ab-angle->ABCF B

Average Error: 31.4 → 31.6

Time: 30.0s

Precision: binary64

Cost: 46276

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{-300}:\\ \;\;\;\;\left(2 \cdot \left(-{a}^{2}\right)\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(-\cos \left(\pi \cdot \left(1 + angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \left(2 \cdot {b}^{2}\right)\\ \end{array} \]

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
 (if (<= (- (pow b 2.0) (pow a 2.0)) -5e-300)
   (*
    (* 2.0 (- (pow a 2.0)))
    (*
     (- (sin (* PI (* angle -0.005555555555555556))))
     (cos (* 0.005555555555555556 (* angle PI)))))
   (*
    (*
     (sin (* angle (* 0.005555555555555556 PI)))
     (- (cos (* PI (+ 1.0 (* angle 0.005555555555555556))))))
    (* 2.0 (pow b 2.0)))))

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 tmp;
	if ((pow(b, 2.0) - pow(a, 2.0)) <= -5e-300) {
		tmp = (2.0 * -pow(a, 2.0)) * (-sin((((double) M_PI) * (angle * -0.005555555555555556))) * cos((0.005555555555555556 * (angle * ((double) M_PI)))));
	} else {
		tmp = (sin((angle * (0.005555555555555556 * ((double) M_PI)))) * -cos((((double) M_PI) * (1.0 + (angle * 0.005555555555555556))))) * (2.0 * pow(b, 2.0));
	}
	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 tmp;
	if ((Math.pow(b, 2.0) - Math.pow(a, 2.0)) <= -5e-300) {
		tmp = (2.0 * -Math.pow(a, 2.0)) * (-Math.sin((Math.PI * (angle * -0.005555555555555556))) * Math.cos((0.005555555555555556 * (angle * Math.PI))));
	} else {
		tmp = (Math.sin((angle * (0.005555555555555556 * Math.PI))) * -Math.cos((Math.PI * (1.0 + (angle * 0.005555555555555556))))) * (2.0 * Math.pow(b, 2.0));
	}
	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):
	tmp = 0
	if (math.pow(b, 2.0) - math.pow(a, 2.0)) <= -5e-300:
		tmp = (2.0 * -math.pow(a, 2.0)) * (-math.sin((math.pi * (angle * -0.005555555555555556))) * math.cos((0.005555555555555556 * (angle * math.pi))))
	else:
		tmp = (math.sin((angle * (0.005555555555555556 * math.pi))) * -math.cos((math.pi * (1.0 + (angle * 0.005555555555555556))))) * (2.0 * math.pow(b, 2.0))
	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)
	tmp = 0.0
	if (Float64((b ^ 2.0) - (a ^ 2.0)) <= -5e-300)
		tmp = Float64(Float64(2.0 * Float64(-(a ^ 2.0))) * Float64(Float64(-sin(Float64(pi * Float64(angle * -0.005555555555555556)))) * cos(Float64(0.005555555555555556 * Float64(angle * pi)))));
	else
		tmp = Float64(Float64(sin(Float64(angle * Float64(0.005555555555555556 * pi))) * Float64(-cos(Float64(pi * Float64(1.0 + Float64(angle * 0.005555555555555556)))))) * Float64(2.0 * (b ^ 2.0)));
	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)
	tmp = 0.0;
	if (((b ^ 2.0) - (a ^ 2.0)) <= -5e-300)
		tmp = (2.0 * -(a ^ 2.0)) * (-sin((pi * (angle * -0.005555555555555556))) * cos((0.005555555555555556 * (angle * pi))));
	else
		tmp = (sin((angle * (0.005555555555555556 * pi))) * -cos((pi * (1.0 + (angle * 0.005555555555555556))))) * (2.0 * (b ^ 2.0));
	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_] := If[LessEqual[N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision], -5e-300], N[(N[(2.0 * (-N[Power[a, 2.0], $MachinePrecision])), $MachinePrecision] * N[((-N[Sin[N[(Pi * N[(angle * -0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]) * N[Cos[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Sin[N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Cos[N[(Pi * N[(1.0 + N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] * N[(2.0 * N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -4.99999999999999996e-300

   1. Initial program 33.9

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

   2. Simplified 33.9

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

      [Start] 33.9	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 33.9	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-43 [=>] 33.9	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in angle around inf 34.0

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

   4. Applied egg-rr 33.9

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

   5. Taylor expanded in b around 0 34.1

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

   6. Simplified 34.1

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

      [Start] 34.1	\[ \left(2 \cdot \left(-1 \cdot {a}^{2}\right)\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
      rational.json-simplify-2 [=>] 34.1	\[ \left(2 \cdot \color{blue}{\left({a}^{2} \cdot -1\right)}\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]
      rational.json-simplify-8 [<=] 34.1	\[ \left(2 \cdot \color{blue}{\left(-{a}^{2}\right)}\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \]

   if -4.99999999999999996e-300 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 29.4

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

   2. Simplified 29.4

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

      [Start] 29.4	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 29.4	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-43 [=>] 29.4	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in b around inf 29.5

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

   4. Simplified 29.5

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

      [Start] 29.5	\[ 2 \cdot \left({b}^{2} \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational.json-simplify-43 [=>] 29.5	\[ \color{blue}{{b}^{2} \cdot \left(\left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot 2\right)} \]
      rational.json-simplify-43 [=>] 29.5	\[ \color{blue}{\left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {b}^{2}\right)} \]
      rational.json-simplify-2 [=>] 29.5	\[ \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)} \cdot \left(2 \cdot {b}^{2}\right) \]
      rational.json-simplify-2 [=>] 29.5	\[ \left(\sin \left(0.005555555555555556 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {b}^{2}\right) \]
      rational.json-simplify-43 [<=] 29.5	\[ \left(\sin \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot \left(2 \cdot {b}^{2}\right) \]
      rational.json-simplify-2 [=>] 29.5	\[ \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \color{blue}{\left(\pi \cdot angle\right)}\right)\right) \cdot \left(2 \cdot {b}^{2}\right) \]
      rational.json-simplify-43 [<=] 29.5	\[ \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \cos \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right) \cdot \left(2 \cdot {b}^{2}\right) \]

   5. Applied egg-rr 29.7

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

4. Final simplification 31.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{-300}:\\ \;\;\;\;\left(2 \cdot \left(-{a}^{2}\right)\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(-\cos \left(\pi \cdot \left(1 + angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \left(2 \cdot {b}^{2}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	31.6
Cost	46212

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-282}:\\ \;\;\;\;\left(2 \cdot \left(-{a}^{2}\right)\right) \cdot \left(\left(-\sin \left(\pi \cdot \left(angle \cdot -0.005555555555555556\right)\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot {b}^{2}\right) \cdot \sin t_0\right) \cdot \cos t_0\\ \end{array} \]

Alternative 2
Error	31.4
Cost	46084

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ t_1 := -0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{-283}:\\ \;\;\;\;2 \cdot \left(\sin t_1 \cdot \left({a}^{2} \cdot \cos t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left({b}^{2} \cdot \sin t_0\right) \cdot \cos t_0\right)\\ \end{array} \]

Alternative 3
Error	31.5
Cost	46084

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-282}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(\sin \left(\pi \cdot \left(-0.005555555555555556 \cdot angle\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left({b}^{2} \cdot \sin t_0\right) \cdot \cos t_0\right)\\ \end{array} \]

Alternative 4
Error	31.5
Cost	46084

\[\begin{array}{l} t_0 := \pi \cdot \left(0.005555555555555556 \cdot angle\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-282}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(\sin \left(\pi \cdot \left(-0.005555555555555556 \cdot angle\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sin t_0\right) \cdot \left({b}^{2} \cdot \cos t_0\right)\\ \end{array} \]

Alternative 5
Error	31.6
Cost	46084

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-282}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(\sin \left(\pi \cdot \left(-0.005555555555555556 \cdot angle\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(2 \cdot {b}^{2}\right) \cdot \sin t_0\right) \cdot \cos t_0\\ \end{array} \]

Alternative 6
Error	31.4
Cost	39488

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin t_0\right) \cdot \cos t_0 \end{array} \]

Alternative 7
Error	31.2
Cost	39488

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

Alternative 8
Error	31.2
Cost	39488

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

Alternative 9
Error	31.3
Cost	39488

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

Alternative 10
Error	31.3
Cost	39488

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

Alternative 11
Error	31.4
Cost	39488

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

Alternative 12
Error	31.4
Cost	39488

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin t_0 \cdot \cos t_0\right) \end{array} \]

Alternative 13
Error	32.4
Cost	33092

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-317}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(\sin \left(-0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	32.2
Cost	26496

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

Alternative 15
Error	37.5
Cost	20040

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-67}:\\ \;\;\;\;\left({a}^{2} \cdot \left(angle \cdot \pi\right)\right) \cdot -0.011111111111111112\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left({a}^{2} \cdot \pi\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 16
Error	34.2
Cost	19840

\[0.011111111111111112 \cdot \left(angle \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \pi\right)\right) \]

Alternative 17
Error	34.2
Cost	19840

\[0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left({b}^{2} - {a}^{2}\right)\right) \]

Alternative 18
Error	34.1
Cost	19840

\[angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot \left({b}^{2} - {a}^{2}\right)\right)\right) \]

Alternative 19
Error	38.4
Cost	13512

\[\begin{array}{l} t_0 := angle \cdot \left(\left({a}^{2} \cdot \pi\right) \cdot -0.011111111111111112\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot {b}^{2}\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	38.3
Cost	13512

\[\begin{array}{l} t_0 := {a}^{2} \cdot \pi\\ \mathbf{if}\;a \leq -1.1 \cdot 10^{-69}:\\ \;\;\;\;t_0 \cdot \left(angle \cdot -0.011111111111111112\right)\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot {b}^{2}\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(t_0 \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 21
Error	38.4
Cost	13512

\[\begin{array}{l} \mathbf{if}\;a \leq -1.48 \cdot 10^{-67}:\\ \;\;\;\;\left({a}^{2} \cdot \left(angle \cdot \pi\right)\right) \cdot -0.011111111111111112\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+38}:\\ \;\;\;\;angle \cdot \left(\left(\pi \cdot {b}^{2}\right) \cdot 0.011111111111111112\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\left({a}^{2} \cdot \pi\right) \cdot -0.011111111111111112\right)\\ \end{array} \]

Alternative 22
Error	43.4
Cost	13248

\[0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right) \]

Alternative 23
Error	43.4
Cost	13248

\[0.011111111111111112 \cdot \left({b}^{2} \cdot \left(angle \cdot \pi\right)\right) \]

Alternative 24
Error	43.4
Cost	13248

\[angle \cdot \left(\left(\pi \cdot {b}^{2}\right) \cdot 0.011111111111111112\right) \]

Reproduce

herbie shell --seed 2023074 
(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)))))