ab-angle->ABCF B

Percentage Accurate: 54.8% → 67.2%

Time: 31.1s

Precision: binary64

Cost: 27596

• 31.9% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ t_1 := \pi \cdot \frac{angle}{180}\\ t_2 := \sin t_1\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t_2 \cdot \left(\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \cos t_1\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 4000000000000:\\ \;\;\;\;2 \cdot \left(\left(\left(b + a\right) \cdot \sin t_0\right) \cdot \left(\left(b - a\right) \cdot \cos t_0\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

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 (* 0.005555555555555556 (* PI angle)))
        (t_1 (* PI (/ angle 180.0)))
        (t_2 (sin t_1)))
   (if (<= (/ angle 180.0) -5e+171)
     (*
      (* 2.0 (* (+ b a) (- b a)))
      (sin (* PI (* angle 0.005555555555555556))))
     (if (<= (/ angle 180.0) -1e+19)
       (* t_2 (* (* 2.0 (+ (* b b) (* a a))) (cos t_1)))
       (if (<= (/ angle 180.0) 4000000000000.0)
         (* 2.0 (* (* (+ b a) (sin t_0)) (* (- b a) (cos t_0))))
         (if (<= (/ angle 180.0) 5e+224)
           (* (fma b b (* a (- a))) (* 2.0 t_2))
           (*
            0.011111111111111112
            (* (cbrt (pow (* (+ b a) PI) 3.0)) (* (- b a) angle)))))))))

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 = 0.005555555555555556 * (((double) M_PI) * angle);
	double t_1 = ((double) M_PI) * (angle / 180.0);
	double t_2 = sin(t_1);
	double tmp;
	if ((angle / 180.0) <= -5e+171) {
		tmp = (2.0 * ((b + a) * (b - a))) * sin((((double) M_PI) * (angle * 0.005555555555555556)));
	} else if ((angle / 180.0) <= -1e+19) {
		tmp = t_2 * ((2.0 * ((b * b) + (a * a))) * cos(t_1));
	} else if ((angle / 180.0) <= 4000000000000.0) {
		tmp = 2.0 * (((b + a) * sin(t_0)) * ((b - a) * cos(t_0)));
	} else if ((angle / 180.0) <= 5e+224) {
		tmp = fma(b, b, (a * -a)) * (2.0 * t_2);
	} else {
		tmp = 0.011111111111111112 * (cbrt(pow(((b + a) * ((double) M_PI)), 3.0)) * ((b - a) * angle));
	}
	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 = Float64(0.005555555555555556 * Float64(pi * angle))
	t_1 = Float64(pi * Float64(angle / 180.0))
	t_2 = sin(t_1)
	tmp = 0.0
	if (Float64(angle / 180.0) <= -5e+171)
		tmp = Float64(Float64(2.0 * Float64(Float64(b + a) * Float64(b - a))) * sin(Float64(pi * Float64(angle * 0.005555555555555556))));
	elseif (Float64(angle / 180.0) <= -1e+19)
		tmp = Float64(t_2 * Float64(Float64(2.0 * Float64(Float64(b * b) + Float64(a * a))) * cos(t_1)));
	elseif (Float64(angle / 180.0) <= 4000000000000.0)
		tmp = Float64(2.0 * Float64(Float64(Float64(b + a) * sin(t_0)) * Float64(Float64(b - a) * cos(t_0))));
	elseif (Float64(angle / 180.0) <= 5e+224)
		tmp = Float64(fma(b, b, Float64(a * Float64(-a))) * Float64(2.0 * t_2));
	else
		tmp = Float64(0.011111111111111112 * Float64(cbrt((Float64(Float64(b + a) * pi) ^ 3.0)) * Float64(Float64(b - a) * angle)));
	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[(0.005555555555555556 * N[(Pi * angle), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sin[t$95$1], $MachinePrecision]}, If[LessEqual[N[(angle / 180.0), $MachinePrecision], -5e+171], N[(N[(2.0 * N[(N[(b + a), $MachinePrecision] * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], -1e+19], N[(t$95$2 * N[(N[(2.0 * N[(N[(b * b), $MachinePrecision] + N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 4000000000000.0], N[(2.0 * N[(N[(N[(b + a), $MachinePrecision] * N[Sin[t$95$0], $MachinePrecision]), $MachinePrecision] * N[(N[(b - a), $MachinePrecision] * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 5e+224], N[(N[(b * b + N[(a * (-a)), $MachinePrecision]), $MachinePrecision] * N[(2.0 * t$95$2), $MachinePrecision]), $MachinePrecision], N[(0.011111111111111112 * N[(N[Power[N[Power[N[(N[(b + a), $MachinePrecision] * Pi), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $MachinePrecision] * N[(N[(b - a), $MachinePrecision] * angle), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 angle 180) < -5.0000000000000004e171

   1. Initial program 33.1%

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

   2. Simplified 33.1%

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

      [Start] 33.1%	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 33.1%	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 33.1%	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 33.1%	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 33.1%	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around inf 30.7%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   4. Simplified 36.0%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\color{blue}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      Step-by-step derivation

      [Start] 30.7%	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      *-commutative [=>] 30.7%	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      *-commutative [<=] 30.7%	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot 0.005555555555555556\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      associate-*r* [<=] 36.0%	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      *-commutative [=>] 36.0%	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \color{blue}{\left(0.005555555555555556 \cdot angle\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   5. Taylor expanded in angle around 0 44.9%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right) \cdot \color{blue}{1}\right) \]

   if -5.0000000000000004e171 < (/.f64 angle 180) < -1e19

   1. Initial program 27.0%

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

   2. Simplified 27.0%

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

      [Start] 27.0%	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 27.0%	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 27.0%	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 27.0%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-neg [=>] 27.0%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 27.0%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 35.8%

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

      [Start] 27.0%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-udef [=>] 27.0%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\left(b \cdot b + \left(-a \cdot a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 10.7%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + \color{blue}{\sqrt{-a \cdot a} \cdot \sqrt{-a \cdot a}}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [=>] 35.5%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + \color{blue}{\sqrt{\left(-a \cdot a\right) \cdot \left(-a \cdot a\right)}}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqr-neg [=>] 35.5%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + \sqrt{\color{blue}{\left(a \cdot a\right) \cdot \left(a \cdot a\right)}}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [<=] 35.8%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + \color{blue}{\sqrt{a \cdot a} \cdot \sqrt{a \cdot a}}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [<=] 35.8%	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + \color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   if -1e19 < (/.f64 angle 180) < 4e12

   1. Initial program 78.0%

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

   2. Simplified 83.4%

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

      [Start] 78.0%	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 78.0%	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 78.0%	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 78.0%	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 83.4%	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around inf 99.0%

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

   4. Simplified 99.0%

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

      [Start] 99.0%	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      associate-*r* [=>] 99.0%	\[ 2 \cdot \color{blue}{\left(\left(\left(b - a\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)} \]
      *-commutative [=>] 99.0%	\[ 2 \cdot \color{blue}{\left(\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right) \cdot \left(\left(b - a\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]
      +-commutative [<=] 99.0%	\[ 2 \cdot \left(\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(b - a\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]

   if 4e12 < (/.f64 angle 180) < 4.99999999999999964e224

   1. Initial program 24.7%

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

   2. Simplified 31.0%

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

      [Start] 24.7%	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 24.7%	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 24.7%	\[ \color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 24.7%	\[ \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      fma-neg [=>] 31.0%	\[ \left(\color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)} \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 31.0%	\[ \left(\mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 31.0%	\[ \left(\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-a\right)}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Taylor expanded in angle around 0 44.0%

      \[\leadsto \left(\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \color{blue}{1} \]

   if 4.99999999999999964e224 < (/.f64 angle 180)

   1. Initial program 20.1%

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

   2. Simplified 28.4%

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

      [Start] 20.1%	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 20.1%	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 20.1%	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 20.1%	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 28.4%	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around 0 51.6%

      \[\leadsto \color{blue}{0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot \left(a + b\right)\right)\right)\right)} \]

   4. Simplified 51.6%

      \[\leadsto \color{blue}{0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 51.6%	\[ 0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot \left(a + b\right)\right)\right)\right) \]
      associate-*r* [=>] 51.6%	\[ 0.011111111111111112 \cdot \color{blue}{\left(\left(angle \cdot \left(b - a\right)\right) \cdot \left(\pi \cdot \left(a + b\right)\right)\right)} \]
      *-commutative [=>] 51.6%	\[ 0.011111111111111112 \cdot \color{blue}{\left(\left(\pi \cdot \left(a + b\right)\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)} \]
      +-commutative [<=] 51.6%	\[ 0.011111111111111112 \cdot \left(\left(\pi \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]

   5. Applied egg-rr 51.9%

      \[\leadsto 0.011111111111111112 \cdot \left(\color{blue}{\sqrt[3]{{\left(\pi \cdot \left(b + a\right)\right)}^{3}}} \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]
      Step-by-step derivation

      [Start] 51.6%	\[ 0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]
      add-cbrt-cube [=>] 51.9%	\[ 0.011111111111111112 \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\pi \cdot \left(b + a\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)}} \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]
      pow3 [=>] 51.9%	\[ 0.011111111111111112 \cdot \left(\sqrt[3]{\color{blue}{{\left(\pi \cdot \left(b + a\right)\right)}^{3}}} \cdot \left(angle \cdot \left(b - a\right)\right)\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+19}:\\ \;\;\;\;\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 4000000000000:\\ \;\;\;\;2 \cdot \left(\left(\left(b + a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right) \cdot \left(\left(b - a\right) \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	67.2%
Cost	27596

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ t_1 := \pi \cdot \frac{angle}{180}\\ t_2 := \sin t_1\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+171}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t_2 \cdot \left(\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \cos t_1\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 4000000000000:\\ \;\;\;\;2 \cdot \left(\left(\left(b + a\right) \cdot \sin t_0\right) \cdot \left(\left(b - a\right) \cdot \cos t_0\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot t_2\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	63.8%
Cost	33412

\[\begin{array}{l} \mathbf{if}\;{b}^{2} \leq 10^{-113}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(\pi \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	66.8%
Cost	27596

\[\begin{array}{l} t_0 := \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ t_1 := 0.005555555555555556 \cdot \left(\pi \cdot angle\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -2 \cdot 10^{+205}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot t_0\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+19}:\\ \;\;\;\;{\left(b + a\right)}^{2} \cdot \left(2 \cdot t_0\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 4000000000000:\\ \;\;\;\;2 \cdot \left(\left(\left(b + a\right) \cdot \sin t_1\right) \cdot \left(\left(b - a\right) \cdot \cos t_1\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	64.5%
Cost	20876

\[\begin{array}{l} t_0 := \left(b - a\right) \cdot angle\\ t_1 := {\left(\left(b + a\right) \cdot \pi\right)}^{3}\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+154}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+100}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+212}:\\ \;\;\;\;0.011111111111111112 \cdot \left(t_0 \cdot {t_1}^{0.3333333333333333}\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{t_1} \cdot t_0\right)\\ \end{array} \]

Alternative 5
Accuracy	64.8%
Cost	20812

\[\begin{array}{l} t_0 := 2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t_0 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-25}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;t_0 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	64.8%
Cost	20812

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+154}:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-25}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\sqrt[3]{{\left(\left(b + a\right) \cdot \pi\right)}^{3}} \cdot \left(\left(b - a\right) \cdot angle\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	64.8%
Cost	14476

\[\begin{array}{l} t_0 := 2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t_0 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-25}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 5 \cdot 10^{+224}:\\ \;\;\;\;t_0 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	63.4%
Cost	13960

\[\begin{array}{l} t_0 := \left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-128}:\\ \;\;\;\;t_0 \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \mathbf{elif}\;b \leq 31:\\ \;\;\;\;\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\\ \end{array} \]

Alternative 9
Accuracy	56.5%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+181} \lor \neg \left(b \leq 1.12 \cdot 10^{-45}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(b - a\right) \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	53.5%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;a \leq -50000000 \lor \neg \left(a \leq 650000\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(b - a\right) \cdot angle\right) \cdot \left(a \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	54.7%
Cost	7305

\[\begin{array}{l} t_0 := \left(b - a\right) \cdot angle\\ \mathbf{if}\;a \leq -75000000 \lor \neg \left(a \leq 1650000\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(t_0 \cdot \left(a \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(t_0 \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	63.0%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(b - a\right) \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	63.0%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(b - a\right) \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	63.0%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -4.2 \cdot 10^{+27}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(b - a\right) \cdot angle\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot angle\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 15
Accuracy	46.4%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -68000000 \lor \neg \left(a \leq 5 \cdot 10^{+117}\right):\\ \;\;\;\;angle \cdot \left(a \cdot \left(a \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	46.3%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -2000000000:\\ \;\;\;\;angle \cdot \left(a \cdot \left(a \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+117}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	46.3%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -240000000:\\ \;\;\;\;\pi \cdot \left(-0.011111111111111112 \cdot \left(angle \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+117}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	46.3%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;a \leq -1050000000:\\ \;\;\;\;\pi \cdot \left(-0.011111111111111112 \cdot \left(angle \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+117}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	35.3%
Cost	6912

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

Reproduce

herbie shell --seed 2023263 
(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)))))