ab-angle->ABCF B

Average Error: 31.4 → 22.0

Time: 20.9s

Precision: binary64

Cost: 53192

Math

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

↓

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ t_1 := {b}^{2} - {a}^{2}\\ t_2 := \frac{1}{a + b}\\ t_3 := \pi \cdot \frac{angle}{180}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+128}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{t_2}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\sin t_3 \cdot \left(\cos t_0 \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot t_0\right)}{t_2} \cdot \cos t_3\\ \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* angle (* 0.005555555555555556 PI)))
        (t_1 (- (pow b 2.0) (pow a 2.0)))
        (t_2 (/ 1.0 (+ a b)))
        (t_3 (* PI (/ angle 180.0))))
   (if (<= t_1 -5e+128)
     (/ (* -2.0 (* (- a b) (sin (* 0.005555555555555556 (* angle PI))))) t_2)
     (if (<= t_1 5e+301)
       (* (sin t_3) (* (cos t_0) (* 2.0 (- (* b b) (* a a)))))
       (* (/ (* -2.0 (* (- a b) t_0)) t_2) (cos t_3))))))

C

double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin((((double) M_PI) * (angle / 180.0)))) * cos((((double) M_PI) * (angle / 180.0)));
}

↓

double code(double a, double b, double angle) {
	double t_0 = angle * (0.005555555555555556 * ((double) M_PI));
	double t_1 = pow(b, 2.0) - pow(a, 2.0);
	double t_2 = 1.0 / (a + b);
	double t_3 = ((double) M_PI) * (angle / 180.0);
	double tmp;
	if (t_1 <= -5e+128) {
		tmp = (-2.0 * ((a - b) * sin((0.005555555555555556 * (angle * ((double) M_PI)))))) / t_2;
	} else if (t_1 <= 5e+301) {
		tmp = sin(t_3) * (cos(t_0) * (2.0 * ((b * b) - (a * a))));
	} else {
		tmp = ((-2.0 * ((a - b) * t_0)) / t_2) * cos(t_3);
	}
	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 = angle * (0.005555555555555556 * Math.PI);
	double t_1 = Math.pow(b, 2.0) - Math.pow(a, 2.0);
	double t_2 = 1.0 / (a + b);
	double t_3 = Math.PI * (angle / 180.0);
	double tmp;
	if (t_1 <= -5e+128) {
		tmp = (-2.0 * ((a - b) * Math.sin((0.005555555555555556 * (angle * Math.PI))))) / t_2;
	} else if (t_1 <= 5e+301) {
		tmp = Math.sin(t_3) * (Math.cos(t_0) * (2.0 * ((b * b) - (a * a))));
	} else {
		tmp = ((-2.0 * ((a - b) * t_0)) / t_2) * Math.cos(t_3);
	}
	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 = angle * (0.005555555555555556 * math.pi)
	t_1 = math.pow(b, 2.0) - math.pow(a, 2.0)
	t_2 = 1.0 / (a + b)
	t_3 = math.pi * (angle / 180.0)
	tmp = 0
	if t_1 <= -5e+128:
		tmp = (-2.0 * ((a - b) * math.sin((0.005555555555555556 * (angle * math.pi))))) / t_2
	elif t_1 <= 5e+301:
		tmp = math.sin(t_3) * (math.cos(t_0) * (2.0 * ((b * b) - (a * a))))
	else:
		tmp = ((-2.0 * ((a - b) * t_0)) / t_2) * math.cos(t_3)
	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(angle * Float64(0.005555555555555556 * pi))
	t_1 = Float64((b ^ 2.0) - (a ^ 2.0))
	t_2 = Float64(1.0 / Float64(a + b))
	t_3 = Float64(pi * Float64(angle / 180.0))
	tmp = 0.0
	if (t_1 <= -5e+128)
		tmp = Float64(Float64(-2.0 * Float64(Float64(a - b) * sin(Float64(0.005555555555555556 * Float64(angle * pi))))) / t_2);
	elseif (t_1 <= 5e+301)
		tmp = Float64(sin(t_3) * Float64(cos(t_0) * Float64(2.0 * Float64(Float64(b * b) - Float64(a * a)))));
	else
		tmp = Float64(Float64(Float64(-2.0 * Float64(Float64(a - b) * t_0)) / t_2) * cos(t_3));
	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 = angle * (0.005555555555555556 * pi);
	t_1 = (b ^ 2.0) - (a ^ 2.0);
	t_2 = 1.0 / (a + b);
	t_3 = pi * (angle / 180.0);
	tmp = 0.0;
	if (t_1 <= -5e+128)
		tmp = (-2.0 * ((a - b) * sin((0.005555555555555556 * (angle * pi))))) / t_2;
	elseif (t_1 <= 5e+301)
		tmp = sin(t_3) * (cos(t_0) * (2.0 * ((b * b) - (a * a))));
	else
		tmp = ((-2.0 * ((a - b) * t_0)) / t_2) * cos(t_3);
	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[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(a + b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+128], N[(N[(-2.0 * N[(N[(a - b), $MachinePrecision] * N[Sin[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 5e+301], N[(N[Sin[t$95$3], $MachinePrecision] * N[(N[Cos[t$95$0], $MachinePrecision] * N[(2.0 * N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(-2.0 * N[(N[(a - b), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -5e128

   1. Initial program 41.0

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

   2. Simplified 41.0

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

      [Start] 41.0	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 41.0	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub-neg [=>] 41.0	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 41.0	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      neg-sub0 [=>] 41.0	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-+l- [=>] 41.0	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub0-neg [=>] 41.0	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-lft-neg-out [=>] 41.0	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 41.0	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 41.0	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 41.0	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 41.0	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Applied egg-rr 46.0

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

   4. Simplified 21.0

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

      [Start] 46.0	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 46.0	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \left(a \cdot a - b \cdot b\right)}}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 40.9	\[ \color{blue}{\frac{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 40.9	\[ \frac{\color{blue}{\left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(a - b\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 40.9	\[ \frac{\color{blue}{-2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(a - b\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [<=] 40.9	\[ \frac{-2 \cdot \color{blue}{\left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 40.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 40.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [<=] 41.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 41.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 41.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a - b\right) \cdot \left(a + b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/r* [=>] 21.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\color{blue}{\frac{\frac{a - b}{a - b}}{a + b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-inverses [=>] 21.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{\color{blue}{1}}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 21.0	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{\color{blue}{b + a}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   5. Taylor expanded in angle around 0 21.8

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

   if -5e128 < (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < 5.0000000000000004e301

   1. Initial program 24.3

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

   2. Simplified 24.3

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

      [Start] 24.3	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 24.3	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      unpow2 [=>] 24.3	\[ \left(2 \cdot \left(\color{blue}{b \cdot b} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 24.3	\[ \left(2 \cdot \left(b \cdot b - \color{blue}{a \cdot a}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   3. Applied egg-rr 40.0

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

   4. Simplified 32.6

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

      [Start] 40.0	\[ \left(2 \cdot \sqrt{{\left(b \cdot b - a \cdot a\right)}^{2}}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      unpow2 [=>] 40.0	\[ \left(2 \cdot \sqrt{\color{blue}{\left(b \cdot b - a \cdot a\right) \cdot \left(b \cdot b - a \cdot a\right)}}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      rem-sqrt-square [=>] 32.6	\[ \left(2 \cdot \color{blue}{\left|b \cdot b - a \cdot a\right|}\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      difference-of-squares [=>] 32.6	\[ \left(2 \cdot \left|\color{blue}{\left(b + a\right) \cdot \left(b - a\right)}\right|\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   5. Applied egg-rr 48.1

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

   6. Applied egg-rr 44.0

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

   7. Simplified 24.4

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

      [Start] 44.0	\[ e^{\mathsf{log1p}\left(\sin \left(\frac{angle}{\frac{180}{\pi}}\right) \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\right)} - 1 \]
      expm1-def [=>] 28.6	\[ \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left(\frac{angle}{\frac{180}{\pi}}\right) \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\right)\right)} \]
      expm1-log1p [=>] 24.3	\[ \color{blue}{\sin \left(\frac{angle}{\frac{180}{\pi}}\right) \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)} \]
      associate-/r/ [=>] 24.4	\[ \sin \color{blue}{\left(\frac{angle}{180} \cdot \pi\right)} \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right) \]

   if 5.0000000000000004e301 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 61.9

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

   2. Simplified 61.9

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

      [Start] 61.9	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 61.9	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub-neg [=>] 61.9	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 61.9	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      neg-sub0 [=>] 61.9	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-+l- [=>] 61.9	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      sub0-neg [=>] 61.9	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-lft-neg-out [=>] 61.9	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      distribute-rgt-neg-in [=>] 61.9	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 61.9	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      unpow2 [=>] 61.9	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      metadata-eval [=>] 61.9	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   3. Applied egg-rr 63.0

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

   4. Simplified 5.1

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

      [Start] 63.0	\[ \frac{\left(a \cdot a - b \cdot b\right) \cdot \left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 63.0	\[ \frac{\color{blue}{\left(\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \left(a \cdot a - b \cdot b\right)}}{a - b} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/l* [=>] 61.9	\[ \color{blue}{\frac{\left(a - b\right) \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 61.9	\[ \frac{\color{blue}{\left(-2 \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right) \cdot \left(a - b\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*l* [=>] 61.9	\[ \frac{\color{blue}{-2 \cdot \left(\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(a - b\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [<=] 61.9	\[ \frac{-2 \cdot \color{blue}{\left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)}}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 61.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 61.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [<=] 61.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)}{\frac{a - b}{a \cdot a - b \cdot b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      difference-of-squares [=>] 61.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a + b\right) \cdot \left(a - b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 61.9	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{a - b}{\color{blue}{\left(a - b\right) \cdot \left(a + b\right)}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-/r* [=>] 5.1	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\color{blue}{\frac{\frac{a - b}{a - b}}{a + b}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-inverses [=>] 5.1	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{\color{blue}{1}}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      +-commutative [=>] 5.1	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{\color{blue}{b + a}}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

   5. Taylor expanded in angle around 0 5.3

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

   6. Simplified 5.3

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

      [Start] 5.3	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{b + a}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [=>] 5.4	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)}{\frac{1}{b + a}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      *-commutative [=>] 5.4	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)}{\frac{1}{b + a}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      associate-*r* [<=] 5.3	\[ \frac{-2 \cdot \left(\left(a - b\right) \cdot \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right)}{\frac{1}{b + a}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 22.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{+128}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{a + b}}\\ \mathbf{elif}\;{b}^{2} - {a}^{2} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}{\frac{1}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	21.8
Cost	53192

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+226}:\\ \;\;\;\;\cos \left(\frac{\pi}{\frac{180}{angle}}\right) \cdot \left(-2 \cdot \left(a \cdot \left(a \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;2 \cdot \left(\left(\sin t_0 \cdot \left(b \cdot b - a \cdot a\right)\right) \cdot \cos t_0\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}{\frac{1}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 2
Error	21.9
Cost	46920

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ t_1 := \frac{1}{a + b}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+151}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{t_1}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}{t_1} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 3
Error	21.8
Cost	46920

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+226}:\\ \;\;\;\;\cos \left(\frac{\pi}{\frac{180}{angle}}\right) \cdot \left(-2 \cdot \left(a \cdot \left(a \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right)\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)}{\frac{1}{a + b}} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 4
Error	21.9
Cost	40201

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+151} \lor \neg \left(t_0 \leq 5 \cdot 10^{+307}\right):\\ \;\;\;\;\frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{a + b}}\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 5
Error	21.9
Cost	26944

\[\cos \left(\frac{\pi}{\frac{180}{angle}}\right) \cdot \frac{-2 \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}{\frac{1}{a + b}} \]

Alternative 6
Error	21.8
Cost	26816

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

Alternative 7
Error	22.8
Cost	13833

\[\begin{array}{l} t_0 := angle \cdot \left(a + b\right)\\ \mathbf{if}\;angle \leq -2.3 \cdot 10^{-130} \lor \neg \left(angle \leq 4.4 \cdot 10^{-37}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 8
Error	23.5
Cost	13705

\[\begin{array}{l} t_0 := angle \cdot \left(a + b\right)\\ \mathbf{if}\;angle \leq -0.17 \lor \neg \left(angle \leq 3.5 \cdot 10^{+79}\right):\\ \;\;\;\;\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 9
Error	23.4
Cost	13705

\[\begin{array}{l} t_0 := angle \cdot \left(a + b\right)\\ \mathbf{if}\;angle \leq -1650000000 \lor \neg \left(angle \leq 1.9 \cdot 10^{+36}\right):\\ \;\;\;\;\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-2 \cdot \left(a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 10
Error	23.5
Cost	13704

\[\begin{array}{l} t_0 := angle \cdot \left(a + b\right)\\ \mathbf{if}\;angle \leq -0.17:\\ \;\;\;\;2 \cdot \left(\left(b \cdot b\right) \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{elif}\;angle \leq 3.5 \cdot 10^{+79}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(2 \cdot \left(b \cdot b\right)\right)\\ \end{array} \]

Alternative 11
Error	22.7
Cost	13696

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

Alternative 12
Error	26.4
Cost	7817

\[\begin{array}{l} t_0 := angle \cdot \left(a + b\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{-196} \lor \neg \left(b \leq 1.35 \cdot 10^{-114}\right):\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 13
Error	29.4
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+154} \lor \neg \left(b \leq 3.9 \cdot 10^{+151}\right):\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(\left(a + b\right) \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	29.5
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+143} \lor \neg \left(b \leq 2.8 \cdot 10^{+152}\right):\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 15
Error	29.5
Cost	7433

\[\begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+143} \lor \neg \left(b \leq 7.2 \cdot 10^{+151}\right):\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\left(a + b\right) \cdot \left(\pi \cdot \left(b - a\right)\right)\right)\right)\\ \end{array} \]

Alternative 16
Error	38.2
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -1.06 \cdot 10^{-53} \lor \neg \left(a \leq 16200000\right):\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 17
Error	32.9
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-82} \lor \neg \left(b \leq 3.1 \cdot 10^{-48}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 18
Error	32.9
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-82} \lor \neg \left(b \leq 8.2 \cdot 10^{-48}\right):\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left(a \cdot \left(a \cdot \pi\right)\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 19
Error	43.4
Cost	6912

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

Alternative 20
Error	43.4
Cost	6912

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

Alternative 21
Error	43.3
Cost	6912

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

Reproduce

herbie shell --seed 2023054 
(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)))))