ab-angle->ABCF B

Percentage Accurate: 54.6% → 66.3%

Time: 49.4s

Precision: binary64

Cost: 52808

• 32.6% of points produce a very large (infinite) output. You may want to add a precondition.

Math

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

↓

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot \pi}\\ t_1 := \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\\ \mathbf{if}\;b \leq -5 \cdot 10^{+191}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(t_1 \cdot \cos \left(0.005555555555555556 \cdot {\left({\left(\sqrt[3]{t_0}\right)}^{3}\right)}^{3}\right)\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(t_1 \cdot \cos \left(\sqrt[3]{\pi} \cdot \left(\left(0.005555555555555556 \cdot angle\right) \cdot {\left(\sqrt[3]{\pi}\right)}^{2}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+219}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {t_0}^{3}\right) \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot \sin \left(\frac{1}{\frac{180}{angle \cdot \pi}}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* angle PI)))
        (t_1 (* (sin (* 0.005555555555555556 (* angle PI))) (+ a b))))
   (if (<= b -5e+191)
     (*
      2.0
      (*
       (- b a)
       (* t_1 (cos (* 0.005555555555555556 (pow (pow (cbrt t_0) 3.0) 3.0))))))
     (if (<= b -2.8e-149)
       (*
        2.0
        (*
         (- b a)
         (*
          t_1
          (cos
           (*
            (cbrt PI)
            (* (* 0.005555555555555556 angle) (pow (cbrt PI) 2.0)))))))
       (if (<= b 4.3e+219)
         (*
          2.0
          (* (- b a) (* (cos (* 0.005555555555555556 (pow t_0 3.0))) t_1)))
         (*
          2.0
          (* (* (- b a) (+ a b)) (sin (/ 1.0 (/ 180.0 (* angle PI)))))))))))

C

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

↓

double code(double a, double b, double angle) {
	double t_0 = cbrt((angle * ((double) M_PI)));
	double t_1 = sin((0.005555555555555556 * (angle * ((double) M_PI)))) * (a + b);
	double tmp;
	if (b <= -5e+191) {
		tmp = 2.0 * ((b - a) * (t_1 * cos((0.005555555555555556 * pow(pow(cbrt(t_0), 3.0), 3.0)))));
	} else if (b <= -2.8e-149) {
		tmp = 2.0 * ((b - a) * (t_1 * cos((cbrt(((double) M_PI)) * ((0.005555555555555556 * angle) * pow(cbrt(((double) M_PI)), 2.0))))));
	} else if (b <= 4.3e+219) {
		tmp = 2.0 * ((b - a) * (cos((0.005555555555555556 * pow(t_0, 3.0))) * t_1));
	} else {
		tmp = 2.0 * (((b - a) * (a + b)) * sin((1.0 / (180.0 / (angle * ((double) M_PI))))));
	}
	return tmp;
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt((angle * Math.PI));
	double t_1 = Math.sin((0.005555555555555556 * (angle * Math.PI))) * (a + b);
	double tmp;
	if (b <= -5e+191) {
		tmp = 2.0 * ((b - a) * (t_1 * Math.cos((0.005555555555555556 * Math.pow(Math.pow(Math.cbrt(t_0), 3.0), 3.0)))));
	} else if (b <= -2.8e-149) {
		tmp = 2.0 * ((b - a) * (t_1 * Math.cos((Math.cbrt(Math.PI) * ((0.005555555555555556 * angle) * Math.pow(Math.cbrt(Math.PI), 2.0))))));
	} else if (b <= 4.3e+219) {
		tmp = 2.0 * ((b - a) * (Math.cos((0.005555555555555556 * Math.pow(t_0, 3.0))) * t_1));
	} else {
		tmp = 2.0 * (((b - a) * (a + b)) * Math.sin((1.0 / (180.0 / (angle * Math.PI)))));
	}
	return tmp;
}

Julia

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

↓

function code(a, b, angle)
	t_0 = cbrt(Float64(angle * pi))
	t_1 = Float64(sin(Float64(0.005555555555555556 * Float64(angle * pi))) * Float64(a + b))
	tmp = 0.0
	if (b <= -5e+191)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(t_1 * cos(Float64(0.005555555555555556 * ((cbrt(t_0) ^ 3.0) ^ 3.0))))));
	elseif (b <= -2.8e-149)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(t_1 * cos(Float64(cbrt(pi) * Float64(Float64(0.005555555555555556 * angle) * (cbrt(pi) ^ 2.0)))))));
	elseif (b <= 4.3e+219)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(cos(Float64(0.005555555555555556 * (t_0 ^ 3.0))) * t_1)));
	else
		tmp = Float64(2.0 * Float64(Float64(Float64(b - a) * Float64(a + b)) * sin(Float64(1.0 / Float64(180.0 / Float64(angle * pi))))));
	end
	return tmp
end

Wolfram

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

↓

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(angle * Pi), $MachinePrecision], 1/3], $MachinePrecision]}, Block[{t$95$1 = N[(N[Sin[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(a + b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5e+191], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(t$95$1 * N[Cos[N[(0.005555555555555556 * N[Power[N[Power[N[Power[t$95$0, 1/3], $MachinePrecision], 3.0], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-149], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(t$95$1 * N[Cos[N[(N[Power[Pi, 1/3], $MachinePrecision] * N[(N[(0.005555555555555556 * angle), $MachinePrecision] * N[Power[N[Power[Pi, 1/3], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+219], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(N[Cos[N[(0.005555555555555556 * N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[(b - a), $MachinePrecision] * N[(a + b), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(1.0 / N[(180.0 / N[(angle * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.0000000000000002e191

   1. Initial program 46.7%

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   2. Simplified 54.4%

      \[\leadsto \color{blue}{2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 46.7	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 46.7	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 46.7	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 46.7	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 46.7	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 54.4	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Taylor expanded in angle around inf 65.2%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right)} \]

   4. Applied egg-rr 72.9%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 65.2	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-cube-cbrt [=>] 72.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{\left(\left(\sqrt[3]{angle \cdot \pi} \cdot \sqrt[3]{angle \cdot \pi}\right) \cdot \sqrt[3]{angle \cdot \pi}\right)}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      pow3 [=>] 72.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]

   5. Applied egg-rr 80.6%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{angle \cdot \pi}}\right)}^{3}\right)}}^{3}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 72.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-cube-cbrt [=>] 76.7	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{angle \cdot \pi}} \cdot \sqrt[3]{\sqrt[3]{angle \cdot \pi}}\right) \cdot \sqrt[3]{\sqrt[3]{angle \cdot \pi}}\right)}}^{3}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      pow3 [=>] 80.6	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{angle \cdot \pi}}\right)}^{3}\right)}}^{3}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]

   if -5.0000000000000002e191 < b < -2.7999999999999999e-149

   1. Initial program 49.3%

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   2. Simplified 49.3%

      \[\leadsto \color{blue}{2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 49.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 49.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 49.3	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 49.3	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 49.3	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 49.3	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Taylor expanded in angle around inf 61.5%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right)} \]

   4. Applied egg-rr 38.7%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left({\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)}^{2}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 61.5	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-sqr-sqrt [=>] 38.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)} \cdot \sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      pow2 [=>] 38.7	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left({\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)}^{2}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]

   5. Applied egg-rr 71.0%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(\left(\left(0.005555555555555556 \cdot angle\right) \cdot {\left(\sqrt[3]{\pi}\right)}^{2}\right) \cdot \sqrt[3]{\pi}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 38.7	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left({\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)}^{2}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      unpow2 [=>] 38.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)} \cdot \sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-sqr-sqrt [<=] 61.5	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      associate-*r* [=>] 62.1	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-cube-cbrt [=>] 70.1	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(\left(0.005555555555555556 \cdot angle\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right) \cdot \sqrt[3]{\pi}\right)}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      associate-*r* [=>] 71.0	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \color{blue}{\left(\left(\left(0.005555555555555556 \cdot angle\right) \cdot \left(\sqrt[3]{\pi} \cdot \sqrt[3]{\pi}\right)\right) \cdot \sqrt[3]{\pi}\right)} \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      pow2 [=>] 71.0	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(\left(\left(0.005555555555555556 \cdot angle\right) \cdot \color{blue}{{\left(\sqrt[3]{\pi}\right)}^{2}}\right) \cdot \sqrt[3]{\pi}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]

   if -2.7999999999999999e-149 < b < 4.2999999999999997e219

   1. Initial program 62.6%

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   2. Simplified 62.6%

      \[\leadsto \color{blue}{2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 62.6	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 62.6	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 62.6	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 62.6	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 62.6	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 62.6	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Taylor expanded in angle around inf 70.2%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right)} \]

   4. Applied egg-rr 73.5%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 70.2	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-cube-cbrt [=>] 73.2	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{\left(\left(\sqrt[3]{angle \cdot \pi} \cdot \sqrt[3]{angle \cdot \pi}\right) \cdot \sqrt[3]{angle \cdot \pi}\right)}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      pow3 [=>] 73.5	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \color{blue}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]

   if 4.2999999999999997e219 < b

   1. Initial program 53.4%

      \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   2. Simplified 73.4%

      \[\leadsto \color{blue}{2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 53.4	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 53.4	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 53.4	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 53.4	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 53.4	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 73.4	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Applied egg-rr 53.4%

      \[\leadsto 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \color{blue}{\left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      Step-by-step derivation

      [Start] 73.4	\[ 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      associate-*r/ [=>] 66.8	\[ 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \color{blue}{\left(\frac{\pi \cdot angle}{180}\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      clear-num [=>] 53.4	\[ 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \color{blue}{\left(\frac{1}{\frac{180}{\pi \cdot angle}}\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   4. Taylor expanded in angle around 0 86.8%

      \[\leadsto 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\frac{1}{\frac{180}{\pi \cdot angle}}\right) \cdot \color{blue}{1}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+191}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right) \cdot \cos \left(0.005555555555555556 \cdot {\left({\left(\sqrt[3]{\sqrt[3]{angle \cdot \pi}}\right)}^{3}\right)}^{3}\right)\right)\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-149}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right) \cdot \cos \left(\sqrt[3]{\pi} \cdot \left(\left(0.005555555555555556 \cdot angle\right) \cdot {\left(\sqrt[3]{\pi}\right)}^{2}\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+219}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\left(\sqrt[3]{angle \cdot \pi}\right)}^{3}\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot \sin \left(\frac{1}{\frac{180}{angle \cdot \pi}}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	67.9%
Cost	71940

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot \pi}\\ t_1 := \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\\ t_2 := t_1 \cdot \left(a + b\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\left({\left({\left(\sqrt[3]{t_0}\right)}^{2}\right)}^{1.5}\right)}^{3}\right) \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(t_1\right)\right) \cdot \left(a + b\right)\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {t_0}^{3}\right) \cdot t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(t_2 \cdot \cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	67.9%
Cost	59140

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot \pi}\\ t_1 := \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{-230}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {\left({\left({\left(\sqrt[3]{t_0}\right)}^{2}\right)}^{1.5}\right)}^{3}\right) \cdot t_1\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+152}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot {t_0}^{3}\right) \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(t_1 \cdot \cos \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	67.6%
Cost	33476

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := \left(b - a\right) \cdot \left(a + b\right)\\ t_2 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \left(\sin \left(\left|t_0\right|\right) \cdot \cos t_0\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(\sin t_2 \cdot \left(a + b\right)\right) \cdot \cos t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \sin \left(\frac{1}{\frac{180}{angle \cdot \pi}}\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	67.6%
Cost	27336

\[\begin{array}{l} t_0 := \left(b - a\right) \cdot \left(a + b\right)\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+32}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(\sin t_1 \cdot \left(a + b\right)\right) \cdot \cos t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_0 \cdot \sin \left(\frac{1}{\frac{180}{angle \cdot \pi}}\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	67.9%
Cost	14345

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+50} \lor \neg \left(\frac{angle}{180} \leq 2 \cdot 10^{+56}\right):\\ \;\;\;\;2 \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	68.0%
Cost	14345

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{+135} \lor \neg \left(\frac{angle}{180} \leq 2 \cdot 10^{+56}\right):\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	67.9%
Cost	14344

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{+135}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+49}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot \sin \left(\frac{1}{\frac{180}{angle \cdot \pi}}\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	60.3%
Cost	14221

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+154}:\\ \;\;\;\;\left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-22} \lor \neg \left(a \leq 2.5 \cdot 10^{-149}\right):\\ \;\;\;\;2 \cdot \left(\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	58.3%
Cost	13964

\[\begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{+121}:\\ \;\;\;\;\left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-16}:\\ \;\;\;\;angle \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-147}:\\ \;\;\;\;2 \cdot \left(b \cdot \left(b \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot 0.5\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \pi\right) \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 10
Accuracy	57.6%
Cost	7696

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ t_1 := \left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{+121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.15 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-149}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+115}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	57.7%
Cost	7696

\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ t_1 := \left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.15 \cdot 10^{-19}:\\ \;\;\;\;angle \cdot \left(t_0 \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-149}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+113}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	57.0%
Cost	7565

\[\begin{array}{l} \mathbf{if}\;b \leq -1.45 \cdot 10^{+182} \lor \neg \left(b \leq 1.95 \cdot 10^{+152}\right) \land b \leq 5.4 \cdot 10^{+219}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \pi\right) \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 13
Accuracy	56.9%
Cost	7564

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{+156}:\\ \;\;\;\;2 \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot \left(a + b\right)\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+219}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \pi\right) \cdot \left(\left(\left(b - a\right) \cdot \left(a + b\right)\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 14
Accuracy	38.3%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{+178} \lor \neg \left(b \leq 10^{+59}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	39.1%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+140} \lor \neg \left(b \leq 3.5 \cdot 10^{+18}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	51.5%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{+77} \lor \neg \left(b \leq 0.029\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot -0.011111111111111112\right) \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	53.5%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -8000000000 \lor \neg \left(a \leq 1.4 \cdot 10^{-8}\right):\\ \;\;\;\;\left(a \cdot \left(a \cdot angle\right)\right) \cdot \left(\pi \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(b \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	34.3%
Cost	6912

\[0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right) \]

Reproduce

herbie shell --seed 2023160 
(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)))))