ab-angle->ABCF B

Percentage Accurate: 53.8% → 57.1%

Time: 25.8s

Alternatives: 12

Speedup: 5.5×

• 32.3% 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: 53.8% 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: 57.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\\ t_1 := \frac{angle_m}{180} \cdot \pi\\ t_2 := 2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 10^{+39}:\\ \;\;\;\;\left(t_2 \cdot \sin t_0\right) \cdot \cos t_1\\ \mathbf{elif}\;\frac{angle_m}{180} \leq 5 \cdot 10^{+180}:\\ \;\;\;\;\left(2 \cdot \left|{b}^{2} - {a}^{2}\right|\right) \cdot \sin t_1\\ \mathbf{else}:\\ \;\;\;\;\left(t_2 \cdot \sqrt{{\sin \left(\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)\right)}^{2}}\right) \cdot \cos t_0\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* 0.005555555555555556 (* angle_m PI)))
        (t_1 (* (/ angle_m 180.0) PI))
        (t_2 (* 2.0 (* (- b a) (+ b a)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 1e+39)
      (* (* t_2 (sin t_0)) (cos t_1))
      (if (<= (/ angle_m 180.0) 5e+180)
        (* (* 2.0 (fabs (- (pow b 2.0) (pow a 2.0)))) (sin t_1))
        (*
         (* t_2 (sqrt (pow (sin (* PI (* angle_m 0.005555555555555556))) 2.0)))
         (cos t_0)))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 0.005555555555555556 * (angle_m * ((double) M_PI));
	double t_1 = (angle_m / 180.0) * ((double) M_PI);
	double t_2 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if ((angle_m / 180.0) <= 1e+39) {
		tmp = (t_2 * sin(t_0)) * cos(t_1);
	} else if ((angle_m / 180.0) <= 5e+180) {
		tmp = (2.0 * fabs((pow(b, 2.0) - pow(a, 2.0)))) * sin(t_1);
	} else {
		tmp = (t_2 * sqrt(pow(sin((((double) M_PI) * (angle_m * 0.005555555555555556))), 2.0))) * cos(t_0);
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 0.005555555555555556 * (angle_m * Math.PI);
	double t_1 = (angle_m / 180.0) * Math.PI;
	double t_2 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if ((angle_m / 180.0) <= 1e+39) {
		tmp = (t_2 * Math.sin(t_0)) * Math.cos(t_1);
	} else if ((angle_m / 180.0) <= 5e+180) {
		tmp = (2.0 * Math.abs((Math.pow(b, 2.0) - Math.pow(a, 2.0)))) * Math.sin(t_1);
	} else {
		tmp = (t_2 * Math.sqrt(Math.pow(Math.sin((Math.PI * (angle_m * 0.005555555555555556))), 2.0))) * Math.cos(t_0);
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = 0.005555555555555556 * (angle_m * math.pi)
	t_1 = (angle_m / 180.0) * math.pi
	t_2 = 2.0 * ((b - a) * (b + a))
	tmp = 0
	if (angle_m / 180.0) <= 1e+39:
		tmp = (t_2 * math.sin(t_0)) * math.cos(t_1)
	elif (angle_m / 180.0) <= 5e+180:
		tmp = (2.0 * math.fabs((math.pow(b, 2.0) - math.pow(a, 2.0)))) * math.sin(t_1)
	else:
		tmp = (t_2 * math.sqrt(math.pow(math.sin((math.pi * (angle_m * 0.005555555555555556))), 2.0))) * math.cos(t_0)
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(0.005555555555555556 * Float64(angle_m * pi))
	t_1 = Float64(Float64(angle_m / 180.0) * pi)
	t_2 = Float64(2.0 * Float64(Float64(b - a) * Float64(b + a)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 1e+39)
		tmp = Float64(Float64(t_2 * sin(t_0)) * cos(t_1));
	elseif (Float64(angle_m / 180.0) <= 5e+180)
		tmp = Float64(Float64(2.0 * abs(Float64((b ^ 2.0) - (a ^ 2.0)))) * sin(t_1));
	else
		tmp = Float64(Float64(t_2 * sqrt((sin(Float64(pi * Float64(angle_m * 0.005555555555555556))) ^ 2.0))) * cos(t_0));
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = 0.005555555555555556 * (angle_m * pi);
	t_1 = (angle_m / 180.0) * pi;
	t_2 = 2.0 * ((b - a) * (b + a));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 1e+39)
		tmp = (t_2 * sin(t_0)) * cos(t_1);
	elseif ((angle_m / 180.0) <= 5e+180)
		tmp = (2.0 * abs(((b ^ 2.0) - (a ^ 2.0)))) * sin(t_1);
	else
		tmp = (t_2 * sqrt((sin((pi * (angle_m * 0.005555555555555556))) ^ 2.0))) * cos(t_0);
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 1e+39], N[(N[(t$95$2 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 5e+180], N[(N[(2.0 * N[Abs[N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 * N[Sqrt[N[Power[N[Sin[N[(Pi * N[(angle$95$m * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]]]]

Derivation

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

Alternative 2: 57.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\right) \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\\ t_1 := \cos \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;{b}^{2} \leq 2 \cdot 10^{+209}:\\ \;\;\;\;t_1 \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left|t_1\right|\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* (* 2.0 (* (- b a) (+ b a))) (sin (* (/ angle_m 180.0) PI))))
        (t_1 (cos (* 0.005555555555555556 (* angle_m PI)))))
   (* angle_s (if (<= (pow b 2.0) 2e+209) (* t_1 t_0) (* t_0 (fabs t_1))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * ((double) M_PI)));
	double t_1 = cos((0.005555555555555556 * (angle_m * ((double) M_PI))));
	double tmp;
	if (pow(b, 2.0) <= 2e+209) {
		tmp = t_1 * t_0;
	} else {
		tmp = t_0 * fabs(t_1);
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (2.0 * ((b - a) * (b + a))) * Math.sin(((angle_m / 180.0) * Math.PI));
	double t_1 = Math.cos((0.005555555555555556 * (angle_m * Math.PI)));
	double tmp;
	if (Math.pow(b, 2.0) <= 2e+209) {
		tmp = t_1 * t_0;
	} else {
		tmp = t_0 * Math.abs(t_1);
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = (2.0 * ((b - a) * (b + a))) * math.sin(((angle_m / 180.0) * math.pi))
	t_1 = math.cos((0.005555555555555556 * (angle_m * math.pi)))
	tmp = 0
	if math.pow(b, 2.0) <= 2e+209:
		tmp = t_1 * t_0
	else:
		tmp = t_0 * math.fabs(t_1)
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(Float64(2.0 * Float64(Float64(b - a) * Float64(b + a))) * sin(Float64(Float64(angle_m / 180.0) * pi)))
	t_1 = cos(Float64(0.005555555555555556 * Float64(angle_m * pi)))
	tmp = 0.0
	if ((b ^ 2.0) <= 2e+209)
		tmp = Float64(t_1 * t_0);
	else
		tmp = Float64(t_0 * abs(t_1));
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = (2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * pi));
	t_1 = cos((0.005555555555555556 * (angle_m * pi)));
	tmp = 0.0;
	if ((b ^ 2.0) <= 2e+209)
		tmp = t_1 * t_0;
	else
		tmp = t_0 * abs(t_1);
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Cos[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[Power[b, 2.0], $MachinePrecision], 2e+209], N[(t$95$1 * t$95$0), $MachinePrecision], N[(t$95$0 * N[Abs[t$95$1], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

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

Alternative 3: 57.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \frac{angle_m}{180} \cdot \pi\\ t_1 := 2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;{b}^{2} \leq 2 \cdot 10^{+249}:\\ \;\;\;\;\left(t_1 \cdot \sin \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right)\right) \cdot \cos t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \sin t_0\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* (/ angle_m 180.0) PI)) (t_1 (* 2.0 (* (- b a) (+ b a)))))
   (*
    angle_s
    (if (<= (pow b 2.0) 2e+249)
      (* (* t_1 (sin (* 0.005555555555555556 (* angle_m PI)))) (cos t_0))
      (* t_1 (sin t_0))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (angle_m / 180.0) * ((double) M_PI);
	double t_1 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if (pow(b, 2.0) <= 2e+249) {
		tmp = (t_1 * sin((0.005555555555555556 * (angle_m * ((double) M_PI))))) * cos(t_0);
	} else {
		tmp = t_1 * sin(t_0);
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (angle_m / 180.0) * Math.PI;
	double t_1 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if (Math.pow(b, 2.0) <= 2e+249) {
		tmp = (t_1 * Math.sin((0.005555555555555556 * (angle_m * Math.PI)))) * Math.cos(t_0);
	} else {
		tmp = t_1 * Math.sin(t_0);
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = (angle_m / 180.0) * math.pi
	t_1 = 2.0 * ((b - a) * (b + a))
	tmp = 0
	if math.pow(b, 2.0) <= 2e+249:
		tmp = (t_1 * math.sin((0.005555555555555556 * (angle_m * math.pi)))) * math.cos(t_0)
	else:
		tmp = t_1 * math.sin(t_0)
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(Float64(angle_m / 180.0) * pi)
	t_1 = Float64(2.0 * Float64(Float64(b - a) * Float64(b + a)))
	tmp = 0.0
	if ((b ^ 2.0) <= 2e+249)
		tmp = Float64(Float64(t_1 * sin(Float64(0.005555555555555556 * Float64(angle_m * pi)))) * cos(t_0));
	else
		tmp = Float64(t_1 * sin(t_0));
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = (angle_m / 180.0) * pi;
	t_1 = 2.0 * ((b - a) * (b + a));
	tmp = 0.0;
	if ((b ^ 2.0) <= 2e+249)
		tmp = (t_1 * sin((0.005555555555555556 * (angle_m * pi)))) * cos(t_0);
	else
		tmp = t_1 * sin(t_0);
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[Power[b, 2.0], $MachinePrecision], 2e+249], N[(N[(t$95$1 * N[Sin[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]]

Derivation

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

Alternative 4: 57.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\right) \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;{b}^{2} \leq 10^{+290}:\\ \;\;\;\;\cos \left(0.005555555555555556 \cdot \left(angle_m \cdot \pi\right)\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* (* 2.0 (* (- b a) (+ b a))) (sin (* (/ angle_m 180.0) PI)))))
   (*
    angle_s
    (if (<= (pow b 2.0) 1e+290)
      (* (cos (* 0.005555555555555556 (* angle_m PI))) t_0)
      t_0))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * ((double) M_PI)));
	double tmp;
	if (pow(b, 2.0) <= 1e+290) {
		tmp = cos((0.005555555555555556 * (angle_m * ((double) M_PI)))) * t_0;
	} else {
		tmp = t_0;
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (2.0 * ((b - a) * (b + a))) * Math.sin(((angle_m / 180.0) * Math.PI));
	double tmp;
	if (Math.pow(b, 2.0) <= 1e+290) {
		tmp = Math.cos((0.005555555555555556 * (angle_m * Math.PI))) * t_0;
	} else {
		tmp = t_0;
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = (2.0 * ((b - a) * (b + a))) * math.sin(((angle_m / 180.0) * math.pi))
	tmp = 0
	if math.pow(b, 2.0) <= 1e+290:
		tmp = math.cos((0.005555555555555556 * (angle_m * math.pi))) * t_0
	else:
		tmp = t_0
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(Float64(2.0 * Float64(Float64(b - a) * Float64(b + a))) * sin(Float64(Float64(angle_m / 180.0) * pi)))
	tmp = 0.0
	if ((b ^ 2.0) <= 1e+290)
		tmp = Float64(cos(Float64(0.005555555555555556 * Float64(angle_m * pi))) * t_0);
	else
		tmp = t_0;
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = (2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * pi));
	tmp = 0.0;
	if ((b ^ 2.0) <= 1e+290)
		tmp = cos((0.005555555555555556 * (angle_m * pi))) * t_0;
	else
		tmp = t_0;
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[Power[b, 2.0], $MachinePrecision], 1e+290], N[(N[Cos[N[(0.005555555555555556 * N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$0), $MachinePrecision], t$95$0]), $MachinePrecision]]

Derivation

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

Alternative 5: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := 2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;{a}^{2} \leq 4 \cdot 10^{-292}:\\ \;\;\;\;t_0 \cdot \sin \left(\frac{1}{\frac{180}{angle_m \cdot \pi}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sin \left({\left(\sqrt[3]{\pi \cdot \left(angle_m \cdot 0.005555555555555556\right)}\right)}^{3}\right)\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* 2.0 (* (- b a) (+ b a)))))
   (*
    angle_s
    (if (<= (pow a 2.0) 4e-292)
      (* t_0 (sin (/ 1.0 (/ 180.0 (* angle_m PI)))))
      (*
       t_0
       (sin (pow (cbrt (* PI (* angle_m 0.005555555555555556))) 3.0)))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if (pow(a, 2.0) <= 4e-292) {
		tmp = t_0 * sin((1.0 / (180.0 / (angle_m * ((double) M_PI)))));
	} else {
		tmp = t_0 * sin(pow(cbrt((((double) M_PI) * (angle_m * 0.005555555555555556))), 3.0));
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if (Math.pow(a, 2.0) <= 4e-292) {
		tmp = t_0 * Math.sin((1.0 / (180.0 / (angle_m * Math.PI))));
	} else {
		tmp = t_0 * Math.sin(Math.pow(Math.cbrt((Math.PI * (angle_m * 0.005555555555555556))), 3.0));
	}
	return angle_s * tmp;
}

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(2.0 * Float64(Float64(b - a) * Float64(b + a)))
	tmp = 0.0
	if ((a ^ 2.0) <= 4e-292)
		tmp = Float64(t_0 * sin(Float64(1.0 / Float64(180.0 / Float64(angle_m * pi)))));
	else
		tmp = Float64(t_0 * sin((cbrt(Float64(pi * Float64(angle_m * 0.005555555555555556))) ^ 3.0)));
	end
	return Float64(angle_s * tmp)
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[Power[a, 2.0], $MachinePrecision], 4e-292], N[(t$95$0 * N[Sin[N[(1.0 / N[(180.0 / N[(angle$95$m * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 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]]

Derivation

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

Alternative 6: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := 2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+206}:\\ \;\;\;\;t_0 \cdot \sin \left(\frac{\pi}{\frac{180}{angle_m}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left|\sin \left(angle_m \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right|\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* 2.0 (* (- b a) (+ b a)))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e+206)
      (* t_0 (sin (/ PI (/ 180.0 angle_m))))
      (* t_0 (fabs (sin (* angle_m (* 0.005555555555555556 PI)))))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if ((angle_m / 180.0) <= 2e+206) {
		tmp = t_0 * sin((((double) M_PI) / (180.0 / angle_m)));
	} else {
		tmp = t_0 * fabs(sin((angle_m * (0.005555555555555556 * ((double) M_PI)))));
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = 2.0 * ((b - a) * (b + a));
	double tmp;
	if ((angle_m / 180.0) <= 2e+206) {
		tmp = t_0 * Math.sin((Math.PI / (180.0 / angle_m)));
	} else {
		tmp = t_0 * Math.abs(Math.sin((angle_m * (0.005555555555555556 * Math.PI))));
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = 2.0 * ((b - a) * (b + a))
	tmp = 0
	if (angle_m / 180.0) <= 2e+206:
		tmp = t_0 * math.sin((math.pi / (180.0 / angle_m)))
	else:
		tmp = t_0 * math.fabs(math.sin((angle_m * (0.005555555555555556 * math.pi))))
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(2.0 * Float64(Float64(b - a) * Float64(b + a)))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e+206)
		tmp = Float64(t_0 * sin(Float64(pi / Float64(180.0 / angle_m))));
	else
		tmp = Float64(t_0 * abs(sin(Float64(angle_m * Float64(0.005555555555555556 * pi)))));
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = 2.0 * ((b - a) * (b + a));
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e+206)
		tmp = t_0 * sin((pi / (180.0 / angle_m)));
	else
		tmp = t_0 * abs(sin((angle_m * (0.005555555555555556 * pi))));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+206], N[(t$95$0 * N[Sin[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[Abs[N[Sin[N[(angle$95$m * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 7: 55.7% accurate, 2.8× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ \begin{array}{l} t_0 := \left(b - a\right) \cdot \left(b + a\right)\\ angle_s \cdot \begin{array}{l} \mathbf{if}\;\frac{angle_m}{180} \leq 2 \cdot 10^{+206}:\\ \;\;\;\;\left(2 \cdot t_0\right) \cdot \sin \left(\frac{\pi}{\frac{180}{angle_m}}\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle_m \cdot \left(\pi \cdot t_0\right)\right)\\ \end{array} \end{array} \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (let* ((t_0 (* (- b a) (+ b a))))
   (*
    angle_s
    (if (<= (/ angle_m 180.0) 2e+206)
      (* (* 2.0 t_0) (sin (/ PI (/ 180.0 angle_m))))
      (* 0.011111111111111112 (* angle_m (* PI t_0)))))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (b - a) * (b + a);
	double tmp;
	if ((angle_m / 180.0) <= 2e+206) {
		tmp = (2.0 * t_0) * sin((((double) M_PI) / (180.0 / angle_m)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (((double) M_PI) * t_0));
	}
	return angle_s * tmp;
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	double t_0 = (b - a) * (b + a);
	double tmp;
	if ((angle_m / 180.0) <= 2e+206) {
		tmp = (2.0 * t_0) * Math.sin((Math.PI / (180.0 / angle_m)));
	} else {
		tmp = 0.011111111111111112 * (angle_m * (Math.PI * t_0));
	}
	return angle_s * tmp;
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	t_0 = (b - a) * (b + a)
	tmp = 0
	if (angle_m / 180.0) <= 2e+206:
		tmp = (2.0 * t_0) * math.sin((math.pi / (180.0 / angle_m)))
	else:
		tmp = 0.011111111111111112 * (angle_m * (math.pi * t_0))
	return angle_s * tmp

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	t_0 = Float64(Float64(b - a) * Float64(b + a))
	tmp = 0.0
	if (Float64(angle_m / 180.0) <= 2e+206)
		tmp = Float64(Float64(2.0 * t_0) * sin(Float64(pi / Float64(180.0 / angle_m))));
	else
		tmp = Float64(0.011111111111111112 * Float64(angle_m * Float64(pi * t_0)));
	end
	return Float64(angle_s * tmp)
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp_2 = code(angle_s, a, b, angle_m)
	t_0 = (b - a) * (b + a);
	tmp = 0.0;
	if ((angle_m / 180.0) <= 2e+206)
		tmp = (2.0 * t_0) * sin((pi / (180.0 / angle_m)));
	else
		tmp = 0.011111111111111112 * (angle_m * (pi * t_0));
	end
	tmp_2 = angle_s * tmp;
end

Wolfram

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_, angle$95$m_] := Block[{t$95$0 = N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]}, N[(angle$95$s * If[LessEqual[N[(angle$95$m / 180.0), $MachinePrecision], 2e+206], N[(N[(2.0 * t$95$0), $MachinePrecision] * N[Sin[N[(Pi / N[(180.0 / angle$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(angle$95$m * N[(Pi * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]]

Derivation

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

Alternative 8: 56.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 9: 56.3% accurate, 2.9× speedup

Math

\[\begin{array}{l} angle_m = \left|angle\right| \\ angle_s = \mathsf{copysign}\left(1, angle\right) \\ angle_s \cdot \left(\left(2 \cdot \left(\left(b - a\right) \cdot \left(b + a\right)\right)\right) \cdot \sin \left(\frac{angle_m}{180} \cdot \pi\right)\right) \end{array} \]

FPCore

angle_m = (fabs.f64 angle)
angle_s = (copysign.f64 1 angle)
(FPCore (angle_s a b angle_m)
 :precision binary64
 (* angle_s (* (* 2.0 (* (- b a) (+ b a))) (sin (* (/ angle_m 180.0) PI)))))

C

angle_m = fabs(angle);
angle_s = copysign(1.0, angle);
double code(double angle_s, double a, double b, double angle_m) {
	return angle_s * ((2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * ((double) M_PI))));
}

Java

angle_m = Math.abs(angle);
angle_s = Math.copySign(1.0, angle);
public static double code(double angle_s, double a, double b, double angle_m) {
	return angle_s * ((2.0 * ((b - a) * (b + a))) * Math.sin(((angle_m / 180.0) * Math.PI)));
}

Python

angle_m = math.fabs(angle)
angle_s = math.copysign(1.0, angle)
def code(angle_s, a, b, angle_m):
	return angle_s * ((2.0 * ((b - a) * (b + a))) * math.sin(((angle_m / 180.0) * math.pi)))

Julia

angle_m = abs(angle)
angle_s = copysign(1.0, angle)
function code(angle_s, a, b, angle_m)
	return Float64(angle_s * Float64(Float64(2.0 * Float64(Float64(b - a) * Float64(b + a))) * sin(Float64(Float64(angle_m / 180.0) * pi))))
end

MATLAB

angle_m = abs(angle);
angle_s = sign(angle) * abs(1.0);
function tmp = code(angle_s, a, b, angle_m)
	tmp = angle_s * ((2.0 * ((b - a) * (b + a))) * sin(((angle_m / 180.0) * pi)));
end

Wolfram

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_, angle$95$m_] := N[(angle$95$s * N[(N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[(angle$95$m / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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

Alternative 10: 56.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 11: 54.6% accurate, 5.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 12: 54.6% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Reproduce

herbie shell --seed 2023350 
(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)))))