ab-angle->ABCF B

Average Accuracy: 51.1% → 66.9%

Time: 23.5s

Precision: binary64

Cost: 53192

Math

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

↓

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ t_1 := \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\\ t_2 := \pi \cdot \frac{angle}{180}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+238}:\\ \;\;\;\;\cos t_2 \cdot \left(\left(a - b\right) \cdot \left(t_1 \cdot \left(-2 \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_0 \leq 10^{+292}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin t_2 \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{t_1}}\\ \end{array} \]

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 (- (pow b 2.0) (pow a 2.0)))
        (t_1 (sin (* PI (* 0.005555555555555556 angle))))
        (t_2 (* PI (/ angle 180.0))))
   (if (<= t_0 -5e+238)
     (* (cos t_2) (* (- a b) (* t_1 (* -2.0 a))))
     (if (<= t_0 1e+292)
       (*
        (* 2.0 (- (* b b) (* a a)))
        (* (sin t_2) (cos (/ PI (/ 180.0 angle)))))
       (* (- a b) (/ (+ a b) (/ (/ (/ (- a b) -2.0) (- a b)) t_1)))))))

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 = pow(b, 2.0) - pow(a, 2.0);
	double t_1 = sin((((double) M_PI) * (0.005555555555555556 * angle)));
	double t_2 = ((double) M_PI) * (angle / 180.0);
	double tmp;
	if (t_0 <= -5e+238) {
		tmp = cos(t_2) * ((a - b) * (t_1 * (-2.0 * a)));
	} else if (t_0 <= 1e+292) {
		tmp = (2.0 * ((b * b) - (a * a))) * (sin(t_2) * cos((((double) M_PI) / (180.0 / angle))));
	} else {
		tmp = (a - b) * ((a + b) / ((((a - b) / -2.0) / (a - b)) / t_1));
	}
	return tmp;
}

Java

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

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.pow(b, 2.0) - Math.pow(a, 2.0);
	double t_1 = Math.sin((Math.PI * (0.005555555555555556 * angle)));
	double t_2 = Math.PI * (angle / 180.0);
	double tmp;
	if (t_0 <= -5e+238) {
		tmp = Math.cos(t_2) * ((a - b) * (t_1 * (-2.0 * a)));
	} else if (t_0 <= 1e+292) {
		tmp = (2.0 * ((b * b) - (a * a))) * (Math.sin(t_2) * Math.cos((Math.PI / (180.0 / angle))));
	} else {
		tmp = (a - b) * ((a + b) / ((((a - b) / -2.0) / (a - b)) / t_1));
	}
	return tmp;
}

Python

def code(a, b, 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)))

↓

def code(a, b, angle):
	t_0 = math.pow(b, 2.0) - math.pow(a, 2.0)
	t_1 = math.sin((math.pi * (0.005555555555555556 * angle)))
	t_2 = math.pi * (angle / 180.0)
	tmp = 0
	if t_0 <= -5e+238:
		tmp = math.cos(t_2) * ((a - b) * (t_1 * (-2.0 * a)))
	elif t_0 <= 1e+292:
		tmp = (2.0 * ((b * b) - (a * a))) * (math.sin(t_2) * math.cos((math.pi / (180.0 / angle))))
	else:
		tmp = (a - b) * ((a + b) / ((((a - b) / -2.0) / (a - b)) / t_1))
	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((b ^ 2.0) - (a ^ 2.0))
	t_1 = sin(Float64(pi * Float64(0.005555555555555556 * angle)))
	t_2 = Float64(pi * Float64(angle / 180.0))
	tmp = 0.0
	if (t_0 <= -5e+238)
		tmp = Float64(cos(t_2) * Float64(Float64(a - b) * Float64(t_1 * Float64(-2.0 * a))));
	elseif (t_0 <= 1e+292)
		tmp = Float64(Float64(2.0 * Float64(Float64(b * b) - Float64(a * a))) * Float64(sin(t_2) * cos(Float64(pi / Float64(180.0 / angle)))));
	else
		tmp = Float64(Float64(a - b) * Float64(Float64(a + b) / Float64(Float64(Float64(Float64(a - b) / -2.0) / Float64(a - b)) / t_1)));
	end
	return tmp
end

MATLAB

function tmp = code(a, b, angle)
	tmp = ((2.0 * ((b ^ 2.0) - (a ^ 2.0))) * sin((pi * (angle / 180.0)))) * cos((pi * (angle / 180.0)));
end

↓

function tmp_2 = code(a, b, angle)
	t_0 = (b ^ 2.0) - (a ^ 2.0);
	t_1 = sin((pi * (0.005555555555555556 * angle)));
	t_2 = pi * (angle / 180.0);
	tmp = 0.0;
	if (t_0 <= -5e+238)
		tmp = cos(t_2) * ((a - b) * (t_1 * (-2.0 * a)));
	elseif (t_0 <= 1e+292)
		tmp = (2.0 * ((b * b) - (a * a))) * (sin(t_2) * cos((pi / (180.0 / angle))));
	else
		tmp = (a - b) * ((a + b) / ((((a - b) / -2.0) / (a - b)) / t_1));
	end
	tmp_2 = 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[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[N[(Pi * N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+238], N[(N[Cos[t$95$2], $MachinePrecision] * N[(N[(a - b), $MachinePrecision] * N[(t$95$1 * N[(-2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+292], N[(N[(2.0 * N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[Sin[t$95$2], $MachinePrecision] * N[Cos[N[(Pi / N[(180.0 / angle), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a - b), $MachinePrecision] * N[(N[(a + b), $MachinePrecision] / N[(N[(N[(N[(a - b), $MachinePrecision] / -2.0), $MachinePrecision] / N[(a - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -4.99999999999999995e238

   1. Initial program 23.8%

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

   2. Simplified 23.8%

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

      [Start] 23.8	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 23.8	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub-neg [=>] 23.8	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 23.8	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      neg-sub0 [=>] 23.8	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-+l- [=>] 23.8	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub0-neg [=>] 23.8	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-lft-neg-out [=>] 23.8	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 23.8	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 23.8	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 23.8	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 23.8	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Applied egg-rr 14.2%

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

      [Start] 23.8	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 24.0	\[ \color{blue}{\left(\left(a \cdot a - b \cdot b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 24.0	\[ \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 77.0	\[ \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      flip-+ [=>] 24.0	\[ \left(\color{blue}{\frac{a \cdot a - b \cdot b}{a - b}} \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l/ [=>] 14.2	\[ \color{blue}{\frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}{a - b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      div-inv [=>] 14.2	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 14.2	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   4. Simplified 76.4%

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

      [Start] 14.2	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 23.8	\[ \color{blue}{\frac{a \cdot a - b \cdot b}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 23.8	\[ \frac{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 76.3	\[ \color{blue}{\frac{a + b}{\frac{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{a - b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/r/ [=>] 76.4	\[ \color{blue}{\left(\frac{a + b}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}} \cdot \left(a - b\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   5. Taylor expanded in b around 0 76.7%

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

   6. Simplified 76.7%

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

      [Start] 76.7	\[ \left(\left(-2 \cdot \left(a \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [=>] 76.7	\[ \left(\color{blue}{\left(\left(-2 \cdot a\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 76.7	\[ \left(\color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-2 \cdot a\right)\right)} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [=>] 76.7	\[ \left(\left(\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)} \cdot \left(-2 \cdot a\right)\right) \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 76.7	\[ \left(\left(\sin \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)} \cdot \left(-2 \cdot a\right)\right) \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   if -4.99999999999999995e238 < (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < 1e292

   1. Initial program 62.1%

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

   2. Simplified 62.1%

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

      [Start] 62.1	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 62.1	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 62.1	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 62.1	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 62.0%

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

      [Start] 62.1	\[ \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      clear-num [=>] 62.0	\[ \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \color{blue}{\frac{1}{\frac{180}{angle}}}\right)\right) \]
      un-div-inv [=>] 62.0	\[ \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \color{blue}{\left(\frac{\pi}{\frac{180}{angle}}\right)}\right) \]

   if 1e292 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 8.0%

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

   2. Simplified 8.0%

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

      [Start] 8.0	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 8.0	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub-neg [=>] 8.0	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 8.0	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      neg-sub0 [=>] 8.0	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-+l- [=>] 8.0	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub0-neg [=>] 8.0	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-lft-neg-out [=>] 8.0	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 8.0	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 8.0	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 8.0	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 8.0	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Applied egg-rr 3.7%

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

      [Start] 8.0	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 8.2	\[ \color{blue}{\left(\left(a \cdot a - b \cdot b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 8.2	\[ \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 90.4	\[ \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      flip-+ [=>] 8.2	\[ \left(\color{blue}{\frac{a \cdot a - b \cdot b}{a - b}} \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l/ [=>] 3.7	\[ \color{blue}{\frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)}{a - b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      div-inv [=>] 3.7	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \color{blue}{\left(angle \cdot \frac{1}{180}\right)}\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 3.7	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot \color{blue}{0.005555555555555556}\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   4. Simplified 90.1%

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

      [Start] 3.7	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 8.2	\[ \color{blue}{\frac{a \cdot a - b \cdot b}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 8.2	\[ \frac{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 90.0	\[ \color{blue}{\frac{a + b}{\frac{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{a - b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/r/ [=>] 90.1	\[ \color{blue}{\left(\frac{a + b}{\frac{a - b}{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}} \cdot \left(a - b\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   5. Applied egg-rr 3.1%

      \[\leadsto \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\color{blue}{e^{\mathsf{log1p}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} - 1}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      Proof

      [Start] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      expm1-log1p-u [=>] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      expm1-udef [=>] 3.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\color{blue}{e^{\mathsf{log1p}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} - 1}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   6. Simplified 90.1%

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

      [Start] 3.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{e^{\mathsf{log1p}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} - 1}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      expm1-def [=>] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      expm1-log1p [=>] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [=>] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 90.1	\[ \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \color{blue}{\left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}} \cdot \left(a - b\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   7. Taylor expanded in angle around 0 89.6%

      \[\leadsto \left(\frac{b + a}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}} \cdot \left(a - b\right)\right) \cdot \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{+238}:\\ \;\;\;\;\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(a - b\right) \cdot \left(\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right) \cdot \left(-2 \cdot a\right)\right)\right)\\ \mathbf{elif}\;{b}^{2} - {a}^{2} \leq 10^{+292}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	66.5%
Cost	53192

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := \frac{\frac{a - b}{-2}}{a - b}\\ t_2 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{t_1}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\\ \mathbf{elif}\;t_2 \leq 10^{+292}:\\ \;\;\;\;2 \cdot \left(\sin t_0 \cdot \left(\cos t_0 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{t_1}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}\\ \end{array} \]

Alternative 2
Accuracy	66.5%
Cost	53192

\[\begin{array}{l} t_0 := \frac{\frac{a - b}{-2}}{a - b}\\ t_1 := \pi \cdot \frac{angle}{180}\\ t_2 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{t_0}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}}\\ \mathbf{elif}\;t_2 \leq 10^{+292}:\\ \;\;\;\;\left(2 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \left(\cos t_1 \cdot \sin t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{t_0}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}\\ \end{array} \]

Alternative 3
Accuracy	66.7%
Cost	52936

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ t_1 := \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\\ t_2 := \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t_2 \cdot \left(-2 \cdot \left(a \cdot \left(t_1 \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_0 \leq 10^{+292}:\\ \;\;\;\;t_2 \cdot \left(t_1 \cdot \left(2 \cdot \left(b \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{a + b}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)}}\\ \end{array} \]

Alternative 4
Accuracy	67.0%
Cost	46208

\[\left(\left(-2 \cdot \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(a + b\right)\right)\right) \cdot \left(a - b\right)\right) \cdot \cos \left(\sqrt[3]{angle} \cdot \frac{\pi \cdot {\left(\sqrt[3]{angle}\right)}^{2}}{180}\right) \]

Alternative 5
Accuracy	67.0%
Cost	27328

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \left(\left(a - b\right) \cdot \frac{a + b}{\frac{\frac{\frac{a - b}{-2}}{a - b}}{\sin t_0}}\right) \cdot \cos t_0 \end{array} \]

Alternative 6
Accuracy	66.9%
Cost	27328

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

Alternative 7
Accuracy	66.9%
Cost	27328

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

Alternative 8
Accuracy	65.3%
Cost	14208

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

Alternative 9
Accuracy	66.6%
Cost	14089

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -5000 \lor \neg \left(\frac{angle}{180} \leq 10^{-47}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 10
Accuracy	62.3%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;angle \leq -3100:\\ \;\;\;\;\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 11
Accuracy	62.3%
Cost	13572

\[\begin{array}{l} \mathbf{if}\;angle \leq -62000:\\ \;\;\;\;\left(a \cdot a\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 12
Accuracy	61.6%
Cost	13444

\[\begin{array}{l} \mathbf{if}\;angle \leq -240000:\\ \;\;\;\;-0.011111111111111112 \cdot \left|\pi \cdot \left(angle \cdot \left(a \cdot a\right)\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 13
Accuracy	61.4%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(\pi \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	61.5%
Cost	7300

\[\begin{array}{l} \mathbf{if}\;angle \leq -6.5 \cdot 10^{+26}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(\pi \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(a + b\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 15
Accuracy	40.7%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{+153} \lor \neg \left(a \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(a \cdot \left(\pi \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	49.2%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-26} \lor \neg \left(a \leq 1.35 \cdot 10^{-20}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(\pi \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	49.2%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-27} \lor \neg \left(a \leq 1.7 \cdot 10^{-20}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(b \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 18
Accuracy	51.3%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{-58} \lor \neg \left(b \leq 1.45 \cdot 10^{-37}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(\pi \cdot \left(angle \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 19
Accuracy	51.3%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-57} \lor \neg \left(b \leq 4.5 \cdot 10^{-39}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot -0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 20
Accuracy	38.7%
Cost	6912

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

Reproduce

herbie shell --seed 2023135 
(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)))))