ab-angle->ABCF B

Average Error: 31.9 → 32.6

Time: 20.3s

Precision: binary64

Cost: 46212

Math

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

↓

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ t_1 := \sin t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \left(\cos t_0 \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}{1} \cdot \left(t_1 \cdot {b}^{2}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (* angle (* 0.005555555555555556 PI))) (t_1 (sin t_0)))
   (if (<= (- (pow b 2.0) (pow a 2.0)) -1e-175)
     (* (pow a 2.0) (* -2.0 (* (cos t_0) t_1)))
     (*
      2.0
      (*
       (/ (cos (* PI (* angle 0.005555555555555556))) 1.0)
       (* t_1 (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 t_0 = angle * (0.005555555555555556 * ((double) M_PI));
	double t_1 = sin(t_0);
	double tmp;
	if ((pow(b, 2.0) - pow(a, 2.0)) <= -1e-175) {
		tmp = pow(a, 2.0) * (-2.0 * (cos(t_0) * t_1));
	} else {
		tmp = 2.0 * ((cos((((double) M_PI) * (angle * 0.005555555555555556))) / 1.0) * (t_1 * 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 t_0 = angle * (0.005555555555555556 * Math.PI);
	double t_1 = Math.sin(t_0);
	double tmp;
	if ((Math.pow(b, 2.0) - Math.pow(a, 2.0)) <= -1e-175) {
		tmp = Math.pow(a, 2.0) * (-2.0 * (Math.cos(t_0) * t_1));
	} else {
		tmp = 2.0 * ((Math.cos((Math.PI * (angle * 0.005555555555555556))) / 1.0) * (t_1 * 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):
	t_0 = angle * (0.005555555555555556 * math.pi)
	t_1 = math.sin(t_0)
	tmp = 0
	if (math.pow(b, 2.0) - math.pow(a, 2.0)) <= -1e-175:
		tmp = math.pow(a, 2.0) * (-2.0 * (math.cos(t_0) * t_1))
	else:
		tmp = 2.0 * ((math.cos((math.pi * (angle * 0.005555555555555556))) / 1.0) * (t_1 * 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)
	t_0 = Float64(angle * Float64(0.005555555555555556 * pi))
	t_1 = sin(t_0)
	tmp = 0.0
	if (Float64((b ^ 2.0) - (a ^ 2.0)) <= -1e-175)
		tmp = Float64((a ^ 2.0) * Float64(-2.0 * Float64(cos(t_0) * t_1)));
	else
		tmp = Float64(2.0 * Float64(Float64(cos(Float64(pi * Float64(angle * 0.005555555555555556))) / 1.0) * Float64(t_1 * (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)
	t_0 = angle * (0.005555555555555556 * pi);
	t_1 = sin(t_0);
	tmp = 0.0;
	if (((b ^ 2.0) - (a ^ 2.0)) <= -1e-175)
		tmp = (a ^ 2.0) * (-2.0 * (cos(t_0) * t_1));
	else
		tmp = 2.0 * ((cos((pi * (angle * 0.005555555555555556))) / 1.0) * (t_1 * (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_] := Block[{t$95$0 = N[(angle * N[(0.005555555555555556 * Pi), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sin[t$95$0], $MachinePrecision]}, If[LessEqual[N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision], -1e-175], N[(N[Power[a, 2.0], $MachinePrecision] * N[(-2.0 * N[(N[Cos[t$95$0], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[(N[Cos[N[(Pi * N[(angle * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 1.0), $MachinePrecision] * N[(t$95$1 * N[Power[b, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -1e-175

   1. Initial program 35.5

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

   2. Simplified 35.5

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

      [Start] 35.5	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 35.5	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 35.5	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 35.5	\[ \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in b around 0 35.8

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

   4. Simplified 35.8

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

      [Start] 35.8	\[ -2 \cdot \left({a}^{2} \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 35.8	\[ \color{blue}{{a}^{2} \cdot \left(-2 \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 35.8	\[ {a}^{2} \cdot \left(-2 \cdot \left(\cos \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 35.8	\[ {a}^{2} \cdot \left(-2 \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \sin \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)}\right)\right) \]

   if -1e-175 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 29.5

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

   2. Simplified 29.5

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

      [Start] 29.5	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 29.5	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 29.5	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 29.5	\[ \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in b around inf 30.3

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

   4. Simplified 30.4

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

      [Start] 30.3	\[ 2 \cdot \left({b}^{2} \cdot \left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 30.3	\[ 2 \cdot \color{blue}{\left(\cos \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 30.4	\[ 2 \cdot \left(\cos \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 30.4	\[ 2 \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot {b}^{2}\right)}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 30.4	\[ 2 \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left(\sin \color{blue}{\left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)} \cdot {b}^{2}\right)\right) \]

   5. Applied egg-rr 30.5

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

4. Final simplification 32.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{\cos \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}{1} \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot {b}^{2}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	33.2
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \sin t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(\cos t_0 \cdot \left({a}^{2} \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot t_1\right)\\ \end{array} \]

Alternative 2
Error	32.5
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \cos t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(t_1 \cdot \left({a}^{2} \cdot \sin t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(t_1 \cdot \left(\sin \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot {b}^{2}\right)\right)\\ \end{array} \]

Alternative 3
Error	32.5
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(\cos t_0 \cdot \left({a}^{2} \cdot \sin t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos t_1 \cdot \left(\sin t_1 \cdot {b}^{2}\right)\right)\\ \end{array} \]

Alternative 4
Error	32.5
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \sin t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(\cos t_0 \cdot \left({a}^{2} \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\cos \left(angle \cdot \left(0.005555555555555556 \cdot \pi\right)\right) \cdot \left({b}^{2} \cdot t_1\right)\right)\\ \end{array} \]

Alternative 5
Error	32.6
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(\cos t_0 \cdot \left({a}^{2} \cdot \sin t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left(\sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right) \cdot {b}^{2}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 6
Error	32.6
Cost	46084

\[\begin{array}{l} t_0 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ t_1 := \sin t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;-2 \cdot \left(\cos t_0 \cdot \left({a}^{2} \cdot t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left({b}^{2} \cdot t_1\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 7
Error	32.5
Cost	46084

\[\begin{array}{l} t_0 := angle \cdot \left(0.005555555555555556 \cdot \pi\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq -1 \cdot 10^{-175}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \left(\cos t_0 \cdot \sin t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \end{array} \]

Alternative 8
Error	31.9
Cost	39488

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

Alternative 9
Error	31.9
Cost	39488

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

Alternative 10
Error	32.0
Cost	39488

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

Alternative 11
Error	33.6
Cost	33092

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -2 \cdot 10^{-168}:\\ \;\;\;\;\left({a}^{2} \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\right) \cdot 1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 12
Error	34.4
Cost	33028

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{-168}:\\ \;\;\;\;angle \cdot \left(0.011111111111111112 \cdot \left(\pi \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	34.4
Cost	32964

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -2 \cdot 10^{-168}:\\ \;\;\;\;-\left(\left({a}^{2} \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot angle\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	33.0
Cost	26496

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

Alternative 15
Error	38.5
Cost	13576

\[\begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{-10}:\\ \;\;\;\;angle \cdot \left({b}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-107}:\\ \;\;\;\;-\left(\left({a}^{2} \cdot \pi\right) \cdot 0.011111111111111112\right) \cdot angle\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \end{array} \]

Alternative 16
Error	38.6
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-107}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Error	38.5
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \mathbf{if}\;b \leq -3.2 \cdot 10^{-14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-108}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	38.5
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{-13}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-108}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 19
Error	38.6
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-9}:\\ \;\;\;\;angle \cdot \left({b}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-107}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot {b}^{2}\right)\right)\\ \end{array} \]

Alternative 20
Error	44.2
Cost	13248

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

Reproduce

herbie shell --seed 2023090 
(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)))))