ab-angle->ABCF B

Percentage Accurate: 54.9% → 67.6%

Time: 1.1min

Precision: binary64

Cost: 66380

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \pi\right)\\ t_1 := e^{\mathsf{log1p}\left(t_0\right)}\\ t_2 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin t_0 \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin t_2 \cdot \left(\left(a + b\right) \cdot \cos t_2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \left(\sin t_1 \cdot \cos 1 - \cos t_1 \cdot \sin 1\right)\right)\right)\right)\\ \end{array} \]

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 (* 0.011111111111111112 (* angle PI)))
        (t_1 (exp (log1p t_0)))
        (t_2 (* angle (* PI 0.005555555555555556))))
   (if (<= (/ angle 180.0) -1e+182)
     (* 2.0 (* (+ a b) (sqrt (pow (* (sin t_0) (* 0.5 (- b a))) 2.0))))
     (if (<= (/ angle 180.0) -1e-70)
       (*
        (sin (* (/ angle 180.0) PI))
        (*
         (* 2.0 (fma b b (* a (- a))))
         (cos (* 0.005555555555555556 (* angle PI)))))
       (if (<= (/ angle 180.0) 2e+96)
         (* 2.0 (* (- b a) (* (sin t_2) (* (+ a b) (cos t_2)))))
         (*
          2.0
          (*
           (+ a b)
           (*
            (- b a)
            (* 0.5 (- (* (sin t_1) (cos 1.0)) (* (cos t_1) (sin 1.0))))))))))))

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 = 0.011111111111111112 * (angle * ((double) M_PI));
	double t_1 = exp(log1p(t_0));
	double t_2 = angle * (((double) M_PI) * 0.005555555555555556);
	double tmp;
	if ((angle / 180.0) <= -1e+182) {
		tmp = 2.0 * ((a + b) * sqrt(pow((sin(t_0) * (0.5 * (b - a))), 2.0)));
	} else if ((angle / 180.0) <= -1e-70) {
		tmp = sin(((angle / 180.0) * ((double) M_PI))) * ((2.0 * fma(b, b, (a * -a))) * cos((0.005555555555555556 * (angle * ((double) M_PI)))));
	} else if ((angle / 180.0) <= 2e+96) {
		tmp = 2.0 * ((b - a) * (sin(t_2) * ((a + b) * cos(t_2))));
	} else {
		tmp = 2.0 * ((a + b) * ((b - a) * (0.5 * ((sin(t_1) * cos(1.0)) - (cos(t_1) * sin(1.0))))));
	}
	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(0.011111111111111112 * Float64(angle * pi))
	t_1 = exp(log1p(t_0))
	t_2 = Float64(angle * Float64(pi * 0.005555555555555556))
	tmp = 0.0
	if (Float64(angle / 180.0) <= -1e+182)
		tmp = Float64(2.0 * Float64(Float64(a + b) * sqrt((Float64(sin(t_0) * Float64(0.5 * Float64(b - a))) ^ 2.0))));
	elseif (Float64(angle / 180.0) <= -1e-70)
		tmp = Float64(sin(Float64(Float64(angle / 180.0) * pi)) * Float64(Float64(2.0 * fma(b, b, Float64(a * Float64(-a)))) * cos(Float64(0.005555555555555556 * Float64(angle * pi)))));
	elseif (Float64(angle / 180.0) <= 2e+96)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(sin(t_2) * Float64(Float64(a + b) * cos(t_2)))));
	else
		tmp = Float64(2.0 * Float64(Float64(a + b) * Float64(Float64(b - a) * Float64(0.5 * Float64(Float64(sin(t_1) * cos(1.0)) - Float64(cos(t_1) * sin(1.0)))))));
	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[(0.011111111111111112 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[Log[1 + t$95$0], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(angle / 180.0), $MachinePrecision], -1e+182], N[(2.0 * N[(N[(a + b), $MachinePrecision] * N[Sqrt[N[Power[N[(N[Sin[t$95$0], $MachinePrecision] * N[(0.5 * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], -1e-70], N[(N[Sin[N[(N[(angle / 180.0), $MachinePrecision] * Pi), $MachinePrecision]], $MachinePrecision] * N[(N[(2.0 * N[(b * b + N[(a * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 2e+96], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(N[Sin[t$95$2], $MachinePrecision] * N[(N[(a + b), $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(a + b), $MachinePrecision] * N[(N[(b - a), $MachinePrecision] * N[(0.5 * N[(N[(N[Sin[t$95$1], $MachinePrecision] * N[Cos[1.0], $MachinePrecision]), $MachinePrecision] - N[(N[Cos[t$95$1], $MachinePrecision] * N[Sin[1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 angle 180) < -1.0000000000000001e182

   1. Initial program 30.1%

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

   2. Simplified 34.1%

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

      [Start] 30.1	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 30.1	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 30.1	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 30.1	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 30.1	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 34.1	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Applied egg-rr 10.6%

      \[\leadsto 2 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} - 1\right)} \]
      Step-by-step derivation

      [Start] 34.1	\[ 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      expm1-log1p-u [=>] 16.9	\[ 2 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)} \]
      expm1-udef [=>] 15.2	\[ 2 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} - 1\right)} \]

   4. Simplified 30.2%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 10.6	\[ 2 \cdot \left(e^{\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} - 1\right) \]
      expm1-def [=>] 12.2	\[ 2 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)\right)} \]
      expm1-log1p [=>] 30.2	\[ 2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} \]
      +-commutative [=>] 30.2	\[ 2 \cdot \left(\color{blue}{\left(a + b\right)} \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right) \]
      +-lft-identity [=>] 30.2	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\color{blue}{\sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)} \cdot 0.5\right)\right)\right) \]
      *-commutative [=>] 30.2	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \color{blue}{\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \cdot 0.5\right)\right)\right) \]

   5. Applied egg-rr 42.8%

      \[\leadsto 2 \cdot \left(\left(a + b\right) \cdot \color{blue}{\sqrt{{\left(\sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}}\right) \]
      Step-by-step derivation

      [Start] 30.2	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)\right) \]
      add-sqr-sqrt [=>] 16.1	\[ 2 \cdot \left(\left(a + b\right) \cdot \color{blue}{\left(\sqrt{\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)} \cdot \sqrt{\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)}\right)}\right) \]
      sqrt-unprod [=>] 42.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \color{blue}{\sqrt{\left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)}}\right) \]
      pow2 [=>] 42.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{\color{blue}{{\left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)}^{2}}}\right) \]
      *-commutative [=>] 42.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\color{blue}{\left(\left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right) \cdot \left(b - a\right)\right)}}^{2}}\right) \]
      associate-*l* [=>] 42.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\color{blue}{\left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}}^{2}}\right) \]
      *-commutative [=>] 42.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \color{blue}{\left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)} \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right) \]
      associate-*r* [=>] 42.8	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \left(\color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)} \cdot 2\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right) \]
      associate-*l* [=>] 42.8	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \color{blue}{\left(\left(\pi \cdot angle\right) \cdot \left(0.005555555555555556 \cdot 2\right)\right)} \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right) \]
      metadata-eval [=>] 42.8	\[ 2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \left(\left(\pi \cdot angle\right) \cdot \color{blue}{0.011111111111111112}\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right) \]

   if -1.0000000000000001e182 < (/.f64 angle 180) < -9.99999999999999996e-71

   1. Initial program 43.3%

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

   2. Simplified 51.5%

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

      [Start] 43.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 43.3	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 43.3	\[ \color{blue}{\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 43.3	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      fma-neg [=>] 51.5	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \color{blue}{\mathsf{fma}\left(b, b, -{a}^{2}\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 51.5	\[ \sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, -\color{blue}{a \cdot a}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around inf 56.0%

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

   if -9.99999999999999996e-71 < (/.f64 angle 180) < 2.0000000000000001e96

   1. Initial program 65.3%

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

   2. Simplified 69.7%

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

      [Start] 65.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 65.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 65.3	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 65.3	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 65.3	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 69.7	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Taylor expanded in b around 0 66.9%

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

   4. Simplified 91.5%

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

      [Start] 66.9

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

      +-commutative [=>] 66.9

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

   if 2.0000000000000001e96 < (/.f64 angle 180)

   1. Initial program 42.2%

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

   2. Simplified 44.2%

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

      [Start] 42.2	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 42.2	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      associate-*l* [=>] 42.2	\[ \color{blue}{2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      unpow2 [=>] 42.2	\[ 2 \cdot \left(\left(\color{blue}{b \cdot b} - {a}^{2}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      unpow2 [=>] 42.2	\[ 2 \cdot \left(\left(b \cdot b - \color{blue}{a \cdot a}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      difference-of-squares [=>] 44.2	\[ 2 \cdot \left(\color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]

   3. Applied egg-rr 24.1%

      \[\leadsto 2 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} - 1\right)} \]
      Step-by-step derivation

      [Start] 44.2	\[ 2 \cdot \left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \]
      expm1-log1p-u [=>] 20.9	\[ 2 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)} \]
      expm1-udef [=>] 20.0	\[ 2 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\left(\left(b + a\right) \cdot \left(b - a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} - 1\right)} \]

   4. Simplified 48.3%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)\right)} \]
      Step-by-step derivation

      [Start] 24.1	\[ 2 \cdot \left(e^{\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} - 1\right) \]
      expm1-def [=>] 25.0	\[ 2 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)\right)} \]
      expm1-log1p [=>] 48.3	\[ 2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right)} \]
      +-commutative [=>] 48.3	\[ 2 \cdot \left(\color{blue}{\left(a + b\right)} \cdot \left(\left(b - a\right) \cdot \left(\left(0 + \sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)\right) \cdot 0.5\right)\right)\right) \]
      +-lft-identity [=>] 48.3	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\color{blue}{\sin \left(\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2\right)} \cdot 0.5\right)\right)\right) \]
      *-commutative [=>] 48.3	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \color{blue}{\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} \cdot 0.5\right)\right)\right) \]

   5. Applied egg-rr 60.6%

      \[\leadsto 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\color{blue}{\left(\sin \left(e^{\mathsf{log1p}\left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}\right) \cdot \sin 1\right)} \cdot 0.5\right)\right)\right) \]
      Step-by-step derivation

      [Start] 48.3	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot 0.5\right)\right)\right) \]
      expm1-log1p-u [=>] 51.7	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\right)} \cdot 0.5\right)\right)\right) \]
      expm1-udef [=>] 52.1	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin \color{blue}{\left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)} - 1\right)} \cdot 0.5\right)\right)\right) \]
      sin-diff [=>] 60.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\color{blue}{\left(\sin \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \sin 1\right)} \cdot 0.5\right)\right)\right) \]
      *-commutative [=>] 60.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot 2}\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \sin 1\right) \cdot 0.5\right)\right)\right) \]
      associate-*r* [=>] 60.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\color{blue}{\left(\left(\pi \cdot angle\right) \cdot 0.005555555555555556\right)} \cdot 2\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \sin 1\right) \cdot 0.5\right)\right)\right) \]
      associate-*l* [=>] 60.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\color{blue}{\left(\pi \cdot angle\right) \cdot \left(0.005555555555555556 \cdot 2\right)}\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \sin 1\right) \cdot 0.5\right)\right)\right) \]
      metadata-eval [=>] 60.6	\[ 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\left(\pi \cdot angle\right) \cdot \color{blue}{0.011111111111111112}\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}\right) \cdot \sin 1\right) \cdot 0.5\right)\right)\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right) \cdot \left(\left(a + b\right) \cdot \cos \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \left(\sin \left(e^{\mathsf{log1p}\left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)}\right) \cdot \sin 1\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	66.7%
Cost	85508

\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ \mathbf{if}\;\left(\sin t_0 \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \cos t_0 \leq -\infty:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot {\left(\sqrt[3]{0.5 \cdot \sin \left(\sqrt{\pi} \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \sqrt{\pi}\right)\right)}\right)}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot {\left(\sqrt[3]{0.5 \cdot \sin \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.011111111111111112\right)}\right)}^{3}\right)}\right)}^{3}\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	66.9%
Cost	85508

\[\begin{array}{l} t_0 := \frac{angle}{180} \cdot \pi\\ \mathbf{if}\;\left(\sin t_0 \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \cdot \cos t_0 \leq 4 \cdot 10^{+64}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot {\left(\sqrt[3]{0.5 \cdot \sin \left(\sqrt{\pi} \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \sqrt{\pi}\right)\right)}\right)}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot {\left(\sqrt[3]{0.5 \cdot \sin \left({\left(\sqrt[3]{angle \cdot 0.011111111111111112} \cdot \sqrt[3]{\pi}\right)}^{3}\right)}\right)}^{3}\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	67.3%
Cost	40268

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+96}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin t_0 \cdot \left(\left(a + b\right) \cdot \cos t_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot {\left(\sqrt[3]{0.5 \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\right)}\right)}^{3}\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	67.4%
Cost	33672

\[\begin{array}{l} t_0 := angle \cdot \left(\pi \cdot 0.005555555555555556\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -1 \cdot 10^{+182}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \sqrt{{\left(\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(0.5 \cdot \left(b - a\right)\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\sin \left(\frac{angle}{180} \cdot \pi\right) \cdot \left(\left(2 \cdot \mathsf{fma}\left(b, b, a \cdot \left(-a\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{+140}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\sin t_0 \cdot \left(\left(a + b\right) \cdot \cos t_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{a + b}{\frac{2}{b - a}} \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	66.8%
Cost	27212

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+274}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+211}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.85 \cdot 10^{-68}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_0 \cdot \left(\left(a + b\right) \cdot \sin t_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	66.8%
Cost	27212

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+270}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\right)}\right)}^{3}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+211}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-69}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_0 \cdot \left(\left(a + b\right) \cdot \sin t_0\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 7
Accuracy	66.6%
Cost	14348

\[\begin{array}{l} t_0 := 2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{+211}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	66.6%
Cost	14348

\[\begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+269}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(0.5 \cdot \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{+211}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-157}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \frac{0.5}{\frac{1}{b - a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	63.3%
Cost	14224

\[\begin{array}{l} t_0 := \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;b \leq -9.5 \cdot 10^{+274}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(t_0 \cdot \left(b \cdot 0.5\right)\right)\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+211}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-43}:\\ \;\;\;\;2 \cdot \left(\frac{a + b}{\frac{2}{b - a}} \cdot t_0\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-157}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(-0.5 \cdot \left(a \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	65.2%
Cost	14220

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-128}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \frac{angle \cdot 0.005555555555555556}{\frac{\frac{1}{b - a}}{\pi}}\right)\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-143}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(0.5 \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+95}:\\ \;\;\;\;2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(0.5 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	65.1%
Cost	13960

\[\begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{-130}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \frac{angle \cdot 0.005555555555555556}{\frac{\frac{1}{b - a}}{\pi}}\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-52}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \left(0.5 \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b - a\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	64.0%
Cost	13832

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-146}:\\ \;\;\;\;2 \cdot \left(\left(a + b\right) \cdot \frac{angle \cdot 0.005555555555555556}{\frac{\frac{1}{b - a}}{\pi}}\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+89}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(b - a\right)\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	51.9%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-22} \lor \neg \left(b \leq 1.85 \cdot 10^{+82}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	52.0%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{-22}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{+66}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	52.1%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-22}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot b\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	56.6%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;b \leq 10^{+167}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\left(a + b\right) \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	52.0%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{-22} \lor \neg \left(b \leq 1.56 \cdot 10^{+90}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	52.0%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{-23} \lor \neg \left(b \leq 3.75 \cdot 10^{+81}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right) \cdot -0.011111111111111112\\ \end{array} \]

Alternative 19
Accuracy	62.5%
Cost	7168

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

Alternative 20
Accuracy	62.5%
Cost	7168

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

Alternative 21
Accuracy	62.6%
Cost	7168

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

Alternative 22
Accuracy	35.3%
Cost	6912

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

Alternative 23
Accuracy	38.2%
Cost	6912

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

Reproduce

herbie shell --seed 2023162 
(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)))))