ab-angle->ABCF B

Average Accuracy: 33.7% → 44.5%

Time: 29.3s

Precision: binary64

Cost: 46088

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\sqrt[3]{angle} \cdot \left({\left(\sqrt[3]{angle}\right)}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}^{3} \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

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 (<= (/ angle 180.0) -0.0005)
   (*
    (- (* b b) (* a a))
    (sin
     (* (cbrt angle) (* (pow (cbrt angle) 2.0) (* PI 0.011111111111111112)))))
   (if (<= (/ angle 180.0) 2e-23)
     (* (* 0.011111111111111112 (* angle (- b a))) (* PI (+ b a)))
     (*
      (pow (cbrt (fma b b (- (* a a)))) 3.0)
      (sin (expm1 (log1p (* angle (* PI 0.011111111111111112)))))))))

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 ((angle / 180.0) <= -0.0005) {
		tmp = ((b * b) - (a * a)) * sin((cbrt(angle) * (pow(cbrt(angle), 2.0) * (((double) M_PI) * 0.011111111111111112))));
	} else if ((angle / 180.0) <= 2e-23) {
		tmp = (0.011111111111111112 * (angle * (b - a))) * (((double) M_PI) * (b + a));
	} else {
		tmp = pow(cbrt(fma(b, b, -(a * a))), 3.0) * sin(expm1(log1p((angle * (((double) M_PI) * 0.011111111111111112)))));
	}
	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(angle / 180.0) <= -0.0005)
		tmp = Float64(Float64(Float64(b * b) - Float64(a * a)) * sin(Float64(cbrt(angle) * Float64((cbrt(angle) ^ 2.0) * Float64(pi * 0.011111111111111112)))));
	elseif (Float64(angle / 180.0) <= 2e-23)
		tmp = Float64(Float64(0.011111111111111112 * Float64(angle * Float64(b - a))) * Float64(pi * Float64(b + a)));
	else
		tmp = Float64((cbrt(fma(b, b, Float64(-Float64(a * a)))) ^ 3.0) * sin(expm1(log1p(Float64(angle * Float64(pi * 0.011111111111111112))))));
	end
	return 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[(angle / 180.0), $MachinePrecision], -0.0005], N[(N[(N[(b * b), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(N[Power[angle, 1/3], $MachinePrecision] * N[(N[Power[N[Power[angle, 1/3], $MachinePrecision], 2.0], $MachinePrecision] * N[(Pi * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(angle / 180.0), $MachinePrecision], 2e-23], N[(N[(0.011111111111111112 * N[(angle * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(Pi * N[(b + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[N[Power[N[(b * b + (-N[(a * a), $MachinePrecision])), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] * N[Sin[N[(Exp[N[Log[1 + N[(angle * N[(Pi * 0.011111111111111112), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 angle 180) < -5.0000000000000001e-4

   1. Initial program 10.9%

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

   2. Simplified 10.9%

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

   3. Applied egg-rr 4.4%

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

   4. Simplified 11.7%

      \[\leadsto \color{blue}{\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)} \]

   5. Applied egg-rr 1.3%

      \[\leadsto \left(b \cdot b - a \cdot a\right) \cdot \sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)} \]

   6. Applied egg-rr 12.0%

      \[\leadsto \left(b \cdot b - a \cdot a\right) \cdot \sin \color{blue}{\left(\left(\left(\pi \cdot 0.011111111111111112\right) \cdot {\left(\sqrt[3]{angle}\right)}^{2}\right) \cdot \sqrt[3]{angle}\right)} \]

   if -5.0000000000000001e-4 < (/.f64 angle 180) < 1.99999999999999992e-23

   1. Initial program 62.4%

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

   2. Simplified 62.4%

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

   3. Applied egg-rr 19.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(2 \cdot \mathsf{fma}\left(b, b, -a \cdot a\right)\right)}^{3} \cdot {\left(\left(0 + \sin \left(2 \cdot \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot 0.5\right)}^{3}}} \]

   4. Simplified 19.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)}^{3} \cdot \left(0.125 \cdot \left({\left(b \cdot b - a \cdot a\right)}^{3} \cdot 8\right)\right)}} \]

   5. Taylor expanded in angle around 0 62.4%

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

   6. Simplified 79.3%

      \[\leadsto \color{blue}{\left(\left(angle \cdot \left(b + a\right)\right) \cdot \left(b - a\right)\right) \cdot \left(0.011111111111111112 \cdot \pi\right)} \]

   7. Taylor expanded in angle around 0 62.5%

      \[\leadsto \color{blue}{\left(angle \cdot \left(\left(b - a\right) \cdot \left(a + b\right)\right)\right)} \cdot \left(0.011111111111111112 \cdot \pi\right) \]

   8. Simplified 79.3%

      \[\leadsto \color{blue}{\left(\left(b + a\right) \cdot \left(angle \cdot \left(b - a\right)\right)\right)} \cdot \left(0.011111111111111112 \cdot \pi\right) \]

   9. Taylor expanded in angle around 0 62.5%

      \[\leadsto \color{blue}{0.011111111111111112 \cdot \left(angle \cdot \left(\left(b - a\right) \cdot \left(\pi \cdot \left(a + b\right)\right)\right)\right)} \]

   10. Simplified 79.3%

       \[\leadsto \color{blue}{\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(a + b\right)\right)} \]

   if 1.99999999999999992e-23 < (/.f64 angle 180)

   1. Initial program 16.0%

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

   2. Simplified 16.0%

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

   3. Applied egg-rr 11.3%

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

   4. Simplified 16.6%

      \[\leadsto \color{blue}{\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)} \]

   5. Applied egg-rr 17.2%

      \[\leadsto \left(b \cdot b - a \cdot a\right) \cdot \sin \color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)} \]

   6. Applied egg-rr 17.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}^{3}} \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\sqrt[3]{angle} \cdot \left({\left(\sqrt[3]{angle}\right)}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{\mathsf{fma}\left(b, b, -a \cdot a\right)}\right)}^{3} \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	44.5%
Cost	39944

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(\sqrt[3]{angle} \cdot \left({\left(\sqrt[3]{angle}\right)}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 2 \cdot 10^{-23}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right) \cdot \left(b \cdot b - \left(a \cdot \sqrt[3]{a \cdot a}\right) \cdot \sqrt[3]{a}\right)\\ \end{array} \]

Alternative 2
Accuracy	44.5%
Cost	33220

\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;t_0 \cdot \sin \left(\sqrt[3]{angle} \cdot \left({\left(\sqrt[3]{angle}\right)}^{2} \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-15}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternative 3
Accuracy	44.5%
Cost	27076

\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ t_1 := 0.005555555555555556 \cdot \left(angle \cdot \pi\right)\\ \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;\left(2 \cdot \cos t_1\right) \cdot \left(t_0 \cdot \sin t_1\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-15}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternative 4
Accuracy	44.5%
Cost	26888

\[\begin{array}{l} t_0 := b \cdot b - a \cdot a\\ \mathbf{if}\;\frac{angle}{180} \leq -0.0005:\\ \;\;\;\;t_0 \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{elif}\;\frac{angle}{180} \leq 10^{-15}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	44.5%
Cost	14089

\[\begin{array}{l} \mathbf{if}\;\frac{angle}{180} \leq -0.0005 \lor \neg \left(\frac{angle}{180} \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(b \cdot b - a \cdot a\right) \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \end{array} \]

Alternative 6
Accuracy	43.3%
Cost	13700

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{if}\;angle \leq -6.2 \cdot 10^{+20}:\\ \;\;\;\;t_0 \cdot \left(b \cdot b + a \cdot a\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot t_0\\ \end{array} \]

Alternative 7
Accuracy	43.1%
Cost	13577

\[\begin{array}{l} \mathbf{if}\;angle \leq -1.05 \cdot 10^{+31} \lor \neg \left(angle \leq 7.5 \cdot 10^{-6}\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \end{array} \]

Alternative 8
Accuracy	43.1%
Cost	13576

\[\begin{array}{l} t_0 := \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{if}\;angle \leq -1.05 \cdot 10^{+31}:\\ \;\;\;\;b \cdot \left(b \cdot t_0\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot t_0\\ \end{array} \]

Alternative 9
Accuracy	42.9%
Cost	13576

\[\begin{array}{l} \mathbf{if}\;angle \leq -6 \cdot 10^{-19}:\\ \;\;\;\;a \cdot \left(a \cdot \left(-\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\right)\\ \mathbf{elif}\;angle \leq 7.5 \cdot 10^{-6}:\\ \;\;\;\;\left(0.011111111111111112 \cdot \left(angle \cdot \left(b - a\right)\right)\right) \cdot \left(\pi \cdot \left(b + a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(0.011111111111111112 \cdot \left(angle \cdot \pi\right)\right)\\ \end{array} \]

Alternative 10
Accuracy	34.6%
Cost	7432

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-55}:\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(a \cdot \left(a \cdot \left(-angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+153}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(b \cdot b - a \cdot a\right) \cdot \left(angle \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 11
Accuracy	33.6%
Cost	7240

\[\begin{array}{l} \mathbf{if}\;a \leq -8.4 \cdot 10^{-54}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-67}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(-a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	33.6%
Cost	7240

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-54}:\\ \;\;\;\;\left(\pi \cdot 0.011111111111111112\right) \cdot \left(a \cdot \left(a \cdot \left(-angle\right)\right)\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-67}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(a \cdot \left(angle \cdot \left(-a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	32.4%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-54} \lor \neg \left(a \leq 3.7 \cdot 10^{-68}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	33.6%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-55} \lor \neg \left(a \leq 2.9 \cdot 10^{-68}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \left(angle \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 15
Accuracy	33.5%
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{-55} \lor \neg \left(a \leq 5.4 \cdot 10^{-71}\right):\\ \;\;\;\;-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot \left(angle \cdot b\right)\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	39.7%
Cost	7168

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

Alternative 17
Accuracy	25.7%
Cost	6912

\[-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \left(angle \cdot \pi\right)\right)\right) \]

Alternative 18
Accuracy	25.7%
Cost	6912

\[-0.011111111111111112 \cdot \left(\pi \cdot \left(a \cdot \left(angle \cdot a\right)\right)\right) \]

Reproduce

herbie shell --seed 2023157 -o generate:proofs
(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)))))