ab-angle->ABCF B

Percentage Accurate: 53.7% → 66.8%

Time: 45.8s

Precision: binary64

Cost: 59208

• 33.0% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ t_1 := \sin t_0\\ t_2 := \pi \cdot \left(angle \cdot 0.005555555555555556\right)\\ t_3 := \cos t_2\\ t_4 := 2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot t_1\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{{\sin t_2}^{2}} \cdot \left(t_4 \cdot \cos t_0\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+97}:\\ \;\;\;\;t_1 \cdot \left(t_4 \cdot t_3\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(t_3 \cdot \sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right)\\ \end{array} \]

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 (* (/ angle 180.0) PI))
        (t_1 (sin t_0))
        (t_2 (* PI (* angle 0.005555555555555556)))
        (t_3 (cos t_2))
        (t_4 (* 2.0 (exp (* 2.0 (log (hypot b a)))))))
   (if (<= (/ angle 180.0) -1e+218)
     (* (fma b b (* a (- a))) (* 2.0 t_1))
     (if (<= (/ angle 180.0) -2e+146)
       (* (sqrt (pow (sin t_2) 2.0)) (* t_4 (cos t_0)))
       (if (<= (/ angle 180.0) -2e+97)
         (* t_1 (* t_4 t_3))
         (if (<= (/ angle 180.0) 1e+77)
           (*
            2.0
            (*
             (- b a)
             (*
              (cos (* 0.005555555555555556 (* angle PI)))
              (* (sin (* angle (* PI 0.005555555555555556))) (+ b a)))))
           (*
            (* 2.0 (+ (* b b) (* a a)))
            (* t_3 (sin (* PI (* angle -0.005555555555555556)))))))))))

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 = (angle / 180.0) * ((double) M_PI);
	double t_1 = sin(t_0);
	double t_2 = ((double) M_PI) * (angle * 0.005555555555555556);
	double t_3 = cos(t_2);
	double t_4 = 2.0 * exp((2.0 * log(hypot(b, a))));
	double tmp;
	if ((angle / 180.0) <= -1e+218) {
		tmp = fma(b, b, (a * -a)) * (2.0 * t_1);
	} else if ((angle / 180.0) <= -2e+146) {
		tmp = sqrt(pow(sin(t_2), 2.0)) * (t_4 * cos(t_0));
	} else if ((angle / 180.0) <= -2e+97) {
		tmp = t_1 * (t_4 * t_3);
	} else if ((angle / 180.0) <= 1e+77) {
		tmp = 2.0 * ((b - a) * (cos((0.005555555555555556 * (angle * ((double) M_PI)))) * (sin((angle * (((double) M_PI) * 0.005555555555555556))) * (b + a))));
	} else {
		tmp = (2.0 * ((b * b) + (a * a))) * (t_3 * sin((((double) M_PI) * (angle * -0.005555555555555556))));
	}
	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(Float64(angle / 180.0) * pi)
	t_1 = sin(t_0)
	t_2 = Float64(pi * Float64(angle * 0.005555555555555556))
	t_3 = cos(t_2)
	t_4 = Float64(2.0 * exp(Float64(2.0 * log(hypot(b, a)))))
	tmp = 0.0
	if (Float64(angle / 180.0) <= -1e+218)
		tmp = Float64(fma(b, b, Float64(a * Float64(-a))) * Float64(2.0 * t_1));
	elseif (Float64(angle / 180.0) <= -2e+146)
		tmp = Float64(sqrt((sin(t_2) ^ 2.0)) * Float64(t_4 * cos(t_0)));
	elseif (Float64(angle / 180.0) <= -2e+97)
		tmp = Float64(t_1 * Float64(t_4 * t_3));
	elseif (Float64(angle / 180.0) <= 1e+77)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(cos(Float64(0.005555555555555556 * Float64(angle * pi))) * Float64(sin(Float64(angle * Float64(pi * 0.005555555555555556))) * Float64(b + a)))));
	else
		tmp = Float64(Float64(2.0 * Float64(Float64(b * b) + Float64(a * a))) * Float64(t_3 * sin(Float64(pi * Float64(angle * -0.005555555555555556)))));
	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[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, Block[{t$95$2 = N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Cos[t$95$2], $MachinePrecision]}, Block[{t$95$4 = N[(2.0 * N[Exp[N[(2.0 * N[Log[N[Sqrt[b ^ 2 + a ^ 2], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(angle / 180.0), $MachinePrecision], -1e+218], N[(N[(b * b + N[(a * (-a)), $MachinePrecision]), $MachinePrecision] * N[(2.0 * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], -2e+146], N[(N[Sqrt[N[Power[N[Sin[t$95$2], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision] * N[(t$95$4 * N[Cos[t$95$0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], -2e+97], N[(t$95$1 * N[(t$95$4 * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 1e+77], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(N[Cos[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[Sin[N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(N[(b * b), $MachinePrecision] + N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 * N[Sin[N[(Pi * N[(angle * -0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 angle 180) < -1.00000000000000008e218

   1. Initial program 40.2%

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

   2. Simplified 45.4%

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

      [Start] 40.2	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 40.2	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 40.2	\[ \color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 40.2	\[ \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      fma-neg [=>] 45.4	\[ \left(\color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)} \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 45.4	\[ \left(\mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 45.4	\[ \left(\mathsf{fma}\left(b, b, \color{blue}{a \cdot \left(-a\right)}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Taylor expanded in angle around 0 65.3%

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

   if -1.00000000000000008e218 < (/.f64 angle 180) < -1.99999999999999987e146

   1. Initial program 36.8%

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

   2. Simplified 36.8%

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

      [Start] 36.8	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 36.8	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 36.8	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 36.8	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-neg [=>] 36.8	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 36.8	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 47.2%

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

      [Start] 36.8	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-exp-log [=>] 18.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{e^{\log \left(\mathsf{fma}\left(b, b, -a \cdot a\right)\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 18.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\log \color{blue}{\left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)} \cdot \sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      pow2 [=>] 18.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\log \color{blue}{\left({\left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}^{2}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      log-pow [=>] 18.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\color{blue}{2 \cdot \log \left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-udef [=>] 18.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{\color{blue}{b \cdot b + \left(-a \cdot a\right)}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 9.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{-a \cdot a} \cdot \sqrt{-a \cdot a}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [=>] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{\left(-a \cdot a\right) \cdot \left(-a \cdot a\right)}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqr-neg [=>] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \sqrt{\color{blue}{\left(a \cdot a\right) \cdot \left(a \cdot a\right)}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [<=] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{a \cdot a} \cdot \sqrt{a \cdot a}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [<=] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{a \cdot a}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      hypot-udef [<=] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \color{blue}{\left(\mathsf{hypot}\left(b, a\right)\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   4. Applied egg-rr 76.8%

      \[\leadsto \color{blue}{\sqrt{{\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      Step-by-step derivation

      [Start] 47.2	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 36.4	\[ \color{blue}{\left(\sqrt{\sin \left(\pi \cdot \frac{angle}{180}\right)} \cdot \sqrt{\sin \left(\pi \cdot \frac{angle}{180}\right)}\right)} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [=>] 76.8	\[ \color{blue}{\sqrt{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      pow2 [=>] 76.8	\[ \sqrt{\color{blue}{{\sin \left(\pi \cdot \frac{angle}{180}\right)}^{2}}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      div-inv [=>] 76.8	\[ \sqrt{{\sin \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)}^{2}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      metadata-eval [=>] 76.8	\[ \sqrt{{\sin \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)}^{2}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   if -1.99999999999999987e146 < (/.f64 angle 180) < -2.0000000000000001e97

   1. Initial program 60.1%

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

   2. Simplified 60.1%

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

      [Start] 60.1	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 60.1	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 60.1	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 60.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-neg [=>] 60.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 60.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 70.1%

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

      [Start] 60.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-exp-log [=>] 40.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{e^{\log \left(\mathsf{fma}\left(b, b, -a \cdot a\right)\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 40.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\log \color{blue}{\left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)} \cdot \sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      pow2 [=>] 40.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\log \color{blue}{\left({\left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}^{2}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      log-pow [=>] 40.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{\color{blue}{2 \cdot \log \left(\sqrt{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-udef [=>] 40.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{\color{blue}{b \cdot b + \left(-a \cdot a\right)}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [=>] 20.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{-a \cdot a} \cdot \sqrt{-a \cdot a}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [=>] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{\left(-a \cdot a\right) \cdot \left(-a \cdot a\right)}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqr-neg [=>] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \sqrt{\color{blue}{\left(a \cdot a\right) \cdot \left(a \cdot a\right)}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      sqrt-unprod [<=] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{\sqrt{a \cdot a} \cdot \sqrt{a \cdot a}}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-sqr-sqrt [<=] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\sqrt{b \cdot b + \color{blue}{a \cdot a}}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      hypot-udef [<=] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \color{blue}{\left(\mathsf{hypot}\left(b, a\right)\right)}}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   4. Applied egg-rr 90.1%

      \[\leadsto \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \color{blue}{\left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 1\right)}\right) \]
      Step-by-step derivation

      [Start] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      *-un-lft-identity [=>] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \color{blue}{\left(1 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)}\right) \]
      *-commutative [=>] 70.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \color{blue}{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot 1\right)}\right) \]
      div-inv [=>] 90.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \left(\cos \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right) \cdot 1\right)\right) \]
      metadata-eval [=>] 90.1	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \left(\cos \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right) \cdot 1\right)\right) \]

   if -2.0000000000000001e97 < (/.f64 angle 180) < 9.99999999999999983e76

   1. Initial program 67.3%

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

   2. Simplified 74.2%

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

      [Start] 67.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 67.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 67.3	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 67.3	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 74.2	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around inf 87.8%

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

   4. Applied egg-rr 87.8%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\color{blue}{\left(0 + \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 87.8	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-log-exp [=>] 27.3	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\color{blue}{\log \left(e^{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      *-un-lft-identity [=>] 27.3	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\log \color{blue}{\left(1 \cdot e^{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      log-prod [=>] 27.3	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\color{blue}{\left(\log 1 + \log \left(e^{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      metadata-eval [=>] 27.3	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(\color{blue}{0} + \log \left(e^{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      add-log-exp [<=] 87.8	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(0 + \color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right) \cdot \left(a + b\right)\right)\right)\right) \]

   5. Simplified 87.9%

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

      [Start] 87.8	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(0 + \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      +-lft-identity [=>] 87.8	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      *-commutative [=>] 87.8	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      associate-*l* [=>] 87.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \color{blue}{\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      *-commutative [=>] 87.9	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \color{blue}{\left(0.005555555555555556 \cdot \pi\right)}\right) \cdot \left(a + b\right)\right)\right)\right) \]

   if 9.99999999999999983e76 < (/.f64 angle 180)

   1. Initial program 32.9%

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

   2. Simplified 34.7%

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

      [Start] 32.9	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 32.9	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 32.9	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 32.9	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-neg [=>] 34.7	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 34.7	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 18.0%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)\right)} - 1} \]
      Step-by-step derivation

      [Start] 34.7	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      expm1-log1p-u [=>] 24.0	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)} \]
      expm1-udef [=>] 22.8	\[ \color{blue}{e^{\mathsf{log1p}\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} - 1} \]

   4. Simplified 25.6%

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

      [Start] 18.0	\[ e^{\mathsf{log1p}\left(\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)\right)} - 1 \]
      expm1-def [=>] 19.2	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)\right)\right)} \]
      expm1-log1p [=>] 24.0	\[ \color{blue}{\left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)} \]
      associate-*r* [=>] 25.9	\[ \left(\sin \color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)} \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [<=] 25.9	\[ \left(\sin \left(\color{blue}{\left(angle \cdot \pi\right)} \cdot 0.005555555555555556\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [<=] 25.9	\[ \left(\sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)} \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      associate-*r* [=>] 25.6	\[ \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)}\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [<=] 25.6	\[ \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(\color{blue}{\left(angle \cdot \pi\right)} \cdot 0.005555555555555556\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [<=] 25.6	\[ \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]

   5. Applied egg-rr 9.0%

      \[\leadsto \left(\sin \color{blue}{\left({\left({\left(angle \cdot \pi\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\right)}^{0.5}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      Step-by-step derivation

      [Start] 25.6	\[ \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      add-sqr-sqrt [=>] 29.2	\[ \left(\sin \color{blue}{\left(\sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)} \cdot \sqrt{0.005555555555555556 \cdot \left(angle \cdot \pi\right)}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      sqrt-unprod [=>] 10.8	\[ \left(\sin \color{blue}{\left(\sqrt{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      pow1/2 [=>] 10.8	\[ \left(\sin \color{blue}{\left({\left(\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{0.5}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [=>] 10.8	\[ \left(\sin \left({\left(\color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)} \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      *-commutative [=>] 10.8	\[ \left(\sin \left({\left(\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right) \cdot \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)}\right)}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      swap-sqr [=>] 9.0	\[ \left(\sin \left({\color{blue}{\left(\left(\left(angle \cdot \pi\right) \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.005555555555555556 \cdot 0.005555555555555556\right)\right)}}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      pow2 [=>] 9.0	\[ \left(\sin \left({\left(\color{blue}{{\left(angle \cdot \pi\right)}^{2}} \cdot \left(0.005555555555555556 \cdot 0.005555555555555556\right)\right)}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      metadata-eval [=>] 9.0	\[ \left(\sin \left({\left({\left(angle \cdot \pi\right)}^{2} \cdot \color{blue}{3.08641975308642 \cdot 10^{-5}}\right)}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]

   6. Simplified 9.0%

      \[\leadsto \left(\sin \color{blue}{\left(\sqrt{{\left(angle \cdot \pi\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      Step-by-step derivation

      [Start] 9.0	\[ \left(\sin \left({\left({\left(angle \cdot \pi\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}\right)}^{0.5}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]
      unpow1/2 [=>] 9.0	\[ \left(\sin \color{blue}{\left(\sqrt{{\left(angle \cdot \pi\right)}^{2} \cdot 3.08641975308642 \cdot 10^{-5}}\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right) \]

   7. Taylor expanded in angle around -inf 44.3%

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

   8. Simplified 47.6%

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

      [Start] 44.3	\[ 2 \cdot \left(\left({b}^{2} + {a}^{2}\right) \cdot \left(\sin \left(-0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      associate-*r* [=>] 44.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} + {a}^{2}\right)\right) \cdot \left(\sin \left(-0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} \]
      unpow2 [=>] 44.3	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} + {a}^{2}\right)\right) \cdot \left(\sin \left(-0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
      unpow2 [=>] 44.3	\[ \left(2 \cdot \left(b \cdot b + \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(-0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
      associate-*r* [=>] 41.7	\[ \left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\sin \color{blue}{\left(\left(-0.005555555555555556 \cdot angle\right) \cdot \pi\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
      *-commutative [=>] 41.7	\[ \left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\sin \left(\left(-0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \cos \color{blue}{\left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)}\right) \]
      *-commutative [=>] 41.7	\[ \left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\sin \left(\left(-0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \cos \left(\color{blue}{\left(\pi \cdot angle\right)} \cdot 0.005555555555555556\right)\right) \]
      associate-*r* [<=] 47.6	\[ \left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\sin \left(\left(-0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \cos \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \]
      *-commutative [=>] 47.6	\[ \left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\sin \left(\left(-0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \cos \left(\pi \cdot \color{blue}{\left(0.005555555555555556 \cdot angle\right)}\right)\right) \]

3. Recombined 5 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+146}:\\ \;\;\;\;\sqrt{{\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}^{2}} \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+97}:\\ \;\;\;\;\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	66.7%
Cost	46604

\[\begin{array}{l} t_0 := \sin \left(\frac{angle}{180} \cdot \pi\right)\\ t_1 := \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\\ t_2 := \cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot t_0\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+146}:\\ \;\;\;\;{\left(\sqrt[3]{t_1 \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+97}:\\ \;\;\;\;t_0 \cdot \left(\left(2 \cdot e^{2 \cdot \log \left(\mathsf{hypot}\left(b, a\right)\right)}\right) \cdot t_2\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(t_1 \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(t_2 \cdot \sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	66.8%
Cost	39624

\[\begin{array}{l} t_0 := \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+71}:\\ \;\;\;\;{\left(\sqrt[3]{t_0 \cdot \left(2 \cdot {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\right)}\right)}^{3}\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(t_0 \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	65.7%
Cost	27856

\[\begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_2 := \sin t_1\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+146}:\\ \;\;\;\;\left(2 \cdot t_0\right) \cdot t_2\\ \mathbf{elif}\;\frac{angle}{180} \leq -5 \cdot 10^{+109}:\\ \;\;\;\;t_0 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+91}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_1 \cdot \left(\left(b + a\right) \cdot t_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \sqrt{{\left(\pi \cdot \left(b + a\right)\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	67.0%
Cost	27856

\[\begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+138}:\\ \;\;\;\;\left(2 \cdot t_0\right) \cdot \sin t_1\\ \mathbf{elif}\;\frac{angle}{180} \leq -5 \cdot 10^{+103}:\\ \;\;\;\;t_0 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+77}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_1 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b + a \cdot a\right)\right) \cdot \left(\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	66.7%
Cost	27596

\[\begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{+146}:\\ \;\;\;\;\left(2 \cdot t_0\right) \cdot \sin t_1\\ \mathbf{elif}\;\frac{angle}{180} \leq -4 \cdot 10^{+106}:\\ \;\;\;\;t_0 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_1 \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(b + a\right)\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	63.7%
Cost	26892

\[\begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(b, a\right)\right)}^{2}\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -2 \cdot 10^{+93}:\\ \;\;\;\;\left(2 \cdot t_0\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -0.5:\\ \;\;\;\;t_0 \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+37}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b - a\right)\right) \cdot \left(angle \cdot \left(b + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \sqrt{{\left(\pi \cdot \left(b + a\right)\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	63.8%
Cost	26372

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.5:\\ \;\;\;\;{\left(\mathsf{hypot}\left(b, a\right)\right)}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+37}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b - a\right)\right) \cdot \left(angle \cdot \left(b + a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \sqrt{{\left(\pi \cdot \left(b + a\right)\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	63.8%
Cost	20552

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right) \cdot \left(2 \cdot \sin \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-10}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \sqrt{{\left(\pi \cdot \left(b + a\right)\right)}^{2}}\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	63.9%
Cost	20292

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

Alternative 10
Accuracy	65.1%
Cost	14088

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq 2 \cdot 10^{-5}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\left(b + a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b + a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	64.3%
Cost	13964

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b + a \cdot a\right)\right)\right)\\ \mathbf{if}\;angle \leq -4.7 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 0.0032:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b - a\right)\right) \cdot \left(angle \cdot \left(b + a\right)\right)\right)\\ \mathbf{elif}\;angle \leq 6.8 \cdot 10^{+170}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Accuracy	49.5%
Cost	7568

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 0.00136:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+185}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+200}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Accuracy	54.2%
Cost	7564

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b + a \cdot a\right)\right)\right)\\ \mathbf{if}\;angle \leq -4.7 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 2 \cdot 10^{+170}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\right)\right)\\ \mathbf{elif}\;angle \leq 3.5 \cdot 10^{+234}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	49.7%
Cost	7440

\[\begin{array}{l} t_0 := angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ t_1 := 0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{if}\;b \leq -9 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.00046:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{+196}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{+200}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	63.4%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;angle \leq -4.7 \cdot 10^{+65} \lor \neg \left(angle \leq 1.95 \cdot 10^{+170}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b + a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\pi \cdot \left(b - a\right)\right) \cdot \left(angle \cdot \left(b + a\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	49.4%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+52}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;b \leq 0.0056:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	49.4%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+52}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b \cdot \pi\right) \cdot \left(angle \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-5}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	39.2%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+117} \lor \neg \left(b \leq 5 \cdot 10^{+124}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	39.2%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+150} \lor \neg \left(b \leq 2 \cdot 10^{+53}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 20
Accuracy	39.2%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+112}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-35}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 21
Accuracy	39.2%
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+135}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+132}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 22
Accuracy	34.6%
Cost	6912

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

Alternative 23
Accuracy	34.6%
Cost	6912

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

Reproduce

herbie shell --seed 2023159 
(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)))))