ab-angle->ABCF B

Percentage Accurate: 53.9% → 66.6%

Time: 44.7s

Precision: binary64

Cost: 91976

• 32.8% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \pi \cdot \left(angle \cdot 0.005555555555555556\right)\\ t_2 := e^{\mathsf{log1p}\left(t_1\right)}\\ \mathbf{if}\;\frac{angle}{180} \leq -10000000000:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos t_0 \cdot \left(\left(a + b\right) \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(t_0\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin t_2 \cdot \cos 1 - \cos t_2 \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{t_1}\right)}^{3}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* 0.005555555555555556 (* angle PI)))
        (t_1 (* PI (* angle 0.005555555555555556)))
        (t_2 (exp (log1p t_1))))
   (if (<= (/ angle 180.0) -10000000000.0)
     (*
      (+ a b)
      (* (- b a) (sqrt (pow (sin (* angle (* PI 0.011111111111111112))) 2.0))))
     (if (<= (/ angle 180.0) 2e+85)
       (* 2.0 (* (- b a) (* (cos t_0) (* (+ a b) (sin (expm1 (log1p t_0)))))))
       (*
        (* 2.0 (* (+ a b) (- b a)))
        (*
         (- (* (sin t_2) (cos 1.0)) (* (cos t_2) (sin 1.0)))
         (cos (pow (cbrt t_1) 3.0))))))))

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 = 0.005555555555555556 * (angle * ((double) M_PI));
	double t_1 = ((double) M_PI) * (angle * 0.005555555555555556);
	double t_2 = exp(log1p(t_1));
	double tmp;
	if ((angle / 180.0) <= -10000000000.0) {
		tmp = (a + b) * ((b - a) * sqrt(pow(sin((angle * (((double) M_PI) * 0.011111111111111112))), 2.0)));
	} else if ((angle / 180.0) <= 2e+85) {
		tmp = 2.0 * ((b - a) * (cos(t_0) * ((a + b) * sin(expm1(log1p(t_0))))));
	} else {
		tmp = (2.0 * ((a + b) * (b - a))) * (((sin(t_2) * cos(1.0)) - (cos(t_2) * sin(1.0))) * cos(pow(cbrt(t_1), 3.0)));
	}
	return tmp;
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = 0.005555555555555556 * (angle * Math.PI);
	double t_1 = Math.PI * (angle * 0.005555555555555556);
	double t_2 = Math.exp(Math.log1p(t_1));
	double tmp;
	if ((angle / 180.0) <= -10000000000.0) {
		tmp = (a + b) * ((b - a) * Math.sqrt(Math.pow(Math.sin((angle * (Math.PI * 0.011111111111111112))), 2.0)));
	} else if ((angle / 180.0) <= 2e+85) {
		tmp = 2.0 * ((b - a) * (Math.cos(t_0) * ((a + b) * Math.sin(Math.expm1(Math.log1p(t_0))))));
	} else {
		tmp = (2.0 * ((a + b) * (b - a))) * (((Math.sin(t_2) * Math.cos(1.0)) - (Math.cos(t_2) * Math.sin(1.0))) * Math.cos(Math.pow(Math.cbrt(t_1), 3.0)));
	}
	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(0.005555555555555556 * Float64(angle * pi))
	t_1 = Float64(pi * Float64(angle * 0.005555555555555556))
	t_2 = exp(log1p(t_1))
	tmp = 0.0
	if (Float64(angle / 180.0) <= -10000000000.0)
		tmp = Float64(Float64(a + b) * Float64(Float64(b - a) * sqrt((sin(Float64(angle * Float64(pi * 0.011111111111111112))) ^ 2.0))));
	elseif (Float64(angle / 180.0) <= 2e+85)
		tmp = Float64(2.0 * Float64(Float64(b - a) * Float64(cos(t_0) * Float64(Float64(a + b) * sin(expm1(log1p(t_0)))))));
	else
		tmp = Float64(Float64(2.0 * Float64(Float64(a + b) * Float64(b - a))) * Float64(Float64(Float64(sin(t_2) * cos(1.0)) - Float64(cos(t_2) * sin(1.0))) * cos((cbrt(t_1) ^ 3.0))));
	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[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[Log[1 + t$95$1], $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(angle / 180.0), $MachinePrecision], -10000000000.0], N[(N[(a + b), $MachinePrecision] * N[(N[(b - a), $MachinePrecision] * N[Sqrt[N[Power[N[Sin[N[(angle * N[(Pi * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 2e+85], N[(2.0 * N[(N[(b - a), $MachinePrecision] * N[(N[Cos[t$95$0], $MachinePrecision] * N[(N[(a + b), $MachinePrecision] * N[Sin[N[(Exp[N[Log[1 + t$95$0], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(N[(a + b), $MachinePrecision] * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[Sin[t$95$2], $MachinePrecision] * N[Cos[1.0], $MachinePrecision]), $MachinePrecision] - N[(N[Cos[t$95$2], $MachinePrecision] * N[Sin[1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[Power[N[Power[t$95$1, 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 angle 180) < -1e10

   1. Initial program 30.3%

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

   2. Simplified 31.9%

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

      [Start] 30.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 30.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 30.3	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 30.3	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 31.9	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 27.4%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)}\right) \]
      Step-by-step derivation

      [Start] 31.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-cube-cbrt [=>] 25.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right) \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)}\right) \]
      pow3 [=>] 28.1	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\pi \cdot \frac{angle}{180}}\right)}^{3}\right)}\right) \]
      div-inv [=>] 27.4	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}}\right)}^{3}\right)\right) \]
      metadata-eval [=>] 27.4	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)}\right)}^{3}\right)\right) \]

   4. Applied egg-rr 18.9%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(2 \cdot \frac{\left(b \cdot b - a \cdot a\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)}{2}\right)} - 1} \]
      Step-by-step derivation

      [Start] 27.4	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      expm1-log1p-u [=>] 15.7	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)\right)\right)} \]
      expm1-udef [=>] 14.8	\[ \color{blue}{e^{\mathsf{log1p}\left(\left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)\right)} - 1} \]

   5. Simplified 32.1%

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

      [Start] 18.9	\[ e^{\mathsf{log1p}\left(2 \cdot \frac{\left(b \cdot b - a \cdot a\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)}{2}\right)} - 1 \]
      expm1-def [=>] 19.8	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(2 \cdot \frac{\left(b \cdot b - a \cdot a\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)}{2}\right)\right)} \]
      expm1-log1p [=>] 28.5	\[ \color{blue}{2 \cdot \frac{\left(b \cdot b - a \cdot a\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)}{2}} \]
      associate-/l* [=>] 28.5	\[ 2 \cdot \color{blue}{\frac{b \cdot b - a \cdot a}{\frac{2}{\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}}} \]
      associate-*r/ [=>] 28.5	\[ \color{blue}{\frac{2 \cdot \left(b \cdot b - a \cdot a\right)}{\frac{2}{\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)}}} \]
      associate-/r/ [=>] 28.5	\[ \color{blue}{\frac{2 \cdot \left(b \cdot b - a \cdot a\right)}{2} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)} \]
      *-commutative [=>] 28.5	\[ \frac{\color{blue}{\left(b \cdot b - a \cdot a\right) \cdot 2}}{2} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      associate-/l* [=>] 28.5	\[ \color{blue}{\frac{b \cdot b - a \cdot a}{\frac{2}{2}}} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      metadata-eval [=>] 28.5	\[ \frac{b \cdot b - a \cdot a}{\color{blue}{1}} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      /-rgt-identity [=>] 28.5	\[ \color{blue}{\left(b \cdot b - a \cdot a\right)} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      difference-of-squares [=>] 30.2	\[ \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)} \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      +-commutative [<=] 30.2	\[ \left(\color{blue}{\left(a + b\right)} \cdot \left(b - a\right)\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right) \]
      associate-*l* [=>] 30.2	\[ \color{blue}{\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\sin 0 + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)\right)} \]
      sin-0 [=>] 30.2	\[ \left(a + b\right) \cdot \left(\left(b - a\right) \cdot \left(\color{blue}{0} + \sin \left(\left(\pi \cdot angle\right) \cdot 0.011111111111111112\right)\right)\right) \]

   6. Applied egg-rr 42.5%

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

      [Start] 32.1	\[ \left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right) \]
      add-sqr-sqrt [=>] 24.8	\[ \left(a + b\right) \cdot \left(\left(b - a\right) \cdot \color{blue}{\left(\sqrt{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)} \cdot \sqrt{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}\right)}\right) \]
      sqrt-unprod [=>] 42.5	\[ \left(a + b\right) \cdot \left(\left(b - a\right) \cdot \color{blue}{\sqrt{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}}\right) \]
      pow2 [=>] 42.5	\[ \left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{\color{blue}{{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}^{2}}}\right) \]

   if -1e10 < (/.f64 angle 180) < 2e85

   1. Initial program 75.0%

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

   2. Simplified 79.7%

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

      [Start] 75.0	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 75.0	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 75.0	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 75.0	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 79.7	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Taylor expanded in angle around inf 93.5%

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

   4. Applied egg-rr 94.5%

      \[\leadsto 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]
      Step-by-step derivation

      [Start] 93.5	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right)\right) \]
      expm1-log1p-u [=>] 94.5	\[ 2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \left(a + b\right)\right)\right)\right) \]

   if 2e85 < (/.f64 angle 180)

   1. Initial program 30.5%

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

   2. Simplified 30.5%

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

      [Start] 30.5	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 30.5	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 30.5	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 30.5	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 30.5	\[ \left(2 \cdot \color{blue}{\left(\left(b + a\right) \cdot \left(b - a\right)\right)}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 26.2%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)}\right) \]
      Step-by-step derivation

      [Start] 30.5	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      add-cube-cbrt [=>] 29.1	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\pi \cdot \frac{angle}{180}} \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right) \cdot \sqrt[3]{\pi \cdot \frac{angle}{180}}\right)}\right) \]
      pow3 [=>] 27.1	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\pi \cdot \frac{angle}{180}}\right)}^{3}\right)}\right) \]
      div-inv [=>] 26.2	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}}\right)}^{3}\right)\right) \]
      metadata-eval [=>] 26.2	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)}\right)}^{3}\right)\right) \]

   4. Applied egg-rr 41.9%

      \[\leadsto \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\color{blue}{\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \sin 1\right)} \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      Step-by-step derivation

      [Start] 26.2	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      expm1-log1p-u [=>] 43.6	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      expm1-udef [=>] 40.1	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \color{blue}{\left(e^{\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)} - 1\right)} \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      sin-diff [=>] 41.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\color{blue}{\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sin 1\right)} \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      div-inv [=>] 41.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      metadata-eval [=>] 41.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \frac{angle}{180}\right)}\right) \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      div-inv [=>] 41.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)}\right) \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]
      metadata-eval [=>] 41.9	\[ \left(2 \cdot \left(\left(b + a\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)}\right) \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -10000000000:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{+85}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(a + b\right) \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\left(\sin \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \cos 1 - \cos \left(e^{\mathsf{log1p}\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \sin 1\right) \cdot \cos \left({\left(\sqrt[3]{\pi \cdot \left(angle \cdot 0.005555555555555556\right)}\right)}^{3}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	68.0%
Cost	40136

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}^{2}}\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 1.5 \cdot 10^{+274}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(a + b\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right) \cdot \left(\sin \left(e^{\log \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right) \cdot \cos \left(\frac{angle}{180} \cdot \pi\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	68.0%
Cost	27076

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{{\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(b - a\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left(a + b\right) \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	67.8%
Cost	26692

\[\begin{array}{l} t_0 := \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot \sqrt{{t_0}^{2}}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(b - a\right) \cdot t_0\right)\\ \end{array} \]

Alternative 4
Accuracy	62.0%
Cost	13972

\[\begin{array}{l} t_0 := \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ t_1 := t_0 \cdot \left(b \cdot b\right)\\ \mathbf{if}\;angle \leq -4.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;angle \leq 260000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{elif}\;angle \leq 2.4 \cdot 10^{+123}:\\ \;\;\;\;t_0 \cdot \left(-a \cdot a\right)\\ \mathbf{elif}\;angle \leq 5.4 \cdot 10^{+180}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;angle \leq 2.7 \cdot 10^{+277}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	62.4%
Cost	13968

\[\begin{array}{l} t_0 := \left(a + b\right) \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{if}\;angle \leq -2.6:\\ \;\;\;\;t_0\\ \mathbf{elif}\;angle \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{elif}\;angle \leq 1.05 \cdot 10^{+127}:\\ \;\;\;\;a \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;angle \leq 2.45 \cdot 10^{+182}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	62.4%
Cost	13900

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.8:\\ \;\;\;\;\left(a + b\right) \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 0.55:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{elif}\;angle \leq 2.4 \cdot 10^{+121}:\\ \;\;\;\;\left(a + b\right) \cdot \left(\left(-a\right) \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(b \cdot b\right)\\ \end{array} \]

Alternative 7
Accuracy	62.4%
Cost	13900

\[\begin{array}{l} t_0 := \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;angle \leq -8:\\ \;\;\;\;\left(a + b\right) \cdot \left(b \cdot t_0\right)\\ \mathbf{elif}\;angle \leq 1.9:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{elif}\;angle \leq 1.5 \cdot 10^{+121}:\\ \;\;\;\;\left(a + b\right) \cdot \left(a \cdot \left(-t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(b \cdot b\right)\\ \end{array} \]

Alternative 8
Accuracy	64.1%
Cost	13840

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{-85}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(\left(-a\right) \cdot t_0\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{+253}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b - a\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+291}:\\ \;\;\;\;b \cdot \left(b \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 9
Accuracy	66.9%
Cost	13833

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.5 \cdot 10^{-83} \lor \neg \left(angle \leq 2.5 \cdot 10^{-19}\right):\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(b - a\right)\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	64.8%
Cost	13708

\[\begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+181}:\\ \;\;\;\;a \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right) \cdot \left(-a\right)\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b - a\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(b - a\right) \cdot \pi\right) \cdot \left(\left(a + b\right) \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	67.8%
Cost	13568

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

Alternative 12
Accuracy	60.9%
Cost	13444

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{if}\;angle \leq -24500:\\ \;\;\;\;\left|t_0\right|\\ \mathbf{elif}\;angle \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Accuracy	61.6%
Cost	13444

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.9:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{elif}\;angle \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	61.6%
Cost	13444

\[\begin{array}{l} \mathbf{if}\;angle \leq -6:\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(b \cdot b\right)\\ \mathbf{elif}\;angle \leq 1.1 \cdot 10^{+51}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	57.1%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+53} \lor \neg \left(b \leq 1.5 \cdot 10^{+137}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\left(a + b\right) \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	57.1%
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -1.65 \cdot 10^{+53} \lor \neg \left(b \leq 1.05 \cdot 10^{+140}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	61.1%
Cost	7432

\[\begin{array}{l} \mathbf{if}\;angle \leq -24500:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;angle \leq 5.2 \cdot 10^{+51}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(\left(a + b\right) \cdot \pi\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	52.1%
Cost	7305

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+27} \lor \neg \left(b \leq 2.4 \cdot 10^{+18}\right):\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(b \cdot \left(angle \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	52.1%
Cost	7304

\[\begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(b \cdot \left(angle \cdot b\right)\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(\pi \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 20
Accuracy	52.1%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+27} \lor \neg \left(b \leq 2.8 \cdot 10^{+18}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 21
Accuracy	52.1%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+27} \lor \neg \left(b \leq 1.5 \cdot 10^{+19}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(a \cdot \pi\right)\right) \cdot \left(angle \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 22
Accuracy	52.1%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+27} \lor \neg \left(b \leq 4.5 \cdot 10^{+19}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 23
Accuracy	52.1%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.62 \cdot 10^{+32} \lor \neg \left(b \leq 2.25 \cdot 10^{+18}\right):\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(b \cdot \left(angle \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 24
Accuracy	34.8%
Cost	6912

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

Alternative 25
Accuracy	34.8%
Cost	6912

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

Alternative 26
Accuracy	38.4%
Cost	6912

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

Reproduce

herbie shell --seed 2023161 
(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)))))