ab-angle->ABCF B

Average Error: 31.7 → 32.0

Time: 25.7s

Precision: binary64

Cost: 46212

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-{a}^{2}\right)\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\pi \cdot \left(1 - 0.005555555555555556 \cdot angle\right)\right) \cdot \left(-2 \cdot \left({b}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \end{array} \]

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
 (if (<= (- (pow b 2.0) (pow a 2.0)) -5e-311)
   (*
    (* (sin (* 0.005555555555555556 (* angle PI))) (- (pow a 2.0)))
    (* 2.0 (cos (* PI (/ angle 180.0)))))
   (*
    (cos (* PI (- 1.0 (* 0.005555555555555556 angle))))
    (* -2.0 (* (pow b 2.0) (sin (* angle (* PI 0.005555555555555556))))))))

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-311) {
		tmp = (sin((0.005555555555555556 * (angle * ((double) M_PI)))) * -pow(a, 2.0)) * (2.0 * cos((((double) M_PI) * (angle / 180.0))));
	} else {
		tmp = cos((((double) M_PI) * (1.0 - (0.005555555555555556 * angle)))) * (-2.0 * (pow(b, 2.0) * sin((angle * (((double) M_PI) * 0.005555555555555556)))));
	}
	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-311) {
		tmp = (Math.sin((0.005555555555555556 * (angle * Math.PI))) * -Math.pow(a, 2.0)) * (2.0 * Math.cos((Math.PI * (angle / 180.0))));
	} else {
		tmp = Math.cos((Math.PI * (1.0 - (0.005555555555555556 * angle)))) * (-2.0 * (Math.pow(b, 2.0) * Math.sin((angle * (Math.PI * 0.005555555555555556)))));
	}
	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-311:
		tmp = (math.sin((0.005555555555555556 * (angle * math.pi))) * -math.pow(a, 2.0)) * (2.0 * math.cos((math.pi * (angle / 180.0))))
	else:
		tmp = math.cos((math.pi * (1.0 - (0.005555555555555556 * angle)))) * (-2.0 * (math.pow(b, 2.0) * math.sin((angle * (math.pi * 0.005555555555555556)))))
	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-311)
		tmp = Float64(Float64(sin(Float64(0.005555555555555556 * Float64(angle * pi))) * Float64(-(a ^ 2.0))) * Float64(2.0 * cos(Float64(pi * Float64(angle / 180.0)))));
	else
		tmp = Float64(cos(Float64(pi * Float64(1.0 - Float64(0.005555555555555556 * angle)))) * Float64(-2.0 * Float64((b ^ 2.0) * sin(Float64(angle * Float64(pi * 0.005555555555555556))))));
	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-311)
		tmp = (sin((0.005555555555555556 * (angle * pi))) * -(a ^ 2.0)) * (2.0 * cos((pi * (angle / 180.0))));
	else
		tmp = cos((pi * (1.0 - (0.005555555555555556 * angle)))) * (-2.0 * ((b ^ 2.0) * sin((angle * (pi * 0.005555555555555556)))));
	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-311], N[(N[(N[Sin[N[(0.005555555555555556 * N[(angle * Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * (-N[Power[a, 2.0], $MachinePrecision])), $MachinePrecision] * N[(2.0 * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Cos[N[(Pi * N[(1.0 - N[(0.005555555555555556 * angle), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(-2.0 * N[(N[Power[b, 2.0], $MachinePrecision] * N[Sin[N[(angle * N[(Pi * 0.005555555555555556), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (pow.f64 b 2) (pow.f64 a 2)) < -5.00000000000023e-311

   1. Initial program 34.5

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

   2. Simplified 34.4

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

      [Start] 34.5	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 34.5	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-2 [=>] 34.5	\[ \cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \color{blue}{\left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right)\right)} \]
      rational.json-simplify-43 [=>] 34.4	\[ \cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \color{blue}{\left(2 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)\right)} \]
      rational.json-simplify-2 [=>] 34.4	\[ \cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \color{blue}{\left(\left(\left({b}^{2} - {a}^{2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot 2\right)} \]
      rational.json-simplify-43 [=>] 34.4	\[ \color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in b around 0 34.7

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

   4. Simplified 34.7

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

      [Start] 34.7	\[ \left(-1 \cdot \left({a}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      rational.json-simplify-2 [=>] 34.7	\[ \left(-1 \cdot \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot {a}^{2}\right)}\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      rational.json-simplify-43 [=>] 34.7	\[ \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left({a}^{2} \cdot -1\right)\right)} \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]
      rational.json-simplify-9 [=>] 34.7	\[ \left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \color{blue}{\left(-{a}^{2}\right)}\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right) \]

   if -5.00000000000023e-311 < (-.f64 (pow.f64 b 2) (pow.f64 a 2))

   1. Initial program 29.6

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

   2. Simplified 29.6

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

      [Start] 29.6	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
      rational.json-simplify-2 [=>] 29.6	\[ \color{blue}{\cos \left(\pi \cdot \frac{angle}{180}\right) \cdot \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right)} \]
      rational.json-simplify-43 [=>] 29.6	\[ \color{blue}{\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \left(\sin \left(\pi \cdot \frac{angle}{180}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)} \]

   3. Taylor expanded in angle around inf 29.7

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

   4. Applied egg-rr 29.8

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

   5. Taylor expanded in b around inf 29.9

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

   6. Simplified 29.9

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

      [Start] 29.9	\[ -2 \cdot \left({b}^{2} \cdot \left(\cos \left(\left(1 - 0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \]
      rational.json-simplify-2 [=>] 29.9	\[ -2 \cdot \left({b}^{2} \cdot \color{blue}{\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \cos \left(\left(1 - 0.005555555555555556 \cdot angle\right) \cdot \pi\right)\right)}\right) \]
      rational.json-simplify-43 [<=] 29.9	\[ -2 \cdot \color{blue}{\left(\cos \left(\left(1 - 0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]
      rational.json-simplify-43 [=>] 29.9	\[ \color{blue}{\cos \left(\left(1 - 0.005555555555555556 \cdot angle\right) \cdot \pi\right) \cdot \left(\left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot -2\right)} \]
      rational.json-simplify-2 [=>] 29.9	\[ \cos \color{blue}{\left(\pi \cdot \left(1 - 0.005555555555555556 \cdot angle\right)\right)} \cdot \left(\left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right) \cdot -2\right) \]
      rational.json-simplify-2 [=>] 29.9	\[ \cos \left(\pi \cdot \left(1 - 0.005555555555555556 \cdot angle\right)\right) \cdot \color{blue}{\left(-2 \cdot \left({b}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \]
      rational.json-simplify-43 [=>] 29.9	\[ \cos \left(\pi \cdot \left(1 - 0.005555555555555556 \cdot angle\right)\right) \cdot \left(-2 \cdot \left({b}^{2} \cdot \sin \color{blue}{\left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)}\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 32.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq -5 \cdot 10^{-311}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-{a}^{2}\right)\right) \cdot \left(2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\cos \left(\pi \cdot \left(1 - 0.005555555555555556 \cdot angle\right)\right) \cdot \left(-2 \cdot \left({b}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	31.9
Cost	46148

\[\begin{array}{l} t_0 := \pi \cdot \frac{angle}{180}\\ t_1 := \cos t_0\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\left(2 \cdot \left(-{a}^{2}\right)\right) \cdot \left(\sin t_0 \cdot t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left({b}^{2} \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right) \cdot \left(2 \cdot t_1\right)\\ \end{array} \]

Alternative 2
Error	31.9
Cost	46148

\[\begin{array}{l} t_0 := 2 \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)\\ \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-305}:\\ \;\;\;\;\left(\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right) \cdot \left(-{a}^{2}\right)\right) \cdot t_0\\ \mathbf{else}:\\ \;\;\;\;\left({b}^{2} \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right) \cdot t_0\\ \end{array} \]

Alternative 3
Error	31.7
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 4
Error	31.8
Cost	39488

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

Alternative 5
Error	31.7
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 6
Error	33.0
Cost	33092

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-291}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left({b}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot 0.005555555555555556\right)\right)\right) \cdot 1\right)\\ \end{array} \]

Alternative 7
Error	33.8
Cost	33028

\[\begin{array}{l} t_0 := {b}^{2} - {a}^{2}\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-291}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(t_0 \cdot \pi\right)\right)\\ \end{array} \]

Alternative 8
Error	33.0
Cost	32964

\[\begin{array}{l} \mathbf{if}\;{b}^{2} - {a}^{2} \leq 2 \cdot 10^{-291}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left({b}^{2} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot 2\\ \end{array} \]

Alternative 9
Error	32.9
Cost	26624

\[\frac{\sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right) \cdot \left(1 \cdot \left(\left({b}^{2} - {a}^{2}\right) \cdot 4\right)\right)}{2} \]

Alternative 10
Error	32.8
Cost	26496

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

Alternative 11
Error	32.8
Cost	26496

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

Alternative 12
Error	37.4
Cost	20040

\[\begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{-83}:\\ \;\;\;\;{b}^{2} \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;-2 \cdot \left({a}^{2} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 13
Error	37.3
Cost	20040

\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{-80}:\\ \;\;\;\;{b}^{2} \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 4.35 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \left({a}^{2} \cdot \sin \left(angle \cdot \left(\pi \cdot -0.005555555555555556\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 14
Error	37.4
Cost	20040

\[\begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{-82}:\\ \;\;\;\;{b}^{2} \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;{a}^{2} \cdot \left(-2 \cdot \sin \left(\pi \cdot \left(0.005555555555555556 \cdot angle\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 15
Error	38.3
Cost	13512

\[\begin{array}{l} t_0 := 0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{-84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-105}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 16
Error	38.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{-80}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-105}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left({a}^{2} \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 17
Error	38.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -5.4 \cdot 10^{-81}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-105}:\\ \;\;\;\;angle \cdot \left({a}^{2} \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 18
Error	38.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-80}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-105}:\\ \;\;\;\;\left({a}^{2} \cdot \left(angle \cdot \pi\right)\right) \cdot -0.011111111111111112\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 19
Error	38.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-80}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left({b}^{2} \cdot \pi\right)\right)\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-105}:\\ \;\;\;\;{a}^{2} \cdot \left(angle \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 20
Error	38.3
Cost	13512

\[\begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{-80}:\\ \;\;\;\;{b}^{2} \cdot \left(\pi \cdot \left(angle \cdot 0.011111111111111112\right)\right)\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-105}:\\ \;\;\;\;{a}^{2} \cdot \left(angle \cdot \left(\pi \cdot -0.011111111111111112\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left({b}^{2} \cdot 0.011111111111111112\right)\right)\\ \end{array} \]

Alternative 21
Error	44.0
Cost	13248

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

Reproduce

herbie shell --seed 2023065 
(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)))))