end{array} \]

FPCore

(FPCore (x.re x.im y.re y.im) :precision binary64 (* y.re (atan2 x.im x.re)))

C

double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return y_46_re * atan2(x_46_im, x_46_re);
}

Fortran

real(8) function code(x_46re, x_46im, y_46re, y_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8), intent (in) :: y_46re
    real(8), intent (in) :: y_46im
    code = y_46re * atan2(x_46im, x_46re)
end function

Java

public static double code(double x_46_re, double x_46_im, double y_46_re, double y_46_im) {
	return y_46_re * Math.atan2(x_46_im, x_46_re);
}

Python

def code(x_46_re, x_46_im, y_46_re, y_46_im):
	return y_46_re * math.atan2(x_46_im, x_46_re)

Julia

function code(x_46_re, x_46_im, y_46_re, y_46_im)
	return Float64(y_46_re * atan(x_46_im, x_46_re))
end

MATLAB

function tmp = code(x_46_re, x_46_im, y_46_re, y_46_im)
	tmp = y_46_re * atan2(x_46_im, x_46_re);
end

Wolfram

code[x$46$re_, x$46$im_, y$46$re_, y$46$im_] := N[(y$46$re * N[ArcTan[x$46$im / x$46$re], $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024006 
(FPCore (x.re x.im y.re y.im)
  :name "powComplex, imaginary part"
  :precision binary64
  (* (exp (- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))) (sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))))