ab-angle->ABCF B

Percentage Accurate: 53.9% → 66.5%

Time: 42.1s

Alternatives: 16

Speedup: 5.5×

• 33.3% 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: 53.9% 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: 66.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \frac{angle_m}{180} \cdot \pi\\ t_1 := angle_m \cdot \left(\pi \cdot 0.005555555555555556\right)\\ t_2 := \sqrt{angle_m \cdot \pi}\\ t_3 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ t_4 := 0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right) \cdot \left(b_m - a\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(\left(t_3 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\right) \cdot \cos t_4\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+126}:\\ \;\;\;\;2 \cdot \left(\left(t_3 \cdot \sin t_0\right) \cdot \left(1 + \left(-1.54320987654321 \cdot 10^{-5} \cdot {angle_m}^{2}\right) \cdot {\pi}^{2}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(\left(t_3 \cdot {\left(\sqrt[3]{\sin t_1}\right)}^{3}\right) \cdot \cos t_0\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+224}:\\ \;\;\;\;2 \cdot \left(t_3 \cdot \mathsf{fma}\left(-2.8577960676726107 \cdot 10^{-8}, {\left(angle_m \cdot \pi\right)}^{3}, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(t_3 \cdot \sin t_4\right) \cdot \cos \left(\frac{t_2}{\frac{180}{t_2}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (/ angle_m 180.0) PI))
        (t_1 (* angle_m (* PI 0.005555555555555556)))
        (t_2 (sqrt (* angle_m PI)))
        (t_3 (* (- b_m a) (+ a b_m)))
        (t_4 (* 0.005555555555555556 (* angle_m PI))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (sin (* PI (* angle_m 0.005555555555555556))) (- b_m a))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+102)
        (* 2.0 (* (* t_3 (sin (/ (* angle_m PI) 180.0))) (cos t_4)))
        (if (<= (/ angle_m 180.0) 1e+126)
          (*
           2.0
           (*
            (* t_3 (sin t_0))
            (+
             1.0
             (* (* -1.54320987654321e-5 (pow angle_m 2.0)) (pow PI 2.0)))))
          (if (<= (/ angle_m 180.0) 5e+207)
            (* 2.0 (* (* t_3 (pow (cbrt (sin t_1)) 3.0)) (cos t_0)))
            (if (<= (/ angle_m 180.0) 2e+224)
              (*
               2.0
               (*
                t_3
                (fma -2.8577960676726107e-8 (pow (* angle_m PI) 3.0) t_1)))
              (* 2.0 (* (* t_3 (sin t_4)) (cos (/ t_2 (/ 180.0 t_2)))))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * ((double) M_PI);
	double t_1 = angle_m * (((double) M_PI) * 0.005555555555555556);
	double t_2 = sqrt((angle_m * ((double) M_PI)));
	double t_3 = (b_m - a) * (a + b_m);
	double t_4 = 0.005555555555555556 * (angle_m * ((double) M_PI));
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt((sin((((double) M_PI) * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * ((t_3 * sin(((angle_m * ((double) M_PI)) / 180.0))) * cos(t_4));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * ((t_3 * sin(t_0)) * (1.0 + ((-1.54320987654321e-5 * pow(angle_m, 2.0)) * pow(((double) M_PI), 2.0))));
	} else if ((angle_m / 180.0) <= 5e+207) {
		tmp = 2.0 * ((t_3 * pow(cbrt(sin(t_1)), 3.0)) * cos(t_0));
	} else if ((angle_m / 180.0) <= 2e+224) {
		tmp = 2.0 * (t_3 * fma(-2.8577960676726107e-8, pow((angle_m * ((double) M_PI)), 3.0), t_1));
	} else {
		tmp = 2.0 * ((t_3 * sin(t_4)) * cos((t_2 / (180.0 / t_2))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(angle_m / 180.0) * pi)
	t_1 = Float64(angle_m * Float64(pi * 0.005555555555555556))
	t_2 = sqrt(Float64(angle_m * pi))
	t_3 = Float64(Float64(b_m - a) * Float64(a + b_m))
	t_4 = Float64(0.005555555555555556 * Float64(angle_m * pi))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) * Float64(b_m - a)))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+102)
		tmp = Float64(2.0 * Float64(Float64(t_3 * sin(Float64(Float64(angle_m * pi) / 180.0))) * cos(t_4)));
	elseif (Float64(angle_m / 180.0) <= 1e+126)
		tmp = Float64(2.0 * Float64(Float64(t_3 * sin(t_0)) * Float64(1.0 + Float64(Float64(-1.54320987654321e-5 * (angle_m ^ 2.0)) * (pi ^ 2.0)))));
	elseif (Float64(angle_m / 180.0) <= 5e+207)
		tmp = Float64(2.0 * Float64(Float64(t_3 * (cbrt(sin(t_1)) ^ 3.0)) * cos(t_0)));
	elseif (Float64(angle_m / 180.0) <= 2e+224)
		tmp = Float64(2.0 * Float64(t_3 * fma(-2.8577960676726107e-8, (Float64(angle_m * pi) ^ 3.0), t_1)));
	else
		tmp = Float64(2.0 * Float64(Float64(t_3 * sin(t_4)) * cos(Float64(t_2 / Float64(180.0 / t_2)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(angle$95$m * Pi), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b$95$m - a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+102], N[(2.0 * N[(N[(t$95$3 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$4], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+126], N[(2.0 * N[(N[(t$95$3 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(-1.54320987654321e-5 * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+207], N[(2.0 * N[(N[(t$95$3 * N[Power[N[Power[N[Sin[t$95$1], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+224], N[(2.0 * N[(t$95$3 * N[(-2.8577960676726107e-8 * N[Power[N[(angle$95$m * Pi), $MachinePrecision], 3.0], $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t$95$3 * N[Sin[t$95$4], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(t$95$2 / N[(180.0 / t$95$2), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]), $MachinePrecision]]]]]]

Derivation

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

Alternative 2: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \frac{angle_m}{180} \cdot \pi\\ t_1 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ t_2 := t_1 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\\ t_3 := \cos t_0\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right) \cdot \left(b_m - a\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \cos \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+126}:\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot \sin t_0\right) \cdot \left(1 + \left(-1.54320987654321 \cdot 10^{-5} \cdot {angle_m}^{2}\right) \cdot {\pi}^{2}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 4 \cdot 10^{+195}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot t_3\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_3 \cdot \left(t_1 \cdot \sin \left(\frac{angle_m}{180} \cdot \sqrt[3]{{\pi}^{3}}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (/ angle_m 180.0) PI))
        (t_1 (* (- b_m a) (+ a b_m)))
        (t_2 (* t_1 (sin (/ (* angle_m PI) 180.0))))
        (t_3 (cos t_0)))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (sin (* PI (* angle_m 0.005555555555555556))) (- b_m a))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+102)
        (* 2.0 (* t_2 (cos (* 0.005555555555555556 (* angle_m PI)))))
        (if (<= (/ angle_m 180.0) 1e+126)
          (*
           2.0
           (*
            (* t_1 (sin t_0))
            (+
             1.0
             (* (* -1.54320987654321e-5 (pow angle_m 2.0)) (pow PI 2.0)))))
          (if (<= (/ angle_m 180.0) 4e+195)
            (* 2.0 (* t_2 t_3))
            (*
             2.0
             (*
              t_3
              (* t_1 (sin (* (/ angle_m 180.0) (cbrt (pow PI 3.0))))))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * ((double) M_PI);
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = t_1 * sin(((angle_m * ((double) M_PI)) / 180.0));
	double t_3 = cos(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt((sin((((double) M_PI) * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * (t_2 * cos((0.005555555555555556 * (angle_m * ((double) M_PI)))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * ((t_1 * sin(t_0)) * (1.0 + ((-1.54320987654321e-5 * pow(angle_m, 2.0)) * pow(((double) M_PI), 2.0))));
	} else if ((angle_m / 180.0) <= 4e+195) {
		tmp = 2.0 * (t_2 * t_3);
	} else {
		tmp = 2.0 * (t_3 * (t_1 * sin(((angle_m / 180.0) * cbrt(pow(((double) M_PI), 3.0))))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * Math.PI;
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = t_1 * Math.sin(((angle_m * Math.PI) / 180.0));
	double t_3 = Math.cos(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * Math.pow((Math.cbrt((a + b_m)) * Math.cbrt((Math.sin((Math.PI * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * (t_2 * Math.cos((0.005555555555555556 * (angle_m * Math.PI))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * ((t_1 * Math.sin(t_0)) * (1.0 + ((-1.54320987654321e-5 * Math.pow(angle_m, 2.0)) * Math.pow(Math.PI, 2.0))));
	} else if ((angle_m / 180.0) <= 4e+195) {
		tmp = 2.0 * (t_2 * t_3);
	} else {
		tmp = 2.0 * (t_3 * (t_1 * Math.sin(((angle_m / 180.0) * Math.cbrt(Math.pow(Math.PI, 3.0))))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(angle_m / 180.0) * pi)
	t_1 = Float64(Float64(b_m - a) * Float64(a + b_m))
	t_2 = Float64(t_1 * sin(Float64(Float64(angle_m * pi) / 180.0)))
	t_3 = cos(t_0)
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) * Float64(b_m - a)))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+102)
		tmp = Float64(2.0 * Float64(t_2 * cos(Float64(0.005555555555555556 * Float64(angle_m * pi)))));
	elseif (Float64(angle_m / 180.0) <= 1e+126)
		tmp = Float64(2.0 * Float64(Float64(t_1 * sin(t_0)) * Float64(1.0 + Float64(Float64(-1.54320987654321e-5 * (angle_m ^ 2.0)) * (pi ^ 2.0)))));
	elseif (Float64(angle_m / 180.0) <= 4e+195)
		tmp = Float64(2.0 * Float64(t_2 * t_3));
	else
		tmp = Float64(2.0 * Float64(t_3 * Float64(t_1 * sin(Float64(Float64(angle_m / 180.0) * cbrt((pi ^ 3.0)))))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Cos[t$95$0], $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b$95$m - a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+102], N[(2.0 * N[(t$95$2 * N[Cos[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+126], N[(2.0 * N[(N[(t$95$1 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(-1.54320987654321e-5 * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 4e+195], N[(2.0 * N[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$3 * N[(t$95$1 * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * N[Power[N[Power[Pi, 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]]

Derivation

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

Alternative 3: 66.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \frac{angle_m}{180} \cdot \pi\\ t_1 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ t_2 := \cos t_0\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right) \cdot \left(b_m - a\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+126}:\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot \sin t_0\right) \cdot \left(1 + \left(-1.54320987654321 \cdot 10^{-5} \cdot {angle_m}^{2}\right) \cdot {\pi}^{2}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+205}:\\ \;\;\;\;2 \cdot \left(\left(t_1 \cdot {\left(\sqrt[3]{\sin \left(angle_m \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}\right)}^{3}\right) \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \left(t_1 \cdot \sin \left(\frac{angle_m}{180} \cdot \sqrt[3]{{\pi}^{3}}\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (/ angle_m 180.0) PI))
        (t_1 (* (- b_m a) (+ a b_m)))
        (t_2 (cos t_0)))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (sin (* PI (* angle_m 0.005555555555555556))) (- b_m a))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+102)
        (*
         2.0
         (*
          (* t_1 (sin (/ (* angle_m PI) 180.0)))
          (cos (* 0.005555555555555556 (* angle_m PI)))))
        (if (<= (/ angle_m 180.0) 1e+126)
          (*
           2.0
           (*
            (* t_1 (sin t_0))
            (+
             1.0
             (* (* -1.54320987654321e-5 (pow angle_m 2.0)) (pow PI 2.0)))))
          (if (<= (/ angle_m 180.0) 1e+205)
            (*
             2.0
             (*
              (*
               t_1
               (pow (cbrt (sin (* angle_m (* PI 0.005555555555555556)))) 3.0))
              t_2))
            (*
             2.0
             (*
              t_2
              (* t_1 (sin (* (/ angle_m 180.0) (cbrt (pow PI 3.0))))))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * ((double) M_PI);
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = cos(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt((sin((((double) M_PI) * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * ((t_1 * sin(((angle_m * ((double) M_PI)) / 180.0))) * cos((0.005555555555555556 * (angle_m * ((double) M_PI)))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * ((t_1 * sin(t_0)) * (1.0 + ((-1.54320987654321e-5 * pow(angle_m, 2.0)) * pow(((double) M_PI), 2.0))));
	} else if ((angle_m / 180.0) <= 1e+205) {
		tmp = 2.0 * ((t_1 * pow(cbrt(sin((angle_m * (((double) M_PI) * 0.005555555555555556)))), 3.0)) * t_2);
	} else {
		tmp = 2.0 * (t_2 * (t_1 * sin(((angle_m / 180.0) * cbrt(pow(((double) M_PI), 3.0))))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * Math.PI;
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = Math.cos(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * Math.pow((Math.cbrt((a + b_m)) * Math.cbrt((Math.sin((Math.PI * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * ((t_1 * Math.sin(((angle_m * Math.PI) / 180.0))) * Math.cos((0.005555555555555556 * (angle_m * Math.PI))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * ((t_1 * Math.sin(t_0)) * (1.0 + ((-1.54320987654321e-5 * Math.pow(angle_m, 2.0)) * Math.pow(Math.PI, 2.0))));
	} else if ((angle_m / 180.0) <= 1e+205) {
		tmp = 2.0 * ((t_1 * Math.pow(Math.cbrt(Math.sin((angle_m * (Math.PI * 0.005555555555555556)))), 3.0)) * t_2);
	} else {
		tmp = 2.0 * (t_2 * (t_1 * Math.sin(((angle_m / 180.0) * Math.cbrt(Math.pow(Math.PI, 3.0))))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(angle_m / 180.0) * pi)
	t_1 = Float64(Float64(b_m - a) * Float64(a + b_m))
	t_2 = cos(t_0)
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) * Float64(b_m - a)))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+102)
		tmp = Float64(2.0 * Float64(Float64(t_1 * sin(Float64(Float64(angle_m * pi) / 180.0))) * cos(Float64(0.005555555555555556 * Float64(angle_m * pi)))));
	elseif (Float64(angle_m / 180.0) <= 1e+126)
		tmp = Float64(2.0 * Float64(Float64(t_1 * sin(t_0)) * Float64(1.0 + Float64(Float64(-1.54320987654321e-5 * (angle_m ^ 2.0)) * (pi ^ 2.0)))));
	elseif (Float64(angle_m / 180.0) <= 1e+205)
		tmp = Float64(2.0 * Float64(Float64(t_1 * (cbrt(sin(Float64(angle_m * Float64(pi * 0.005555555555555556)))) ^ 3.0)) * t_2));
	else
		tmp = Float64(2.0 * Float64(t_2 * Float64(t_1 * sin(Float64(Float64(angle_m / 180.0) * cbrt((pi ^ 3.0)))))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Cos[t$95$0], $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b$95$m - a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+102], N[(2.0 * N[(N[(t$95$1 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+126], N[(2.0 * N[(N[(t$95$1 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[(1.0 + N[(N[(-1.54320987654321e-5 * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+205], N[(2.0 * N[(N[(t$95$1 * N[Power[N[Power[N[Sin[N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$2 * N[(t$95$1 * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * N[Power[N[Power[Pi, 3.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]

Derivation

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

Alternative 4: 66.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \frac{angle_m}{180} \cdot \pi\\ t_1 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ t_2 := t_1 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\\ t_3 := t_1 \cdot \sin t_0\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right) \cdot \left(b_m - a\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \cos \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 10^{+126}:\\ \;\;\;\;2 \cdot \left(t_3 \cdot \left(1 + \left(-1.54320987654321 \cdot 10^{-5} \cdot {angle_m}^{2}\right) \cdot {\pi}^{2}\right)\right)\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 4 \cdot 10^{+169}:\\ \;\;\;\;2 \cdot \left(t_2 \cdot \cos t_0\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_3 \cdot \cos \left(\frac{angle_m}{\frac{180}{\pi}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (/ angle_m 180.0) PI))
        (t_1 (* (- b_m a) (+ a b_m)))
        (t_2 (* t_1 (sin (/ (* angle_m PI) 180.0))))
        (t_3 (* t_1 (sin t_0))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (sin (* PI (* angle_m 0.005555555555555556))) (- b_m a))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+102)
        (* 2.0 (* t_2 (cos (* 0.005555555555555556 (* angle_m PI)))))
        (if (<= (/ angle_m 180.0) 1e+126)
          (*
           2.0
           (*
            t_3
            (+
             1.0
             (* (* -1.54320987654321e-5 (pow angle_m 2.0)) (pow PI 2.0)))))
          (if (<= (/ angle_m 180.0) 4e+169)
            (* 2.0 (* t_2 (cos t_0)))
            (* 2.0 (* t_3 (cos (/ angle_m (/ 180.0 PI))))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * ((double) M_PI);
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = t_1 * sin(((angle_m * ((double) M_PI)) / 180.0));
	double t_3 = t_1 * sin(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt((sin((((double) M_PI) * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * (t_2 * cos((0.005555555555555556 * (angle_m * ((double) M_PI)))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * (t_3 * (1.0 + ((-1.54320987654321e-5 * pow(angle_m, 2.0)) * pow(((double) M_PI), 2.0))));
	} else if ((angle_m / 180.0) <= 4e+169) {
		tmp = 2.0 * (t_2 * cos(t_0));
	} else {
		tmp = 2.0 * (t_3 * cos((angle_m / (180.0 / ((double) M_PI)))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (angle_m / 180.0) * Math.PI;
	double t_1 = (b_m - a) * (a + b_m);
	double t_2 = t_1 * Math.sin(((angle_m * Math.PI) / 180.0));
	double t_3 = t_1 * Math.sin(t_0);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * Math.pow((Math.cbrt((a + b_m)) * Math.cbrt((Math.sin((Math.PI * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+102) {
		tmp = 2.0 * (t_2 * Math.cos((0.005555555555555556 * (angle_m * Math.PI))));
	} else if ((angle_m / 180.0) <= 1e+126) {
		tmp = 2.0 * (t_3 * (1.0 + ((-1.54320987654321e-5 * Math.pow(angle_m, 2.0)) * Math.pow(Math.PI, 2.0))));
	} else if ((angle_m / 180.0) <= 4e+169) {
		tmp = 2.0 * (t_2 * Math.cos(t_0));
	} else {
		tmp = 2.0 * (t_3 * Math.cos((angle_m / (180.0 / Math.PI))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(angle_m / 180.0) * pi)
	t_1 = Float64(Float64(b_m - a) * Float64(a + b_m))
	t_2 = Float64(t_1 * sin(Float64(Float64(angle_m * pi) / 180.0)))
	t_3 = Float64(t_1 * sin(t_0))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) * Float64(b_m - a)))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+102)
		tmp = Float64(2.0 * Float64(t_2 * cos(Float64(0.005555555555555556 * Float64(angle_m * pi)))));
	elseif (Float64(angle_m / 180.0) <= 1e+126)
		tmp = Float64(2.0 * Float64(t_3 * Float64(1.0 + Float64(Float64(-1.54320987654321e-5 * (angle_m ^ 2.0)) * (pi ^ 2.0)))));
	elseif (Float64(angle_m / 180.0) <= 4e+169)
		tmp = Float64(2.0 * Float64(t_2 * cos(t_0)));
	else
		tmp = Float64(2.0 * Float64(t_3 * cos(Float64(angle_m / Float64(180.0 / pi)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b$95$m - a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+102], N[(2.0 * N[(t$95$2 * N[Cos[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+126], N[(2.0 * N[(t$95$3 * N[(1.0 + N[(N[(-1.54320987654321e-5 * N[Power[angle$95$m, 2.0], $MachinePrecision]), $MachinePrecision] * N[Power[Pi, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 4e+169], N[(2.0 * N[(t$95$2 * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$3 * N[Cos[N[(angle$95$m / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]), $MachinePrecision]]]]]

Derivation

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

Alternative 5: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\left(b_m - a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+204}:\\ \;\;\;\;2 \cdot \left(\left(t_0 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle_m}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(t_0 \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle_m}{\frac{180}{\pi}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (- b_m a) (sin (* 0.005555555555555556 (* angle_m PI))))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+204)
        (*
         2.0
         (*
          (* t_0 (sin (/ (* angle_m PI) 180.0)))
          (cos (/ PI (/ 180.0 angle_m)))))
        (*
         2.0
         (*
          (* t_0 (sin (* (/ angle_m 180.0) PI)))
          (cos (/ angle_m (/ 180.0 PI))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt(((b_m - a) * sin((0.005555555555555556 * (angle_m * ((double) M_PI))))))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+204) {
		tmp = 2.0 * ((t_0 * sin(((angle_m * ((double) M_PI)) / 180.0))) * cos((((double) M_PI) / (180.0 / angle_m))));
	} else {
		tmp = 2.0 * ((t_0 * sin(((angle_m / 180.0) * ((double) M_PI)))) * cos((angle_m / (180.0 / ((double) M_PI)))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * Math.pow((Math.cbrt((a + b_m)) * Math.cbrt(((b_m - a) * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+204) {
		tmp = 2.0 * ((t_0 * Math.sin(((angle_m * Math.PI) / 180.0))) * Math.cos((Math.PI / (180.0 / angle_m))));
	} else {
		tmp = 2.0 * ((t_0 * Math.sin(((angle_m / 180.0) * Math.PI))) * Math.cos((angle_m / (180.0 / Math.PI))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(Float64(b_m - a) * sin(Float64(0.005555555555555556 * Float64(angle_m * pi)))))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+204)
		tmp = Float64(2.0 * Float64(Float64(t_0 * sin(Float64(Float64(angle_m * pi) / 180.0))) * cos(Float64(pi / Float64(180.0 / angle_m)))));
	else
		tmp = Float64(2.0 * Float64(Float64(t_0 * sin(Float64(Float64(angle_m / 180.0) * pi))) * cos(Float64(angle_m / Float64(180.0 / pi)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[(b$95$m - a), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+204], N[(2.0 * N[(N[(t$95$0 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t$95$0 * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(angle$95$m / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 6: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{-21}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{a + b_m} \cdot \sqrt[3]{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right) \cdot \left(b_m - a\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+204}:\\ \;\;\;\;2 \cdot \left(\left(t_0 \cdot \sin \left(\frac{angle_m \cdot \pi}{180}\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle_m}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(t_0 \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\right) \cdot \cos \left(\frac{angle_m}{\frac{180}{\pi}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e-21)
      (*
       2.0
       (pow
        (*
         (cbrt (+ a b_m))
         (cbrt (* (sin (* PI (* angle_m 0.005555555555555556))) (- b_m a))))
        3.0))
      (if (<= (/ angle_m 180.0) 5e+204)
        (*
         2.0
         (*
          (* t_0 (sin (/ (* angle_m PI) 180.0)))
          (cos (/ PI (/ 180.0 angle_m)))))
        (*
         2.0
         (*
          (* t_0 (sin (* (/ angle_m 180.0) PI)))
          (cos (/ angle_m (/ 180.0 PI))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * pow((cbrt((a + b_m)) * cbrt((sin((((double) M_PI) * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+204) {
		tmp = 2.0 * ((t_0 * sin(((angle_m * ((double) M_PI)) / 180.0))) * cos((((double) M_PI) / (180.0 / angle_m))));
	} else {
		tmp = 2.0 * ((t_0 * sin(((angle_m / 180.0) * ((double) M_PI)))) * cos((angle_m / (180.0 / ((double) M_PI)))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if ((angle_m / 180.0) <= 2e-21) {
		tmp = 2.0 * Math.pow((Math.cbrt((a + b_m)) * Math.cbrt((Math.sin((Math.PI * (angle_m * 0.005555555555555556))) * (b_m - a)))), 3.0);
	} else if ((angle_m / 180.0) <= 5e+204) {
		tmp = 2.0 * ((t_0 * Math.sin(((angle_m * Math.PI) / 180.0))) * Math.cos((Math.PI / (180.0 / angle_m))));
	} else {
		tmp = 2.0 * ((t_0 * Math.sin(((angle_m / 180.0) * Math.PI))) * Math.cos((angle_m / (180.0 / Math.PI))));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e-21)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(a + b_m)) * cbrt(Float64(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) * Float64(b_m - a)))) ^ 3.0));
	elseif (Float64(angle_m / 180.0) <= 5e+204)
		tmp = Float64(2.0 * Float64(Float64(t_0 * sin(Float64(Float64(angle_m * pi) / 180.0))) * cos(Float64(pi / Float64(180.0 / angle_m)))));
	else
		tmp = Float64(2.0 * Float64(Float64(t_0 * sin(Float64(Float64(angle_m / 180.0) * pi))) * cos(Float64(angle_m / Float64(180.0 / pi)))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e-21], N[(2.0 * N[Power[N[(N[Power[N[(a + b$95$m), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[N[(N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b$95$m - a), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+204], N[(2.0 * N[(N[(t$95$0 * N[Sin[N[(N[(angle$95$m * Pi), $MachinePrecision] / 180.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(t$95$0 * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(angle$95$m / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 7: 57.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(\cos \left(\frac{angle_m}{180} \cdot \pi\right) \cdot \left(t_0 \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left({\left(\sqrt[3]{\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 4.5e+207)
      (*
       2.0
       (*
        (cos (* (/ angle_m 180.0) PI))
        (* t_0 (sin (* 0.005555555555555556 (* angle_m PI))))))
      (*
       2.0
       (*
        t_0
        (sin (pow (cbrt (* PI (* angle_m 0.005555555555555556))) 3.0))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 4.5e+207) {
		tmp = 2.0 * (cos(((angle_m / 180.0) * ((double) M_PI))) * (t_0 * sin((0.005555555555555556 * (angle_m * ((double) M_PI))))));
	} else {
		tmp = 2.0 * (t_0 * sin(pow(cbrt((((double) M_PI) * (angle_m * 0.005555555555555556))), 3.0)));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 4.5e+207) {
		tmp = 2.0 * (Math.cos(((angle_m / 180.0) * Math.PI)) * (t_0 * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))));
	} else {
		tmp = 2.0 * (t_0 * Math.sin(Math.pow(Math.cbrt((Math.PI * (angle_m * 0.005555555555555556))), 3.0)));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 4.5e+207)
		tmp = Float64(2.0 * Float64(cos(Float64(Float64(angle_m / 180.0) * pi)) * Float64(t_0 * sin(Float64(0.005555555555555556 * Float64(angle_m * pi))))));
	else
		tmp = Float64(2.0 * Float64(t_0 * sin((cbrt(Float64(pi * Float64(angle_m * 0.005555555555555556))) ^ 3.0))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 4.5e+207], N[(2.0 * N[(N[Cos[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(t$95$0 * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$0 * N[Sin[N[Power[N[Power[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 8: 57.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(\left(t_0 \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right) \cdot \cos \left(\frac{angle_m}{\frac{180}{\pi}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left({\left(\sqrt[3]{\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 5e+207)
      (*
       2.0
       (*
        (* t_0 (sin (* 0.005555555555555556 (* angle_m PI))))
        (cos (/ angle_m (/ 180.0 PI)))))
      (*
       2.0
       (*
        t_0
        (sin (pow (cbrt (* PI (* angle_m 0.005555555555555556))) 3.0))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 5e+207) {
		tmp = 2.0 * ((t_0 * sin((0.005555555555555556 * (angle_m * ((double) M_PI))))) * cos((angle_m / (180.0 / ((double) M_PI)))));
	} else {
		tmp = 2.0 * (t_0 * sin(pow(cbrt((((double) M_PI) * (angle_m * 0.005555555555555556))), 3.0)));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 5e+207) {
		tmp = 2.0 * ((t_0 * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))) * Math.cos((angle_m / (180.0 / Math.PI))));
	} else {
		tmp = 2.0 * (t_0 * Math.sin(Math.pow(Math.cbrt((Math.PI * (angle_m * 0.005555555555555556))), 3.0)));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 5e+207)
		tmp = Float64(2.0 * Float64(Float64(t_0 * sin(Float64(0.005555555555555556 * Float64(angle_m * pi)))) * cos(Float64(angle_m / Float64(180.0 / pi)))));
	else
		tmp = Float64(2.0 * Float64(t_0 * sin((cbrt(Float64(pi * Float64(angle_m * 0.005555555555555556))) ^ 3.0))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 5e+207], N[(2.0 * N[(N[(t$95$0 * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(angle$95$m / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$0 * N[Sin[N[Power[N[Power[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 9: 55.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\\ t_1 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{+209}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \sin \left({\left(\sqrt{t_0}\right)}^{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \sin \left({\left(\sqrt[3]{t_0}\right)}^{3}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* PI (* angle_m 0.005555555555555556)))
        (t_1 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 5e+209)
      (* 2.0 (* t_1 (sin (pow (sqrt t_0) 2.0))))
      (* 2.0 (* t_1 (sin (pow (cbrt t_0) 3.0))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = ((double) M_PI) * (angle_m * 0.005555555555555556);
	double t_1 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 5e+209) {
		tmp = 2.0 * (t_1 * sin(pow(sqrt(t_0), 2.0)));
	} else {
		tmp = 2.0 * (t_1 * sin(pow(cbrt(t_0), 3.0)));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = Math.PI * (angle_m * 0.005555555555555556);
	double t_1 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 5e+209) {
		tmp = 2.0 * (t_1 * Math.sin(Math.pow(Math.sqrt(t_0), 2.0)));
	} else {
		tmp = 2.0 * (t_1 * Math.sin(Math.pow(Math.cbrt(t_0), 3.0)));
	}
	return angle_s * tmp;
}

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(pi * Float64(angle_m * 0.005555555555555556))
	t_1 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 5e+209)
		tmp = Float64(2.0 * Float64(t_1 * sin((sqrt(t_0) ^ 2.0))));
	else
		tmp = Float64(2.0 * Float64(t_1 * sin((cbrt(t_0) ^ 3.0))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 5e+209], N[(2.0 * N[(t$95$1 * N[Sin[N[Power[N[Sqrt[t$95$0], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$1 * N[Sin[N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

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

Alternative 10: 56.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{-35}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{1}{\frac{180}{angle_m \cdot \pi}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)\right)\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 3.2e-35)
      (* 2.0 (* t_0 (sin (/ 1.0 (/ 180.0 (* angle_m PI))))))
      (*
       2.0
       (*
        t_0
        (sin (expm1 (log1p (* PI (* angle_m 0.005555555555555556)))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 3.2e-35) {
		tmp = 2.0 * (t_0 * sin((1.0 / (180.0 / (angle_m * ((double) M_PI))))));
	} else {
		tmp = 2.0 * (t_0 * sin(expm1(log1p((((double) M_PI) * (angle_m * 0.005555555555555556))))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 3.2e-35) {
		tmp = 2.0 * (t_0 * Math.sin((1.0 / (180.0 / (angle_m * Math.PI)))));
	} else {
		tmp = 2.0 * (t_0 * Math.sin(Math.expm1(Math.log1p((Math.PI * (angle_m * 0.005555555555555556))))));
	}
	return angle_s * tmp;
}

Python

b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b_m, angle_m):
	t_0 = (b_m - a) * (a + b_m)
	tmp = 0
	if a <= 3.2e-35:
		tmp = 2.0 * (t_0 * math.sin((1.0 / (180.0 / (angle_m * math.pi)))))
	else:
		tmp = 2.0 * (t_0 * math.sin(math.expm1(math.log1p((math.pi * (angle_m * 0.005555555555555556))))))
	return angle_s * tmp

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 3.2e-35)
		tmp = Float64(2.0 * Float64(t_0 * sin(Float64(1.0 / Float64(180.0 / Float64(angle_m * pi))))));
	else
		tmp = Float64(2.0 * Float64(t_0 * sin(expm1(log1p(Float64(pi * Float64(angle_m * 0.005555555555555556)))))));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 3.2e-35], N[(2.0 * N[(t$95$0 * N[Sin[N[(1.0 / N[(180.0 / N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$0 * N[Sin[N[(Exp[N[Log[1 + N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 11: 55.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 7.5 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{1}{\frac{180}{angle_m \cdot \pi}}\right)\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \left|\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)\right|\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{\pi}{\frac{180}{angle_m}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 7.5e+49)
      (* 2.0 (* t_0 (sin (/ 1.0 (/ 180.0 (* angle_m PI))))))
      (if (<= a 4.5e+207)
        (* 2.0 (* t_0 (fabs (sin (* PI (* angle_m 0.005555555555555556))))))
        (* 2.0 (* t_0 (sin (/ PI (/ 180.0 angle_m))))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 7.5e+49) {
		tmp = 2.0 * (t_0 * sin((1.0 / (180.0 / (angle_m * ((double) M_PI))))));
	} else if (a <= 4.5e+207) {
		tmp = 2.0 * (t_0 * fabs(sin((((double) M_PI) * (angle_m * 0.005555555555555556)))));
	} else {
		tmp = 2.0 * (t_0 * sin((((double) M_PI) / (180.0 / angle_m))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 7.5e+49) {
		tmp = 2.0 * (t_0 * Math.sin((1.0 / (180.0 / (angle_m * Math.PI)))));
	} else if (a <= 4.5e+207) {
		tmp = 2.0 * (t_0 * Math.abs(Math.sin((Math.PI * (angle_m * 0.005555555555555556)))));
	} else {
		tmp = 2.0 * (t_0 * Math.sin((Math.PI / (180.0 / angle_m))));
	}
	return angle_s * tmp;
}

Python

b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b_m, angle_m):
	t_0 = (b_m - a) * (a + b_m)
	tmp = 0
	if a <= 7.5e+49:
		tmp = 2.0 * (t_0 * math.sin((1.0 / (180.0 / (angle_m * math.pi)))))
	elif a <= 4.5e+207:
		tmp = 2.0 * (t_0 * math.fabs(math.sin((math.pi * (angle_m * 0.005555555555555556)))))
	else:
		tmp = 2.0 * (t_0 * math.sin((math.pi / (180.0 / angle_m))))
	return angle_s * tmp

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 7.5e+49)
		tmp = Float64(2.0 * Float64(t_0 * sin(Float64(1.0 / Float64(180.0 / Float64(angle_m * pi))))));
	elseif (a <= 4.5e+207)
		tmp = Float64(2.0 * Float64(t_0 * abs(sin(Float64(pi * Float64(angle_m * 0.005555555555555556))))));
	else
		tmp = Float64(2.0 * Float64(t_0 * sin(Float64(pi / Float64(180.0 / angle_m)))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b_m, angle_m)
	t_0 = (b_m - a) * (a + b_m);
	tmp = 0.0;
	if (a <= 7.5e+49)
		tmp = 2.0 * (t_0 * sin((1.0 / (180.0 / (angle_m * pi)))));
	elseif (a <= 4.5e+207)
		tmp = 2.0 * (t_0 * abs(sin((pi * (angle_m * 0.005555555555555556)))));
	else
		tmp = 2.0 * (t_0 * sin((pi / (180.0 / angle_m))));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 7.5e+49], N[(2.0 * N[(t$95$0 * N[Sin[N[(1.0 / N[(180.0 / N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e+207], N[(2.0 * N[(t$95$0 * N[Abs[N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$0 * N[Sin[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]

Derivation

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

Alternative 12: 55.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} b_m = \left|b\right| \\ angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b_m - a\right) \cdot \left(a + b_m\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;a \leq 3.1 \cdot 10^{+33}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{1}{\frac{180}{angle_m \cdot \pi}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{\pi}{\frac{180}{angle_m}}\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

b_m = (fabs.f64 b)
angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b_m angle_m)
 :precision binary64
 (let* ((t_0 (* (- b_m a) (+ a b_m))))
   (*
    angle_s
    (if (<= a 3.1e+33)
      (* 2.0 (* t_0 (sin (/ 1.0 (/ 180.0 (* angle_m PI))))))
      (* 2.0 (* t_0 (sin (/ PI (/ 180.0 angle_m)))))))))

C

b_m = fabs(b);
angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 3.1e+33) {
		tmp = 2.0 * (t_0 * sin((1.0 / (180.0 / (angle_m * ((double) M_PI))))));
	} else {
		tmp = 2.0 * (t_0 * sin((((double) M_PI) / (180.0 / angle_m))));
	}
	return angle_s * tmp;
}

Java

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, double b_m, double angle_m) {
	double t_0 = (b_m - a) * (a + b_m);
	double tmp;
	if (a <= 3.1e+33) {
		tmp = 2.0 * (t_0 * Math.sin((1.0 / (180.0 / (angle_m * Math.PI)))));
	} else {
		tmp = 2.0 * (t_0 * Math.sin((Math.PI / (180.0 / angle_m))));
	}
	return angle_s * tmp;
}

Python

b_m = math.fabs(b)
angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b_m, angle_m):
	t_0 = (b_m - a) * (a + b_m)
	tmp = 0
	if a <= 3.1e+33:
		tmp = 2.0 * (t_0 * math.sin((1.0 / (180.0 / (angle_m * math.pi)))))
	else:
		tmp = 2.0 * (t_0 * math.sin((math.pi / (180.0 / angle_m))))
	return angle_s * tmp

Julia

b_m = abs(b)
angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b_m, angle_m)
	t_0 = Float64(Float64(b_m - a) * Float64(a + b_m))
	tmp = 0.0
	if (a <= 3.1e+33)
		tmp = Float64(2.0 * Float64(t_0 * sin(Float64(1.0 / Float64(180.0 / Float64(angle_m * pi))))));
	else
		tmp = Float64(2.0 * Float64(t_0 * sin(Float64(pi / Float64(180.0 / angle_m)))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

b_m = abs(b);
angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b_m, angle_m)
	t_0 = (b_m - a) * (a + b_m);
	tmp = 0.0;
	if (a <= 3.1e+33)
		tmp = 2.0 * (t_0 * sin((1.0 / (180.0 / (angle_m * pi)))));
	else
		tmp = 2.0 * (t_0 * sin((pi / (180.0 / angle_m))));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, b$95$m_, angle$95$m_] := Block[{t$95$0 = N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[a, 3.1e+33], N[(2.0 * N[(t$95$0 * N[Sin[N[(1.0 / N[(180.0 / N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(t$95$0 * N[Sin[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 13: 56.0% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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, double b_m, double angle_m) {
	return angle_s * (2.0 * (((b_m - a) * (a + b_m)) * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(2.0 * N[(N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$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 14: 54.3% accurate, 5.4× speedup

Math

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

FPCore

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

C

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

Java

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, double b_m, double angle_m) {
	return angle_s * (2.0 * (((b_m - a) * (a + b_m)) * (angle_m * (Math.PI * 0.005555555555555556))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(2.0 * N[(N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision] * N[(angle$95$m * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 15: 54.3% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Java

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, double b_m, double angle_m) {
	return angle_s * ((angle_m * 0.011111111111111112) * ((b_m - a) * (Math.PI * (a + b_m))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(N[(angle$95$m * 0.011111111111111112), $MachinePrecision] * N[(N[(b$95$m - a), $MachinePrecision] * N[(Pi * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 16: 54.3% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Java

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, double b_m, double angle_m) {
	return angle_s * ((angle_m * (Math.PI * ((b_m - a) * (a + b_m)))) * 0.011111111111111112);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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_, b$95$m_, angle$95$m_] := N[(angle$95$s * N[(N[(angle$95$m * N[(Pi * N[(N[(b$95$m - a), $MachinePrecision] * N[(a + b$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(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)))))