ab-angle->ABCF B

Percentage Accurate: 53.6% → 66.7%

Time: 58.3s

Alternatives: 17

Speedup: 5.5×

• 32.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin t_0\right) \cdot \cos t_0 \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))))
   (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin t_0)) (cos t_0))))

C

double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(t_0)) * cos(t_0);
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = Math.PI * (angle / 180.0);
	return ((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin(t_0)) * Math.cos(t_0);
}

Python

def code(a, b, angle):
	t_0 = math.pi * (angle / 180.0)
	return ((2.0 * (math.pow(b, 2.0) - math.pow(a, 2.0))) * math.sin(t_0)) * math.cos(t_0)

Julia

function code(a, b, angle)
	t_0 = Float64(pi * Float64(angle / 180.0))
	return Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(t_0)) * cos(t_0))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin(t_0)) * cos(t_0);
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]]

Initial Program: 53.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin t_0\right) \cdot \cos t_0 \end{array} \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* PI (/ angle 180.0))))
   (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin t_0)) (cos t_0))))

C

double code(double a, double b, double angle) {
	double t_0 = ((double) M_PI) * (angle / 180.0);
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin(t_0)) * cos(t_0);
}

Java

public static double code(double a, double b, double angle) {
	double t_0 = Math.PI * (angle / 180.0);
	return ((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin(t_0)) * Math.cos(t_0);
}

Python

def code(a, b, angle):
	t_0 = math.pi * (angle / 180.0)
	return ((2.0 * (math.pow(b, 2.0) - math.pow(a, 2.0))) * math.sin(t_0)) * math.cos(t_0)

Julia

function code(a, b, angle)
	t_0 = Float64(pi * Float64(angle / 180.0))
	return Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(t_0)) * cos(t_0))
end

MATLAB

function tmp = code(a, b, angle)
	t_0 = pi * (angle / 180.0);
	tmp = ((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin(t_0)) * cos(t_0);
end

Wolfram

code[a_, b_, angle_] := Block[{t$95$0 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]]

Alternative 1: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left({\left(\sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)}\right)}^{3} \cdot \left(t_1 \cdot \cos \left(angle_m \cdot \frac{\sqrt[3]{\pi \cdot {\pi}^{2}}}{-180}\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+253}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \cos \left(angle_m \cdot \frac{\sqrt{\pi} \cdot \sqrt{\pi}}{-180}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))) (t_1 (* (- b_m a_m) (+ b_m a_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 5e-16)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 2e+138)
        (*
         2.0
         (*
          (pow (cbrt (sin (* PI (* angle_m 0.005555555555555556)))) 3.0)
          (* t_1 (cos (* angle_m (/ (cbrt (* PI (pow PI 2.0))) -180.0))))))
        (if (<= (/ angle_m 180.0) 5e+253)
          (*
           2.0
           (*
            (sin (* (/ angle_m 180.0) PI))
            (* t_1 (cos (* angle_m (/ (* (sqrt PI) (sqrt PI)) -180.0))))))
          (*
           0.011111111111111112
           (*
            angle_m
            (/
             (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
             (+ b_m a_m))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 5e-16) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (pow(cbrt(sin((((double) M_PI) * (angle_m * 0.005555555555555556)))), 3.0) * (t_1 * cos((angle_m * (cbrt((((double) M_PI) * pow(((double) M_PI), 2.0))) / -180.0)))));
	} else if ((angle_m / 180.0) <= 5e+253) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * cos((angle_m * ((sqrt(((double) M_PI)) * sqrt(((double) M_PI))) / -180.0)))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 5e-16) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (Math.pow(Math.cbrt(Math.sin((Math.PI * (angle_m * 0.005555555555555556)))), 3.0) * (t_1 * Math.cos((angle_m * (Math.cbrt((Math.PI * Math.pow(Math.PI, 2.0))) / -180.0)))));
	} else if ((angle_m / 180.0) <= 5e+253) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * Math.cos((angle_m * ((Math.sqrt(Math.PI) * Math.sqrt(Math.PI)) / -180.0)))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 5e-16)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 2e+138)
		tmp = Float64(2.0 * Float64((cbrt(sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))) ^ 3.0) * Float64(t_1 * cos(Float64(angle_m * Float64(cbrt(Float64(pi * (pi ^ 2.0))) / -180.0))))));
	elseif (Float64(angle_m / 180.0) <= 5e+253)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * cos(Float64(angle_m * Float64(Float64(sqrt(pi) * sqrt(pi)) / -180.0))))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e-16], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+138], N[(2.0 * N[(N[Power[N[Power[N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(angle$95$m * N[(N[Power[N[(Pi * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+253], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(angle$95$m * N[(N[(N[Sqrt[Pi], $MachinePrecision] * N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision] / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

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

Alternative 2: 66.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ t_2 := \sin \left(\frac{angle_m}{180} \cdot \pi\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot {\left(\sqrt{angle_m \cdot \pi}\right)}^{2}\right) \cdot \left(t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \left(t_1 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \left(t_1 \cdot \sqrt[3]{{\cos \left(\left(angle_m \cdot 0.005555555555555556\right) \cdot \sqrt[3]{\pi \cdot {\pi}^{2}}\right)}^{3}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (* (- b_m a_m) (+ b_m a_m)))
        (t_2 (sin (* (/ angle_m 180.0) PI))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-12)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (*
         2.0
         (*
          (sin (* 0.005555555555555556 (pow (sqrt (* angle_m PI)) 2.0)))
          (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            t_2
            (*
             t_1
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (*
           2.0
           (*
            t_2
            (*
             t_1
             (cbrt
              (pow
               (cos
                (*
                 (* angle_m 0.005555555555555556)
                 (cbrt (* PI (pow PI 2.0)))))
               3.0)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = sin(((angle_m / 180.0) * ((double) M_PI)));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (sin((0.005555555555555556 * pow(sqrt((angle_m * ((double) M_PI))), 2.0))) * (t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (t_2 * (t_1 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * (t_1 * cbrt(pow(cos(((angle_m * 0.005555555555555556) * cbrt((((double) M_PI) * pow(((double) M_PI), 2.0))))), 3.0))));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = Math.sin(((angle_m / 180.0) * Math.PI));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * Math.pow(Math.sqrt((angle_m * Math.PI)), 2.0))) * (t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (t_2 * (t_1 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * (t_1 * Math.cbrt(Math.pow(Math.cos(((angle_m * 0.005555555555555556) * Math.cbrt((Math.PI * Math.pow(Math.PI, 2.0))))), 3.0))));
	}
	return angle_s * tmp;
}

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	t_2 = sin(Float64(Float64(angle_m / 180.0) * pi))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-12)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * (sqrt(Float64(angle_m * pi)) ^ 2.0))) * Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(t_2 * Float64(t_1 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	else
		tmp = Float64(2.0 * Float64(t_2 * Float64(t_1 * cbrt((cos(Float64(Float64(angle_m * 0.005555555555555556) * cbrt(Float64(pi * (pi ^ 2.0))))) ^ 3.0)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-12], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[Power[N[Sqrt[N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(t$95$2 * N[(t$95$1 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 * N[(t$95$1 * N[Power[N[Power[N[Cos[N[(N[(angle$95$m * 0.005555555555555556), $MachinePrecision] * N[Power[N[(Pi * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 3: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ t_2 := t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot {\left(\sqrt{angle_m \cdot \pi}\right)}^{2}\right) \cdot t_2\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \sin \left(\frac{angle_m}{180} \cdot \left(\sqrt{\pi} \cdot \sqrt{\pi}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (* (- b_m a_m) (+ b_m a_m)))
        (t_2 (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-12)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (*
         2.0
         (*
          (sin (* 0.005555555555555556 (pow (sqrt (* angle_m PI)) 2.0)))
          t_2))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            (sin (* (/ angle_m 180.0) PI))
            (*
             t_1
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (*
           2.0
           (* t_2 (sin (* (/ angle_m 180.0) (* (sqrt PI) (sqrt PI))))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (sin((0.005555555555555556 * pow(sqrt((angle_m * ((double) M_PI))), 2.0))) * t_2);
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * sin(((angle_m / 180.0) * (sqrt(((double) M_PI)) * sqrt(((double) M_PI))))));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * Math.pow(Math.sqrt((angle_m * Math.PI)), 2.0))) * t_2);
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * Math.sin(((angle_m / 180.0) * (Math.sqrt(Math.PI) * Math.sqrt(Math.PI)))));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = (b_m - a_m) * (b_m + a_m)
	t_2 = t_1 * math.cos(((angle_m * math.pi) * -0.005555555555555556))
	tmp = 0
	if (angle_m / 180.0) <= 2e-12:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+198:
		tmp = 2.0 * (math.sin((0.005555555555555556 * math.pow(math.sqrt((angle_m * math.pi)), 2.0))) * t_2)
	elif (angle_m / 180.0) <= 2e+232:
		tmp = 2.0 * (math.sin(((angle_m / 180.0) * math.pi)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (math.pow(math.pi, 2.0) * math.pow(angle_m, 2.0))))))
	else:
		tmp = 2.0 * (t_2 * math.sin(((angle_m / 180.0) * (math.sqrt(math.pi) * math.sqrt(math.pi)))))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	t_2 = Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-12)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * (sqrt(Float64(angle_m * pi)) ^ 2.0))) * t_2));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	else
		tmp = Float64(2.0 * Float64(t_2 * sin(Float64(Float64(angle_m / 180.0) * Float64(sqrt(pi) * sqrt(pi))))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	t_1 = (b_m - a_m) * (b_m + a_m);
	t_2 = t_1 * cos(((angle_m * pi) * -0.005555555555555556));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-12)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+198)
		tmp = 2.0 * (sin((0.005555555555555556 * (sqrt((angle_m * pi)) ^ 2.0))) * t_2);
	elseif ((angle_m / 180.0) <= 2e+232)
		tmp = 2.0 * (sin(((angle_m / 180.0) * pi)) * (t_1 * (1.0 + (-1.54320987654321e-5 * ((pi ^ 2.0) * (angle_m ^ 2.0))))));
	else
		tmp = 2.0 * (t_2 * sin(((angle_m / 180.0) * (sqrt(pi) * sqrt(pi)))));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-12], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[Power[N[Sqrt[N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * N[(N[Sqrt[Pi], $MachinePrecision] * N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ t_2 := t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \log \left(e^{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+252}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left(angle_m \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (* (- b_m a_m) (+ b_m a_m)))
        (t_2 (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 3.8e-7)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (*
         2.0
         (* t_2 (log (exp (sin (* PI (* angle_m 0.005555555555555556)))))))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            (sin (* (/ angle_m 180.0) PI))
            (*
             t_1
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (if (<= (/ angle_m 180.0) 2e+252)
            (*
             2.0
             (*
              t_2
              (log1p (expm1 (sin (* angle_m (* PI 0.005555555555555556)))))))
            (*
             0.011111111111111112
             (*
              angle_m
              (/
               (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
               (+ b_m a_m)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 3.8e-7) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (t_2 * log(exp(sin((((double) M_PI) * (angle_m * 0.005555555555555556))))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (t_2 * log1p(expm1(sin((angle_m * (((double) M_PI) * 0.005555555555555556))))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 3.8e-7) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (t_2 * Math.log(Math.exp(Math.sin((Math.PI * (angle_m * 0.005555555555555556))))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (t_2 * Math.log1p(Math.expm1(Math.sin((angle_m * (Math.PI * 0.005555555555555556))))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = (b_m - a_m) * (b_m + a_m)
	t_2 = t_1 * math.cos(((angle_m * math.pi) * -0.005555555555555556))
	tmp = 0
	if (angle_m / 180.0) <= 3.8e-7:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+198:
		tmp = 2.0 * (t_2 * math.log(math.exp(math.sin((math.pi * (angle_m * 0.005555555555555556))))))
	elif (angle_m / 180.0) <= 2e+232:
		tmp = 2.0 * (math.sin(((angle_m / 180.0) * math.pi)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (math.pow(math.pi, 2.0) * math.pow(angle_m, 2.0))))))
	elif (angle_m / 180.0) <= 2e+252:
		tmp = 2.0 * (t_2 * math.log1p(math.expm1(math.sin((angle_m * (math.pi * 0.005555555555555556))))))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	t_2 = Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 3.8e-7)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(t_2 * log(exp(sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))))));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	elseif (Float64(angle_m / 180.0) <= 2e+252)
		tmp = Float64(2.0 * Float64(t_2 * log1p(expm1(sin(Float64(angle_m * Float64(pi * 0.005555555555555556)))))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 3.8e-7], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(t$95$2 * N[Log[N[Exp[N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+252], N[(2.0 * N[(t$95$2 * N[Log[1 + N[(Exp[N[Sin[N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 66.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ t_2 := t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot t_2\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+227}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right) \cdot \left(t_1 \cdot \cos \left(-0.005555555555555556 \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(angle_m \cdot \pi\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \sin \left(0.005555555555555556 \cdot {\left(\sqrt[3]{angle_m \cdot \pi}\right)}^{3}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (* (- b_m a_m) (+ b_m a_m)))
        (t_2 (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 2e+138)
        (* 2.0 (* (sin (* (/ angle_m 180.0) PI)) t_2))
        (if (<= (/ angle_m 180.0) 2e+227)
          (*
           2.0
           (*
            (sin (* 0.005555555555555556 (* angle_m PI)))
            (*
             t_1
             (cos (* -0.005555555555555556 (expm1 (log1p (* angle_m PI))))))))
          (*
           2.0
           (*
            t_2
            (sin
             (* 0.005555555555555556 (pow (cbrt (* angle_m PI)) 3.0)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * t_2);
	} else if ((angle_m / 180.0) <= 2e+227) {
		tmp = 2.0 * (sin((0.005555555555555556 * (angle_m * ((double) M_PI)))) * (t_1 * cos((-0.005555555555555556 * expm1(log1p((angle_m * ((double) M_PI))))))));
	} else {
		tmp = 2.0 * (t_2 * sin((0.005555555555555556 * pow(cbrt((angle_m * ((double) M_PI))), 3.0))));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * t_2);
	} else if ((angle_m / 180.0) <= 2e+227) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * (angle_m * Math.PI))) * (t_1 * Math.cos((-0.005555555555555556 * Math.expm1(Math.log1p((angle_m * Math.PI)))))));
	} else {
		tmp = 2.0 * (t_2 * Math.sin((0.005555555555555556 * Math.pow(Math.cbrt((angle_m * Math.PI)), 3.0))));
	}
	return angle_s * tmp;
}

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	t_2 = Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 2e+138)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * t_2));
	elseif (Float64(angle_m / 180.0) <= 2e+227)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * Float64(angle_m * pi))) * Float64(t_1 * cos(Float64(-0.005555555555555556 * expm1(log1p(Float64(angle_m * pi))))))));
	else
		tmp = Float64(2.0 * Float64(t_2 * sin(Float64(0.005555555555555556 * (cbrt(Float64(angle_m * pi)) ^ 3.0)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+138], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+227], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(-0.005555555555555556 * N[(Exp[N[Log[1 + N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 * N[Sin[N[(0.005555555555555556 * N[Power[N[Power[N[(angle$95$m * Pi), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 6: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ t_2 := t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-12}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot {\left(\sqrt{angle_m \cdot \pi}\right)}^{2}\right) \cdot t_2\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \sin \left(0.005555555555555556 \cdot {\left(\sqrt[3]{angle_m \cdot \pi}\right)}^{3}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (* (- b_m a_m) (+ b_m a_m)))
        (t_2 (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-12)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (*
         2.0
         (*
          (sin (* 0.005555555555555556 (pow (sqrt (* angle_m PI)) 2.0)))
          t_2))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            (sin (* (/ angle_m 180.0) PI))
            (*
             t_1
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (*
           2.0
           (*
            t_2
            (sin
             (* 0.005555555555555556 (pow (cbrt (* angle_m PI)) 3.0)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (sin((0.005555555555555556 * pow(sqrt((angle_m * ((double) M_PI))), 2.0))) * t_2);
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * sin((0.005555555555555556 * pow(cbrt((angle_m * ((double) M_PI))), 3.0))));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double t_2 = t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556));
	double tmp;
	if ((angle_m / 180.0) <= 2e-12) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * Math.pow(Math.sqrt((angle_m * Math.PI)), 2.0))) * t_2);
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else {
		tmp = 2.0 * (t_2 * Math.sin((0.005555555555555556 * Math.pow(Math.cbrt((angle_m * Math.PI)), 3.0))));
	}
	return angle_s * tmp;
}

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	t_2 = Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-12)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * (sqrt(Float64(angle_m * pi)) ^ 2.0))) * t_2));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	else
		tmp = Float64(2.0 * Float64(t_2 * sin(Float64(0.005555555555555556 * (cbrt(Float64(angle_m * pi)) ^ 3.0)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-12], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[Power[N[Sqrt[N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 * N[Sin[N[(0.005555555555555556 * N[Power[N[Power[N[(angle$95$m * Pi), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+138}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+217}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right) \cdot \left(t_1 \cdot \cos \left(-0.005555555555555556 \cdot \mathsf{expm1}\left(\mathsf{log1p}\left(angle_m \cdot \pi\right)\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))) (t_1 (* (- b_m a_m) (+ b_m a_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 2e+138)
        (*
         2.0
         (*
          (sin (* (/ angle_m 180.0) PI))
          (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))))
        (if (<= (/ angle_m 180.0) 5e+217)
          (*
           2.0
           (*
            (sin (* 0.005555555555555556 (* angle_m PI)))
            (*
             t_1
             (cos (* -0.005555555555555556 (expm1 (log1p (* angle_m PI))))))))
          (if (<= (/ angle_m 180.0) 1e+250)
            (*
             (sin (* angle_m (/ PI -180.0)))
             (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
            (*
             0.011111111111111112
             (*
              angle_m
              (/
               (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
               (+ b_m a_m)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 5e+217) {
		tmp = 2.0 * (sin((0.005555555555555556 * (angle_m * ((double) M_PI)))) * (t_1 * cos((-0.005555555555555556 * expm1(log1p((angle_m * ((double) M_PI))))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+138) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 5e+217) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * (angle_m * Math.PI))) * (t_1 * Math.cos((-0.005555555555555556 * Math.expm1(Math.log1p((angle_m * Math.PI)))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = (b_m - a_m) * (b_m + a_m)
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 2e+138:
		tmp = 2.0 * (math.sin(((angle_m / 180.0) * math.pi)) * (t_1 * math.cos(((angle_m * math.pi) * -0.005555555555555556))))
	elif (angle_m / 180.0) <= 5e+217:
		tmp = 2.0 * (math.sin((0.005555555555555556 * (angle_m * math.pi))) * (t_1 * math.cos((-0.005555555555555556 * math.expm1(math.log1p((angle_m * math.pi)))))))
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 2e+138)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))));
	elseif (Float64(angle_m / 180.0) <= 5e+217)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * Float64(angle_m * pi))) * Float64(t_1 * cos(Float64(-0.005555555555555556 * expm1(log1p(Float64(angle_m * pi))))))));
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+138], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+217], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[Cos[N[(-0.005555555555555556 * N[(Exp[N[Log[1 + N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 8: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 3.8 \cdot 10^{-7}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\right) \cdot \log \left(e^{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(\sin \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_1 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))) (t_1 (* (- b_m a_m) (+ b_m a_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 3.8e-7)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (*
         2.0
         (*
          (* t_1 (cos (* (* angle_m PI) -0.005555555555555556)))
          (log (exp (sin (* PI (* angle_m 0.005555555555555556)))))))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            (sin (* (/ angle_m 180.0) PI))
            (*
             t_1
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (if (<= (/ angle_m 180.0) 1e+250)
            (*
             (sin (* angle_m (/ PI -180.0)))
             (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
            (*
             0.011111111111111112
             (*
              angle_m
              (/
               (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
               (+ b_m a_m)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 3.8e-7) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * ((t_1 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556))) * log(exp(sin((((double) M_PI) * (angle_m * 0.005555555555555556))))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (sin(((angle_m / 180.0) * ((double) M_PI))) * (t_1 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 3.8e-7) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * ((t_1 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556))) * Math.log(Math.exp(Math.sin((Math.PI * (angle_m * 0.005555555555555556))))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (Math.sin(((angle_m / 180.0) * Math.PI)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = (b_m - a_m) * (b_m + a_m)
	tmp = 0
	if (angle_m / 180.0) <= 3.8e-7:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+198:
		tmp = 2.0 * ((t_1 * math.cos(((angle_m * math.pi) * -0.005555555555555556))) * math.log(math.exp(math.sin((math.pi * (angle_m * 0.005555555555555556))))))
	elif (angle_m / 180.0) <= 2e+232:
		tmp = 2.0 * (math.sin(((angle_m / 180.0) * math.pi)) * (t_1 * (1.0 + (-1.54320987654321e-5 * (math.pow(math.pi, 2.0) * math.pow(angle_m, 2.0))))))
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 3.8e-7)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(Float64(t_1 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556))) * log(exp(sin(Float64(pi * Float64(angle_m * 0.005555555555555556)))))));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(sin(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_1 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	t_1 = (b_m - a_m) * (b_m + a_m);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 3.8e-7)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+198)
		tmp = 2.0 * ((t_1 * cos(((angle_m * pi) * -0.005555555555555556))) * log(exp(sin((pi * (angle_m * 0.005555555555555556))))));
	elseif ((angle_m / 180.0) <= 2e+232)
		tmp = 2.0 * (sin(((angle_m / 180.0) * pi)) * (t_1 * (1.0 + (-1.54320987654321e-5 * ((pi ^ 2.0) * (angle_m ^ 2.0))))));
	elseif ((angle_m / 180.0) <= 1e+250)
		tmp = sin((angle_m * (pi / -180.0))) * (2.0 * ((a_m ^ 2.0) - (b_m ^ 2.0)));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * ((b_m ^ 2.0) - (a_m ^ 2.0))) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 3.8e-7], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(N[(t$95$1 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Log[N[Exp[N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$1 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]

Derivation

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

Alternative 9: 65.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \sin \left(\frac{angle_m}{180} \cdot \pi\right)\\ t_1 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_2 := \left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_1 + a_m \cdot t_1\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+198}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \left(t_2 \cdot \cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+232}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \left(t_2 \cdot \left(1 + -1.54320987654321 \cdot 10^{-5} \cdot \left({\pi}^{2} \cdot {angle_m}^{2}\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (sin (* (/ angle_m 180.0) PI)))
        (t_1 (* angle_m (* PI (- b_m a_m))))
        (t_2 (* (- b_m a_m) (+ b_m a_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_1) (* a_m t_1)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+198)
        (* 2.0 (* t_0 (* t_2 (cos (* (* angle_m PI) -0.005555555555555556)))))
        (if (<= (/ angle_m 180.0) 2e+232)
          (*
           2.0
           (*
            t_0
            (*
             t_2
             (+
              1.0
              (* -1.54320987654321e-5 (* (pow PI 2.0) (pow angle_m 2.0)))))))
          (if (<= (/ angle_m 180.0) 1e+250)
            (*
             (sin (* angle_m (/ PI -180.0)))
             (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
            (*
             0.011111111111111112
             (*
              angle_m
              (/
               (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
               (+ b_m a_m)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = sin(((angle_m / 180.0) * ((double) M_PI)));
	double t_1 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_2 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_1) + (a_m * t_1)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (t_0 * (t_2 * cos(((angle_m * ((double) M_PI)) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (t_0 * (t_2 * (1.0 + (-1.54320987654321e-5 * (pow(((double) M_PI), 2.0) * pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = Math.sin(((angle_m / 180.0) * Math.PI));
	double t_1 = angle_m * (Math.PI * (b_m - a_m));
	double t_2 = (b_m - a_m) * (b_m + a_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_1) + (a_m * t_1)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+198) {
		tmp = 2.0 * (t_0 * (t_2 * Math.cos(((angle_m * Math.PI) * -0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 2e+232) {
		tmp = 2.0 * (t_0 * (t_2 * (1.0 + (-1.54320987654321e-5 * (Math.pow(Math.PI, 2.0) * Math.pow(angle_m, 2.0))))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = math.sin(((angle_m / 180.0) * math.pi))
	t_1 = angle_m * (math.pi * (b_m - a_m))
	t_2 = (b_m - a_m) * (b_m + a_m)
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_1) + (a_m * t_1)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+198:
		tmp = 2.0 * (t_0 * (t_2 * math.cos(((angle_m * math.pi) * -0.005555555555555556))))
	elif (angle_m / 180.0) <= 2e+232:
		tmp = 2.0 * (t_0 * (t_2 * (1.0 + (-1.54320987654321e-5 * (math.pow(math.pi, 2.0) * math.pow(angle_m, 2.0))))))
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = sin(Float64(Float64(angle_m / 180.0) * pi))
	t_1 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_2 = Float64(Float64(b_m - a_m) * Float64(b_m + a_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_1) + Float64(a_m * t_1)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+198)
		tmp = Float64(2.0 * Float64(t_0 * Float64(t_2 * cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)))));
	elseif (Float64(angle_m / 180.0) <= 2e+232)
		tmp = Float64(2.0 * Float64(t_0 * Float64(t_2 * Float64(1.0 + Float64(-1.54320987654321e-5 * Float64((pi ^ 2.0) * (angle_m ^ 2.0)))))));
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = sin(((angle_m / 180.0) * pi));
	t_1 = angle_m * (pi * (b_m - a_m));
	t_2 = (b_m - a_m) * (b_m + a_m);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-17)
		tmp = ((b_m * t_1) + (a_m * t_1)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+198)
		tmp = 2.0 * (t_0 * (t_2 * cos(((angle_m * pi) * -0.005555555555555556))));
	elseif ((angle_m / 180.0) <= 2e+232)
		tmp = 2.0 * (t_0 * (t_2 * (1.0 + (-1.54320987654321e-5 * ((pi ^ 2.0) * (angle_m ^ 2.0))))));
	elseif ((angle_m / 180.0) <= 1e+250)
		tmp = sin((angle_m * (pi / -180.0))) * (2.0 * ((a_m ^ 2.0) - (b_m ^ 2.0)));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * ((b_m ^ 2.0) - (a_m ^ 2.0))) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$1), $MachinePrecision] + N[(a$95$m * t$95$1), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+198], N[(2.0 * N[(t$95$0 * N[(t$95$2 * N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+232], N[(2.0 * N[(t$95$0 * N[(t$95$2 * N[(1.0 + N[(-1.54320987654321e-5 * N[(N[Power[Pi, 2.0], $MachinePrecision] * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 10: 65.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := \left(\left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\\ t_2 := {b_m}^{2} - {a_m}^{2}\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+87}:\\ \;\;\;\;2 \cdot \left(\frac{t_2}{2} \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+145}:\\ \;\;\;\;2 \cdot t_1\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+252}:\\ \;\;\;\;2 \cdot \left(\cos \left(\left(angle_m \cdot \pi\right) \cdot -0.005555555555555556\right) \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot t_2}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1
         (*
          (* (- b_m a_m) (+ b_m a_m))
          (sin (* 0.005555555555555556 (* angle_m PI)))))
        (t_2 (- (pow b_m 2.0) (pow a_m 2.0))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+87)
        (*
         2.0
         (* (/ t_2 2.0) (sin (* 2.0 (* PI (* angle_m 0.005555555555555556))))))
        (if (<= (/ angle_m 180.0) 5e+145)
          (* 2.0 t_1)
          (if (<= (/ angle_m 180.0) 2e+252)
            (* 2.0 (* (cos (* (* angle_m PI) -0.005555555555555556)) t_1))
            (*
             0.011111111111111112
             (* angle_m (/ (* (* PI (+ b_m a_m)) t_2) (+ b_m a_m)))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = ((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * ((double) M_PI))));
	double t_2 = pow(b_m, 2.0) - pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+87) {
		tmp = 2.0 * ((t_2 / 2.0) * sin((2.0 * (((double) M_PI) * (angle_m * 0.005555555555555556)))));
	} else if ((angle_m / 180.0) <= 5e+145) {
		tmp = 2.0 * t_1;
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (cos(((angle_m * ((double) M_PI)) * -0.005555555555555556)) * t_1);
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * t_2) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = ((b_m - a_m) * (b_m + a_m)) * Math.sin((0.005555555555555556 * (angle_m * Math.PI)));
	double t_2 = Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+87) {
		tmp = 2.0 * ((t_2 / 2.0) * Math.sin((2.0 * (Math.PI * (angle_m * 0.005555555555555556)))));
	} else if ((angle_m / 180.0) <= 5e+145) {
		tmp = 2.0 * t_1;
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (Math.cos(((angle_m * Math.PI) * -0.005555555555555556)) * t_1);
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * t_2) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = ((b_m - a_m) * (b_m + a_m)) * math.sin((0.005555555555555556 * (angle_m * math.pi)))
	t_2 = math.pow(b_m, 2.0) - math.pow(a_m, 2.0)
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+87:
		tmp = 2.0 * ((t_2 / 2.0) * math.sin((2.0 * (math.pi * (angle_m * 0.005555555555555556)))))
	elif (angle_m / 180.0) <= 5e+145:
		tmp = 2.0 * t_1
	elif (angle_m / 180.0) <= 2e+252:
		tmp = 2.0 * (math.cos(((angle_m * math.pi) * -0.005555555555555556)) * t_1)
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * t_2) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64(Float64(Float64(b_m - a_m) * Float64(b_m + a_m)) * sin(Float64(0.005555555555555556 * Float64(angle_m * pi))))
	t_2 = Float64((b_m ^ 2.0) - (a_m ^ 2.0))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+87)
		tmp = Float64(2.0 * Float64(Float64(t_2 / 2.0) * sin(Float64(2.0 * Float64(pi * Float64(angle_m * 0.005555555555555556))))));
	elseif (Float64(angle_m / 180.0) <= 5e+145)
		tmp = Float64(2.0 * t_1);
	elseif (Float64(angle_m / 180.0) <= 2e+252)
		tmp = Float64(2.0 * Float64(cos(Float64(Float64(angle_m * pi) * -0.005555555555555556)) * t_1));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * t_2) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	t_1 = ((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * pi)));
	t_2 = (b_m ^ 2.0) - (a_m ^ 2.0);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-17)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+87)
		tmp = 2.0 * ((t_2 / 2.0) * sin((2.0 * (pi * (angle_m * 0.005555555555555556)))));
	elseif ((angle_m / 180.0) <= 5e+145)
		tmp = 2.0 * t_1;
	elseif ((angle_m / 180.0) <= 2e+252)
		tmp = 2.0 * (cos(((angle_m * pi) * -0.005555555555555556)) * t_1);
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * t_2) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+87], N[(2.0 * N[(N[(t$95$2 / 2.0), $MachinePrecision] * N[Sin[N[(2.0 * N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+145], N[(2.0 * t$95$1), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+252], N[(2.0 * N[(N[Cos[N[(N[(angle$95$m * Pi), $MachinePrecision] * -0.005555555555555556), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 11: 66.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+252}:\\ \;\;\;\;2 \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right) \cdot \left(\left(\left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\right) \cdot \cos \left(angle_m \cdot \frac{\pi}{-180}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 2e+252)
        (*
         2.0
         (*
          (sin (* 0.005555555555555556 (* angle_m PI)))
          (* (* (- b_m a_m) (+ b_m a_m)) (cos (* angle_m (/ PI -180.0))))))
        (*
         0.011111111111111112
         (*
          angle_m
          (/
           (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
           (+ b_m a_m)))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (sin((0.005555555555555556 * (angle_m * ((double) M_PI)))) * (((b_m - a_m) * (b_m + a_m)) * cos((angle_m * (((double) M_PI) / -180.0)))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 2e+252) {
		tmp = 2.0 * (Math.sin((0.005555555555555556 * (angle_m * Math.PI))) * (((b_m - a_m) * (b_m + a_m)) * Math.cos((angle_m * (Math.PI / -180.0)))));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 2e+252:
		tmp = 2.0 * (math.sin((0.005555555555555556 * (angle_m * math.pi))) * (((b_m - a_m) * (b_m + a_m)) * math.cos((angle_m * (math.pi / -180.0)))))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 2e+252)
		tmp = Float64(2.0 * Float64(sin(Float64(0.005555555555555556 * Float64(angle_m * pi))) * Float64(Float64(Float64(b_m - a_m) * Float64(b_m + a_m)) * cos(Float64(angle_m * Float64(pi / -180.0))))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-17)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 2e+252)
		tmp = 2.0 * (sin((0.005555555555555556 * (angle_m * pi))) * (((b_m - a_m) * (b_m + a_m)) * cos((angle_m * (pi / -180.0)))));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * ((b_m ^ 2.0) - (a_m ^ 2.0))) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+252], N[(2.0 * N[(N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 12: 64.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := {b_m}^{2} - {a_m}^{2}\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;t_1 \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot t_1}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (- (pow b_m 2.0) (pow a_m 2.0))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+75)
        (* t_1 (sin (* 2.0 (* PI (* angle_m 0.005555555555555556)))))
        (if (<= (/ angle_m 180.0) 1e+250)
          (*
           (sin (* angle_m (/ PI -180.0)))
           (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
          (*
           0.011111111111111112
           (* angle_m (/ (* (* PI (+ b_m a_m)) t_1) (+ b_m a_m))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = pow(b_m, 2.0) - pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+75) {
		tmp = t_1 * sin((2.0 * (((double) M_PI) * (angle_m * 0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * t_1) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+75) {
		tmp = t_1 * Math.sin((2.0 * (Math.PI * (angle_m * 0.005555555555555556))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * t_1) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = math.pow(b_m, 2.0) - math.pow(a_m, 2.0)
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+75:
		tmp = t_1 * math.sin((2.0 * (math.pi * (angle_m * 0.005555555555555556))))
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * t_1) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64((b_m ^ 2.0) - (a_m ^ 2.0))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+75)
		tmp = Float64(t_1 * sin(Float64(2.0 * Float64(pi * Float64(angle_m * 0.005555555555555556)))));
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * t_1) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	t_1 = (b_m ^ 2.0) - (a_m ^ 2.0);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-17)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+75)
		tmp = t_1 * sin((2.0 * (pi * (angle_m * 0.005555555555555556))));
	elseif ((angle_m / 180.0) <= 1e+250)
		tmp = sin((angle_m * (pi / -180.0))) * (2.0 * ((a_m ^ 2.0) - (b_m ^ 2.0)));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * t_1) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+75], N[(t$95$1 * N[Sin[N[(2.0 * N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

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

Alternative 13: 64.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ t_1 := {b_m}^{2} - {a_m}^{2}\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+75}:\\ \;\;\;\;2 \cdot \left(\frac{t_1}{2} \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot t_1}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m))))
        (t_1 (- (pow b_m 2.0) (pow a_m 2.0))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-17)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 5e+75)
        (*
         2.0
         (* (/ t_1 2.0) (sin (* 2.0 (* PI (* angle_m 0.005555555555555556))))))
        (if (<= (/ angle_m 180.0) 1e+250)
          (*
           (sin (* angle_m (/ PI -180.0)))
           (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
          (*
           0.011111111111111112
           (* angle_m (/ (* (* PI (+ b_m a_m)) t_1) (+ b_m a_m))))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double t_1 = pow(b_m, 2.0) - pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+75) {
		tmp = 2.0 * ((t_1 / 2.0) * sin((2.0 * (((double) M_PI) * (angle_m * 0.005555555555555556)))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * t_1) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double t_1 = Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-17) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 5e+75) {
		tmp = 2.0 * ((t_1 / 2.0) * Math.sin((2.0 * (Math.PI * (angle_m * 0.005555555555555556)))));
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * t_1) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	t_1 = math.pow(b_m, 2.0) - math.pow(a_m, 2.0)
	tmp = 0
	if (angle_m / 180.0) <= 2e-17:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 5e+75:
		tmp = 2.0 * ((t_1 / 2.0) * math.sin((2.0 * (math.pi * (angle_m * 0.005555555555555556)))))
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * t_1) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	t_1 = Float64((b_m ^ 2.0) - (a_m ^ 2.0))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-17)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 5e+75)
		tmp = Float64(2.0 * Float64(Float64(t_1 / 2.0) * sin(Float64(2.0 * Float64(pi * Float64(angle_m * 0.005555555555555556))))));
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * t_1) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	t_1 = (b_m ^ 2.0) - (a_m ^ 2.0);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e-17)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 5e+75)
		tmp = 2.0 * ((t_1 / 2.0) * sin((2.0 * (pi * (angle_m * 0.005555555555555556)))));
	elseif ((angle_m / 180.0) <= 1e+250)
		tmp = sin((angle_m * (pi / -180.0))) * (2.0 * ((a_m ^ 2.0) - (b_m ^ 2.0)));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * t_1) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-17], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+75], N[(2.0 * N[(N[(t$95$1 / 2.0), $MachinePrecision] * N[Sin[N[(2.0 * N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]), $MachinePrecision]]]

Derivation

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

Alternative 14: 63.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 1000:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+250}:\\ \;\;\;\;\sin \left(angle_m \cdot \frac{\pi}{-180}\right) \cdot \left(2 \cdot \left({a_m}^{2} - {b_m}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \frac{\left(\pi \cdot \left(b_m + a_m\right)\right) \cdot \left({b_m}^{2} - {a_m}^{2}\right)}{b_m + a_m}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 1000.0)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (if (<= (/ angle_m 180.0) 1e+250)
        (*
         (sin (* angle_m (/ PI -180.0)))
         (* 2.0 (- (pow a_m 2.0) (pow b_m 2.0))))
        (*
         0.011111111111111112
         (*
          angle_m
          (/
           (* (* PI (+ b_m a_m)) (- (pow b_m 2.0) (pow a_m 2.0)))
           (+ b_m a_m)))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 1000.0) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = sin((angle_m * (((double) M_PI) / -180.0))) * (2.0 * (pow(a_m, 2.0) - pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((((double) M_PI) * (b_m + a_m)) * (pow(b_m, 2.0) - pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 1000.0) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else if ((angle_m / 180.0) <= 1e+250) {
		tmp = Math.sin((angle_m * (Math.PI / -180.0))) * (2.0 * (Math.pow(a_m, 2.0) - Math.pow(b_m, 2.0)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((Math.PI * (b_m + a_m)) * (Math.pow(b_m, 2.0) - Math.pow(a_m, 2.0))) / (b_m + a_m)));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	tmp = 0
	if (angle_m / 180.0) <= 1000.0:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	elif (angle_m / 180.0) <= 1e+250:
		tmp = math.sin((angle_m * (math.pi / -180.0))) * (2.0 * (math.pow(a_m, 2.0) - math.pow(b_m, 2.0)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (((math.pi * (b_m + a_m)) * (math.pow(b_m, 2.0) - math.pow(a_m, 2.0))) / (b_m + a_m)))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 1000.0)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	elseif (Float64(angle_m / 180.0) <= 1e+250)
		tmp = Float64(sin(Float64(angle_m * Float64(pi / -180.0))) * Float64(2.0 * Float64((a_m ^ 2.0) - (b_m ^ 2.0))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(Float64(Float64(pi * Float64(b_m + a_m)) * Float64((b_m ^ 2.0) - (a_m ^ 2.0))) / Float64(b_m + a_m))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 1000.0)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	elseif ((angle_m / 180.0) <= 1e+250)
		tmp = sin((angle_m * (pi / -180.0))) * (2.0 * ((a_m ^ 2.0) - (b_m ^ 2.0)));
	else
		tmp = 0.011111111111111112 * (angle_m * (((pi * (b_m + a_m)) * ((b_m ^ 2.0) - (a_m ^ 2.0))) / (b_m + a_m)));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1000.0], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+250], N[(N[Sin[N[(angle$95$m * N[(Pi / -180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(2.0 * N[(N[Power[a$95$m, 2.0], $MachinePrecision] - N[Power[b$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(N[(N[(Pi * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[(N[Power[b$95$m, 2.0], $MachinePrecision] - N[Power[a$95$m, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 15: 65.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := angle_m \cdot \left(\pi \cdot \left(b_m - a_m\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 1000:\\ \;\;\;\;\left(b_m \cdot t_0 + a_m \cdot t_0\right) \cdot 0.011111111111111112\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (let* ((t_0 (* angle_m (* PI (- b_m a_m)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 1000.0)
      (* (+ (* b_m t_0) (* a_m t_0)) 0.011111111111111112)
      (*
       2.0
       (*
        (* (- b_m a_m) (+ b_m a_m))
        (sin (* 0.005555555555555556 (* angle_m PI)))))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (((double) M_PI) * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 1000.0) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else {
		tmp = 2.0 * (((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * ((double) M_PI)))));
	}
	return angle_s * tmp;
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	double t_0 = angle_m * (Math.PI * (b_m - a_m));
	double tmp;
	if ((angle_m / 180.0) <= 1000.0) {
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	} else {
		tmp = 2.0 * (((b_m - a_m) * (b_m + a_m)) * Math.sin((0.005555555555555556 * (angle_m * Math.PI))));
	}
	return angle_s * tmp;
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	t_0 = angle_m * (math.pi * (b_m - a_m))
	tmp = 0
	if (angle_m / 180.0) <= 1000.0:
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112
	else:
		tmp = 2.0 * (((b_m - a_m) * (b_m + a_m)) * math.sin((0.005555555555555556 * (angle_m * math.pi))))
	return angle_s * tmp

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	t_0 = Float64(angle_m * Float64(pi * Float64(b_m - a_m)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 1000.0)
		tmp = Float64(Float64(Float64(b_m * t_0) + Float64(a_m * t_0)) * 0.011111111111111112);
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(b_m - a_m) * Float64(b_m + a_m)) * sin(Float64(0.005555555555555556 * Float64(angle_m * pi)))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a_m, b_m, angle_m)
	t_0 = angle_m * (pi * (b_m - a_m));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 1000.0)
		tmp = ((b_m * t_0) + (a_m * t_0)) * 0.011111111111111112;
	else
		tmp = 2.0 * (((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * pi))));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(angle$95$m * N[(Pi * N[(b$95$m - a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1000.0], N[(N[(N[(b$95$m * t$95$0), $MachinePrecision] + N[(a$95$m * t$95$0), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision], N[(2.0 * N[(N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 16: 55.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ angle_s \cdot \left(2 \cdot \left(\left(\left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\right) \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (*
  angle_s
  (*
   2.0
   (*
    (* (- b_m a_m) (+ b_m a_m))
    (sin (* 0.005555555555555556 (* angle_m PI)))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	return angle_s * (2.0 * (((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * ((double) M_PI))))));
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	return angle_s * (2.0 * (((b_m - a_m) * (b_m + a_m)) * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))));
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	return angle_s * (2.0 * (((b_m - a_m) * (b_m + a_m)) * math.sin((0.005555555555555556 * (angle_m * math.pi)))))

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	return Float64(angle_s * Float64(2.0 * Float64(Float64(Float64(b_m - a_m) * Float64(b_m + a_m)) * sin(Float64(0.005555555555555556 * Float64(angle_m * pi))))))
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp = code(angle_s, a_m, b_m, angle_m)
	tmp = angle_s * (2.0 * (((b_m - a_m) * (b_m + a_m)) * sin((0.005555555555555556 * (angle_m * pi)))));
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(2.0 * N[(N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 17: 54.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} a_m = \left|a\right| \\ b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ angle_s \cdot \left(0.011111111111111112 \cdot \left(angle_m \cdot \left(\pi \cdot \left(\left(b_m - a_m\right) \cdot \left(b_m + a_m\right)\right)\right)\right)\right) \end{array} \]

FPCore

a_m = (fabs.f64 a)
b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a_m b_m angle_m)
 :precision binary64
 (*
  angle_s
  (* 0.011111111111111112 (* angle_m (* PI (* (- b_m a_m) (+ b_m a_m)))))))

C

a_m = fabs(a);
b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a_m, double b_m, double angle_m) {
	return angle_s * (0.011111111111111112 * (angle_m * (((double) M_PI) * ((b_m - a_m) * (b_m + a_m)))));
}

Java

a_m = Math.abs(a);
b_m = Math.abs(b);
angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a_m, double b_m, double angle_m) {
	return angle_s * (0.011111111111111112 * (angle_m * (Math.PI * ((b_m - a_m) * (b_m + a_m)))));
}

Python

a_m = math.fabs(a)
b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a_m, b_m, angle_m):
	return angle_s * (0.011111111111111112 * (angle_m * (math.pi * ((b_m - a_m) * (b_m + a_m)))))

Julia

a_m = abs(a)
b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a_m, b_m, angle_m)
	return Float64(angle_s * Float64(0.011111111111111112 * Float64(angle_m * Float64(pi * Float64(Float64(b_m - a_m) * Float64(b_m + a_m))))))
end

MATLAB

a_m = abs(a);
b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp = code(angle_s, a_m, b_m, angle_m)
	tmp = angle_s * (0.011111111111111112 * (angle_m * (pi * ((b_m - a_m) * (b_m + a_m)))));
end

Wolfram

a_m = N[Abs[a], $MachinePrecision]
b_m = N[Abs[b], $MachinePrecision]
angle_m = N[Abs[angle], $MachinePrecision]
angle_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[angle]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[angle$95$s_, a$95$m_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(0.011111111111111112 * N[(angle$95$m * N[(Pi * N[(N[(b$95$m - a$95$m), $MachinePrecision] * N[(b$95$m + a$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024010 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))