ab-angle->ABCF B

Average Error: 30.7 → 30.9

Time: 26.5s

Precision: binary64

Cost: 33156

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(-\frac{\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

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)) -1e-280)
   (*
    2.0
    (* (pow a 2.0) (- (/ (sin (* PI (* angle 0.011111111111111112))) 2.0))))
   (* (sin (* 0.011111111111111112 (* angle PI))) (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)) <= -1e-280) {
		tmp = 2.0 * (pow(a, 2.0) * -(sin((((double) M_PI) * (angle * 0.011111111111111112))) / 2.0));
	} else {
		tmp = sin((0.011111111111111112 * (angle * ((double) M_PI)))) * 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)) <= -1e-280) {
		tmp = 2.0 * (Math.pow(a, 2.0) * -(Math.sin((Math.PI * (angle * 0.011111111111111112))) / 2.0));
	} else {
		tmp = Math.sin((0.011111111111111112 * (angle * Math.PI))) * 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)) <= -1e-280:
		tmp = 2.0 * (math.pow(a, 2.0) * -(math.sin((math.pi * (angle * 0.011111111111111112))) / 2.0))
	else:
		tmp = math.sin((0.011111111111111112 * (angle * math.pi))) * 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)) <= -1e-280)
		tmp = Float64(2.0 * Float64((a ^ 2.0) * Float64(-Float64(sin(Float64(pi * Float64(angle * 0.011111111111111112))) / 2.0))));
	else
		tmp = Float64(sin(Float64(0.011111111111111112 * Float64(angle * pi))) * (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)) <= -1e-280)
		tmp = 2.0 * ((a ^ 2.0) * -(sin((pi * (angle * 0.011111111111111112))) / 2.0));
	else
		tmp = sin((0.011111111111111112 * (angle * pi))) * (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], -1e-280], N[(2.0 * N[(N[Power[a, 2.0], $MachinePrecision] * (-N[(N[Sin[N[(Pi * N[(angle * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 2.0), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], N[(N[Sin[N[(0.011111111111111112 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -9.9999999999999996e-281

   1. Initial program 33.6

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

   2. Simplified 33.6

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

      [Start] 33.6	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 33.6	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-43 [=>] 33.6	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in angle around inf 33.5

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

   4. Simplified 33.5

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

      [Start] 33.5	\[ 2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational.json-simplify-43 [<=] 33.5	\[ 2 \cdot \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]

   5. Taylor expanded in b around 0 33.7

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

   6. Simplified 33.7

      \[\leadsto 2 \cdot \color{blue}{\left({a}^{2} \cdot \left(-\frac{\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}{2}\right)\right)} \]
      Proof

      [Start] 33.7	\[ 2 \cdot \left(-1 \cdot \left({a}^{2} \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)\right) \]
      rational.json-simplify-43 [=>] 33.7	\[ 2 \cdot \color{blue}{\left({a}^{2} \cdot \left(\left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot -1\right)\right)} \]
      rational.json-simplify-9 [=>] 33.7	\[ 2 \cdot \left({a}^{2} \cdot \color{blue}{\left(-\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)}\right) \]
      rational.json-simplify-2 [=>] 33.7	\[ 2 \cdot \left({a}^{2} \cdot \left(-\color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \]
      trig.json-simplify-41 [=>] 33.7	\[ 2 \cdot \left({a}^{2} \cdot \left(-\color{blue}{\frac{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right) + 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) + \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right) - 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}{2}}\right)\right) \]

   if -9.9999999999999996e-281 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 28.6

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

   2. Simplified 28.6

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

      [Start] 28.6	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 28.6	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-43 [=>] 28.6	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-2 [=>] 28.6	\[ \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)} \]
      rational.json-simplify-2 [=>] 28.6	\[ \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \]
      rational.json-simplify-43 [=>] 28.6	\[ \color{blue}{\left({b}^{2} - {a}^{2}\right) \cdot \left(2 \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      rational.json-simplify-43 [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \color{blue}{\left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      rational.json-simplify-5 [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \color{blue}{\left(\pi \cdot \frac{angle}{180} - 0\right)}\right)\right) \]
      metadata-eval [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \left(\pi \cdot \frac{angle}{180} - \color{blue}{\left(0 - 0\right)}\right)\right)\right) \]
      rational.json-simplify-44 [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \color{blue}{\left(0 - \left(0 - \pi \cdot \frac{angle}{180}\right)\right)}\right)\right) \]
      rational.json-simplify-12 [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \left(0 - \color{blue}{\left(-\pi \cdot \frac{angle}{180}\right)}\right)\right)\right) \]
      rational.json-simplify-12 [<=] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \sin \color{blue}{\left(-\left(-\pi \cdot \frac{angle}{180}\right)\right)}\right)\right) \]
      trig.json-simplify-24 [=>] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \color{blue}{\left(-\sin \left(-\pi \cdot \frac{angle}{180}\right)\right)}\right)\right) \]
      rational.json-simplify-8 [=>] 28.6	\[ \left({b}^{2} - {a}^{2}\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \color{blue}{\left(\sin \left(-\pi \cdot \frac{angle}{180}\right) \cdot -1\right)}\right)\right) \]

   3. Taylor expanded in b around inf 28.8

      \[\leadsto \color{blue}{\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \left(-\frac{\sin \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)}{2}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternatives

Alternative 1
Error	30.7
Cost	39488

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

Alternative 2
Error	30.9
Cost	32900

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-280}:\\ \;\;\;\;{a}^{2} \cdot \sin \left(-angle \cdot \left(0.011111111111111112 \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 3
Error	30.7
Cost	26240

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

Alternative 4
Error	35.2
Cost	19976

\[\begin{array}{l} t_0 := \sin \left(angle \cdot \left(0.011111111111111112 \cdot \pi\right)\right) \cdot {b}^{2}\\ \mathbf{if}\;b \leq -3.9 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-{a}^{2}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	36.0
Cost	19912

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-12}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	36.0
Cost	19912

\[\begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-52}:\\ \;\;\;\;\sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-11}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(angle \cdot \left(0.011111111111111112 \cdot \pi\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 7
Error	37.4
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{-8}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-12}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	37.4
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -5.3 \cdot 10^{-5}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-11}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \end{array} \]

Alternative 9
Error	37.4
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-7}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \mathbf{elif}\;b \leq 4.9 \cdot 10^{-12}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({a}^{2} \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \end{array} \]

Alternative 10
Error	37.4
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{-6}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \mathbf{elif}\;b \leq 1.12 \cdot 10^{-10}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \end{array} \]

Alternative 11
Error	37.4
Cost	13512

\[\begin{array}{l} t_0 := angle \cdot \left({b}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 2.55 \cdot 10^{-11}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	37.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -2.85 \cdot 10^{-8}:\\ \;\;\;\;angle \cdot \left({b}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{-11}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 13
Error	37.4
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-6}:\\ \;\;\;\;2 \cdot \left(angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.005555555555555556\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-10}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot {b}^{2}\\ \end{array} \]

Alternative 14
Error	42.8
Cost	13248

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

Reproduce

herbie shell --seed 2023077 
(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)))))